#9881

Awesome!

http://www.worldwisetutoring.com/wp-content/uploads/2015/07/2006-Thomson-Peterson-SAT-II-Math-1-2.pdf

The test is on page 29.

http://www.worldwisetutoring.com/wp-content/uploads/2015/07/2006-Thomson-Peterson-SAT-II-Math-1-2.pdf

The test is on page 29.

#9882

Algebra, geometry and well, stuff to do with functions without going into calculus, and then basic statistics and trigonometry. The feeling I get is that in the US maths classes are very compartmentalised and idk exactly what things go into what and the structure of the whole system (eg I don't really know what "pre-calc" is actually supposed to be). But yeah you don't need calculus or imaginary numbers or any of that fancy stuff.

#9883

Oh also sequences. Sorry for not being too comprehensive but I'm at work and typing from my phone

#9884

Thanks a lot! I appreciate it.

I think what I'm struggling with most are functions and coordinate algebra (coordinate geometry in general I never had to do, like adding line slopes, parabolas, and stuff).

Would you mind if I listed the questions whose specific functions I don't know? You don't have to explain them, just tell me what that bit of math is called haha. Like questions with |x| or all possible values of something.

I think what I'm struggling with most are functions and coordinate algebra (coordinate geometry in general I never had to do, like adding line slopes, parabolas, and stuff).

Would you mind if I listed the questions whose specific functions I don't know? You don't have to explain them, just tell me what that bit of math is called haha. Like questions with |x| or all possible values of something.

#9885

|x| is the absolute value of x, it's equal to x if x is positive and equal to -x if x is negative. Basically you take away the minus sign if there is one and leave x alone if there isn't. And yeah sure, that's what this thread is for.

#9886

Great. Lemme go with:

3) The Pythagorean theorem one. I have no clue why you'd use that to find out the area of the square. Is it just because C is a side of the square? But how do you know that this is the C that corresponds to the pythagorean theorem? Like if I drew any complex shape and then used a + b to describe two lines within that shape, and then placed that shape in a square and labeled a side of it c, how in the world would it follow that I'd be correct to use that?

6) The fraction at the end throws me off. What subject is this? Fractional algebra or something?

7) I understand functions, they're probably the easiest form of math I've ever encountered, I just don't understand how to represent anything on a coordinate plane.

(I also don't know what line slopes are. I've been reading the wiki page on parabolas and hyperbolas for hours and it's not clicking at all.)

9) I don't know what the distance between these points is. Nor how to find a variable point.

10) Line slopes again. Except they're comparing intercepts or something. It really sucks to feel this ignorant about something a week away from the test. Feels like they're rubbing it in now.

12) This uses functions, except they complicate it by adding two functions and asking you to find f(g(x)).

13) Yeah, asks you to identify like what kind of curve an equation is. Curves are crazy ok

14) This is the one that dealt with the constant. It asks: "If x + 1 < 0 then |x| is" and I answered -x cuz YOLO, but I don't understand what that means. So on a number line, the absolute value of x, so long as it's less than zero, is negative x? Everywhere I read about absolute value they keep saying "absolute value is never negative" and "we never say that the absolute value of a number is positive"). I also don't get what the absolute value is representative of.

16) 17) Line slopes. Is this called coordinate geometry? I probably just need to learn this from the beginning.

20) Stuff (y) varying inversely with the square of other stuff (x). The variable k is used for no reason.

21) What are edges? Like... normal English edges? Should I have just imagined and counted? What weird science is this?

22) I think I know this, but just in case I don't: should I look for the tangent of the 30 degree angle?

And, in general, what's up with writing numbers before the square root of something? How could (presumably) multiplying 5 by the square root of three possibly be an answer? Would you just express that as a number?

23) Inverse functions say whaaaa. How do they work

24) All possible values of something. This one was pretty easy, but if I get a question asking me "all possible values", should I use some sort of trick to make it easier? Instead of, like, just using all provided values one by one.

25) Ain't nobody got time fo dat. Sum of the first 40 even integers. This either needs some complex equation I don't know about or they for some reason want me to spend a lotta time on one question.

EDIT: Holy crap this is big. Sorry! Just do what you have time for. single word explanations are acceptable too

3) The Pythagorean theorem one. I have no clue why you'd use that to find out the area of the square. Is it just because C is a side of the square? But how do you know that this is the C that corresponds to the pythagorean theorem? Like if I drew any complex shape and then used a + b to describe two lines within that shape, and then placed that shape in a square and labeled a side of it c, how in the world would it follow that I'd be correct to use that?

6) The fraction at the end throws me off. What subject is this? Fractional algebra or something?

7) I understand functions, they're probably the easiest form of math I've ever encountered, I just don't understand how to represent anything on a coordinate plane.

(I also don't know what line slopes are. I've been reading the wiki page on parabolas and hyperbolas for hours and it's not clicking at all.)

9) I don't know what the distance between these points is. Nor how to find a variable point.

10) Line slopes again. Except they're comparing intercepts or something. It really sucks to feel this ignorant about something a week away from the test. Feels like they're rubbing it in now.

12) This uses functions, except they complicate it by adding two functions and asking you to find f(g(x)).

13) Yeah, asks you to identify like what kind of curve an equation is. Curves are crazy ok

14) This is the one that dealt with the constant. It asks: "If x + 1 < 0 then |x| is" and I answered -x cuz YOLO, but I don't understand what that means. So on a number line, the absolute value of x, so long as it's less than zero, is negative x? Everywhere I read about absolute value they keep saying "absolute value is never negative" and "we never say that the absolute value of a number is positive"). I also don't get what the absolute value is representative of.

16) 17) Line slopes. Is this called coordinate geometry? I probably just need to learn this from the beginning.

20) Stuff (y) varying inversely with the square of other stuff (x). The variable k is used for no reason.

21) What are edges? Like... normal English edges? Should I have just imagined and counted? What weird science is this?

22) I think I know this, but just in case I don't: should I look for the tangent of the 30 degree angle?

And, in general, what's up with writing numbers before the square root of something? How could (presumably) multiplying 5 by the square root of three possibly be an answer? Would you just express that as a number?

23) Inverse functions say whaaaa. How do they work

24) All possible values of something. This one was pretty easy, but if I get a question asking me "all possible values", should I use some sort of trick to make it easier? Instead of, like, just using all provided values one by one.

25) Ain't nobody got time fo dat. Sum of the first 40 even integers. This either needs some complex equation I don't know about or they for some reason want me to spend a lotta time on one question.

EDIT: Holy crap this is big. Sorry! Just do what you have time for. single word explanations are acceptable too

*Last edited by ali.guitarkid7 at Jan 15, 2016,*

#9887

Hey all. I haven't taken a differential equations class in about 3 years, and now all of a sudden my circuits and systems analysis course is all diff eqs. I was going to go through the Khan academy course to brush up. Has anyone done their series on diff eqs before? Is it any good?

#9888

Well not really, finding c is the goal of the problem since you know that the area will be c^23) The Pythagorean theorem one. I have no clue why you'd use that to find out the area of the square. Is it just because C is a side of the square?

What makes it applicable is the fact that you have a right triangle, which is what the Pythagorean theorem deals with. If you can come up with a right triangle anywhere where you can figure out the length of the sides, you'll be able to apply the Pythagorean theorem. I'm not really sure if I understood your answer properly to be honest, so say something if I wasn't clear.But how do you know that this is the C that corresponds to the pythagorean theorem? Like if I drew any complex shape and then used a + b to describe two lines within that shape, and then placed that shape in a square and labeled a side of it c, how in the world would it follow that I'd be correct to use that?

Anyway you have those 4 triangles, it doesn't matter that they are 4, just focus on one of them. Its sides are a, b and c, c being the hypotenuse. so a^2 + b^2 = c^2, and c^2 was the area of the square.

The fraction at the end is just a number like any number But anyway, the standard procedure for equations where you have fractions is to multiply both sides by the denominators so that you have stuff in the end that you can add and subtract:6) The fraction at the end throws me off. What subject is this? Fractional algebra or something?

x/4 + (x+1)/3 = 3/2

The first x is over 4, so let's multiply the whole thing by 4:

x + 4(x+1)/3 = 4*3/2

or x + 4(x+1)/3 = 6

We still have to get rid of that 3 fraction so let's multiply the whole thing by 3:

3x + 4(x+1) = 18

and now it's much simpler

Ok I just saw the solution and they do a stupid unnecessary thing in the middle.

7) I understand functions, they're probably the easiest form of math I've ever encountered, I just don't understand how to represent anything on a coordinate plane.

What about representing things on a coordinate plane don't you understand?

For this problem, in any case, you need to know that the value of y along the x axis is always zero, so a function crosses the x axis when its value is zero, so you just need to solve f(x) = 0.

Note that you can exclude b) and c) right away because y is not zero in these solutions. The rest of them, you can just try them out, so for instance, a) is saying basically that f(2)=0 and f(1)=0, so you can go there and check.

(I also don't know what line slopes are. I've been reading the wiki page on parabolas and hyperbolas for hours and it's not clicking at all.)

The line slope is a property of a line, not a parabola or a hyperbola. It's the ratio of how much y increases over how much x increases between any two points.

9) I don't know what the distance between these points is. Nor how to find a variable point.

You can find the distance between two points on a coordinate plane with the Pythagorean theorem. You just write out the formula (you'll be able to find that stuff on wiki or something) and equal it to 5.

And yeah sorry it's nearly 3am, so I'll answer the rest tomorrow.

#9889

Great. Lemme go with:

3) The Pythagorean theorem one. I have no clue why you'd use that to find out the area of the square. Is it just because C is a side of the square? But how do you know that this is the C that corresponds to the pythagorean theorem? Like if I drew any complex shape and then used a + b to describe two lines within that shape, and then placed that shape in a square and labeled a side of it c, how in the world would it follow that I'd be correct to use that?

You use the Pythagorean theorem because the question specifically asks to express the area in terms of "a" and "b" where "a" and "b" are the sides of a right triangle. To find how a is a side of the right triangle. Subtract "b" by (b-a) The Pythagorean theorem relates the sides of a right sided triangle.

6) The fraction at the end throws me off. What subject is this? Fractional algebra or something?

Don't be ignorant. It's Pre-algebra or Algebra 1. On the left side of the equation, give them a common denominator and solve.

7) I understand functions, they're probably the easiest form of math I've ever encountered, I just don't understand how to represent anything on a coordinate plane.

All the question is asking of you is to find the roots of the quadratic equation. Just use the quadratic formula or factor it. The answers tells you the factors.

9) I don't know what the distance between these points is. Nor how to find a variable point.

You use the distance formula. The distance formula is an extension of the Pythagorean theorem. d = Sqrt[(Change in x)^2 + (Change in y)^2] The answers shows you how to do this. Subtract the x components P1 from P2. Do the same with the y compononents and solve for a.

10) Line slopes again. Except they're comparing intercepts or something. It really sucks to feel this ignorant about something a week away from the test. Feels like they're rubbing it in now.

Draw them out. You can see if it if you draw them out.

12) This uses functions, except they complicate it by adding two functions and asking you to find f(g(x)).

I thought you said functions were easy...

f(g(x)) is a composition of functions. You need to replace the variable x in function f with function g(x) = x+1. Therefore, f(g(x)) = (x+1) + 1 which simplifies to x + 2

13) Yeah, asks you to identify like what kind of curve an equation is. Curves are crazy ok

All quadratic equations are parabolas

14) This is the one that dealt with the constant. It asks: "If x + 1 < 0 then |x| is" and I answered -x cuz YOLO, but I don't understand what that means. So on a number line, the absolute value of x, so long as it's less than zero, is negative x? Everywhere I read about absolute value they keep saying "absolute value is never negative" and "we never say that the absolute value of a number is positive"). I also don't get what the absolute value is representative of.

This is what the previous poster was saying. If x < 0 then the absolute value of x; |x| = -x. x<-1 for all x from the previous inequality. Therefore, we know |x| is -x because x <0

16) 17) Line slopes. Is this called coordinate geometry? I probably just need to learn this from the beginning.

I would call it that. You should've learned this in Algebra 1 or Algebra 2.

20) Stuff (y) varying inversely with the square of other stuff (x). The variable k is used for no reason.

The letter k used is a constant, not a variable. This is from Algebra II I believe. If y varies inversely with the square of a variable x, it means that y drops every time the square of x increases.

21) What are edges? Like... normal English edges? Should I have just imagined and counted? What weird science is this?

Yes, you should've imagined and counted. This is Euclidean geometry.

22) I think I know this, but just in case I don't: should I look for the tangent of the 30 degree angle?

And, in general, what's up with writing numbers before the square root of something? How could (presumably) multiplying 5 by the square root of three possibly be an answer? Would you just express that as a number?

This problem has nothing to do with tangent lines. The answer tells you that it's just 4 times 5....which is the area of a parallelogram.

23) Inverse functions say whaaaa. How do they work

Inverse functions gives you the original value of a function. Say g(x) is the inverse function of x for example. Then g(f(x) = x. For example. If f(x) = x^2 then g(x) = x^-2 and g(f(x)) = x. I learned this in Pre-Calculus personally

24) All possible values of something. This one was pretty easy, but if I get a question asking me "all possible values", should I use some sort of trick to make it easier? Instead of, like, just using all provided values one by one.

Algebra 2. The answers explain this pretty well. There is no trick. You just have to have to mathematical intuition.

25) Ain't nobody got time fo dat. Sum of the first 40 even integers. This either needs some complex equation I don't know about or they for some reason want me to spend a lotta time on one question.

The answers explain how to do this. They factored out a 2 and then used the summation formula for everything inside the parenthesis 2[1+2+3+4...] This is from Algebra II

3) The Pythagorean theorem one. I have no clue why you'd use that to find out the area of the square. Is it just because C is a side of the square? But how do you know that this is the C that corresponds to the pythagorean theorem? Like if I drew any complex shape and then used a + b to describe two lines within that shape, and then placed that shape in a square and labeled a side of it c, how in the world would it follow that I'd be correct to use that?

You use the Pythagorean theorem because the question specifically asks to express the area in terms of "a" and "b" where "a" and "b" are the sides of a right triangle. To find how a is a side of the right triangle. Subtract "b" by (b-a) The Pythagorean theorem relates the sides of a right sided triangle.

6) The fraction at the end throws me off. What subject is this? Fractional algebra or something?

Don't be ignorant. It's Pre-algebra or Algebra 1. On the left side of the equation, give them a common denominator and solve.

7) I understand functions, they're probably the easiest form of math I've ever encountered, I just don't understand how to represent anything on a coordinate plane.

All the question is asking of you is to find the roots of the quadratic equation. Just use the quadratic formula or factor it. The answers tells you the factors.

9) I don't know what the distance between these points is. Nor how to find a variable point.

You use the distance formula. The distance formula is an extension of the Pythagorean theorem. d = Sqrt[(Change in x)^2 + (Change in y)^2] The answers shows you how to do this. Subtract the x components P1 from P2. Do the same with the y compononents and solve for a.

10) Line slopes again. Except they're comparing intercepts or something. It really sucks to feel this ignorant about something a week away from the test. Feels like they're rubbing it in now.

Draw them out. You can see if it if you draw them out.

12) This uses functions, except they complicate it by adding two functions and asking you to find f(g(x)).

I thought you said functions were easy...

f(g(x)) is a composition of functions. You need to replace the variable x in function f with function g(x) = x+1. Therefore, f(g(x)) = (x+1) + 1 which simplifies to x + 2

13) Yeah, asks you to identify like what kind of curve an equation is. Curves are crazy ok

All quadratic equations are parabolas

14) This is the one that dealt with the constant. It asks: "If x + 1 < 0 then |x| is" and I answered -x cuz YOLO, but I don't understand what that means. So on a number line, the absolute value of x, so long as it's less than zero, is negative x? Everywhere I read about absolute value they keep saying "absolute value is never negative" and "we never say that the absolute value of a number is positive"). I also don't get what the absolute value is representative of.

This is what the previous poster was saying. If x < 0 then the absolute value of x; |x| = -x. x<-1 for all x from the previous inequality. Therefore, we know |x| is -x because x <0

16) 17) Line slopes. Is this called coordinate geometry? I probably just need to learn this from the beginning.

I would call it that. You should've learned this in Algebra 1 or Algebra 2.

20) Stuff (y) varying inversely with the square of other stuff (x). The variable k is used for no reason.

The letter k used is a constant, not a variable. This is from Algebra II I believe. If y varies inversely with the square of a variable x, it means that y drops every time the square of x increases.

21) What are edges? Like... normal English edges? Should I have just imagined and counted? What weird science is this?

Yes, you should've imagined and counted. This is Euclidean geometry.

22) I think I know this, but just in case I don't: should I look for the tangent of the 30 degree angle?

And, in general, what's up with writing numbers before the square root of something? How could (presumably) multiplying 5 by the square root of three possibly be an answer? Would you just express that as a number?

This problem has nothing to do with tangent lines. The answer tells you that it's just 4 times 5....which is the area of a parallelogram.

23) Inverse functions say whaaaa. How do they work

Inverse functions gives you the original value of a function. Say g(x) is the inverse function of x for example. Then g(f(x) = x. For example. If f(x) = x^2 then g(x) = x^-2 and g(f(x)) = x. I learned this in Pre-Calculus personally

24) All possible values of something. This one was pretty easy, but if I get a question asking me "all possible values", should I use some sort of trick to make it easier? Instead of, like, just using all provided values one by one.

Algebra 2. The answers explain this pretty well. There is no trick. You just have to have to mathematical intuition.

25) Ain't nobody got time fo dat. Sum of the first 40 even integers. This either needs some complex equation I don't know about or they for some reason want me to spend a lotta time on one question.

The answers explain how to do this. They factored out a 2 and then used the summation formula for everything inside the parenthesis 2[1+2+3+4...] This is from Algebra II

#9890

Well not really, finding c is the goal of the problem since you know that the area will be c^2

What makes it applicable is the fact that you have a right triangle, which is what the Pythagorean theorem deals with. If you can come up with a right triangle anywhere where you can figure out the length of the sides, you'll be able to apply the Pythagorean theorem. I'm not really sure if I understood your answer properly to be honest, so say something if I wasn't clear.

What still throws me off is the b - a thing. Is it saying that a is (b - a) or is it something else? Because if it's the former, then what is a? Is it the the sides of the smaller square?

The fraction at the end is just a number like any number But anyway, the standard procedure for equations where you have fractions is to multiply both sides by the denominators so that you have stuff in the end that you can add and subtract:

x/4 + (x+1)/3 = 3/2

The first x is over 4, so let's multiply the whole thing by 4:

x + 4(x+1)/3 = 4*3/2

or x + 4(x+1)/3 = 6

We still have to get rid of that 3 fraction so let's multiply the whole thing by 3:

3x + 4(x+1) = 18

and now it's much simpler

Ok I just saw the solution and they do a stupid unnecessary thing in the middle.

On second look this was way simpler than I'd thought. You're basically just adding stuff to get 1.5, right? So I just looked for a number that facilitated that lol.

What about representing things on a coordinate plane don't you understand?

For this problem, in any case, you need to know that the value of y along the x axis is always zero, so a function crosses the x axis when its value is zero, so you just need to solve f(x) = 0.

Note that you can exclude b) and c) right away because y is not zero in these solutions. The rest of them, you can just try them out, so for instance, a) is saying basically that f(2)=0 and f(1)=0, so you can go there and check.

Well, for example I get the Cartesian thing where y = x + something (and whatever variations on that like 2y + 5x -3 = g) but functions just tend to be self-fulfilling, and there's no y on this. So if I substitute x for 2, as in (a):

f(x) = x^2 + 3x + 2

f(2) = 4 + 6 + 2

and that's a huge nope, right? So it's basically saying that x has to equal itself when put it through the function?

And how do you know that y = 0 as opposed to just something they didn't tell you?

The line slope is a property of a line, not a parabola or a hyperbola. It's the ratio of how much y increases over how much x increases between any two points.

So for example, if it asks you something like subtract (-2, 4) and (8, 3), my assumption is always to just go -2 - 8; 4 - 3 = (-10, 1) and I am never correct. Or if it asks "What's the distance between these two points?"

And what are parabolas? If they ask a question like (13):

The equation x^2 + 9 = 2y^2 is an example of which of the following curves?

How would you be able to tell the curve? Cuz how am I gonna know that any one point is equal in distance from all points on the plane?

You can find the distance between two points on a coordinate plane with the Pythagorean theorem. You just write out the formula (you'll be able to find that stuff on wiki or something) and equal it to 5.

Alright, yeah, I found it. So basically, the distance between these two points is the hypotenuse of a triangle whose third side is just wherever the x and y coordinates for those two points meet. So you're really just arbitrarily turning it into a hypotenuse because that's just an easier solve.

And yeah sorry it's nearly 3am, so I'll answer the rest tomorrow.

No worries, I'm starting to get the general direction of what my weaknesses are. Thanks a bunch for all of this, by the way.

You use the Pythagorean theorem because the question specifically asks to express the area in terms of "a" and "b" where "a" and "b" are the sides of a right triangle. To find how a is a side of the right triangle. Subtract "b" by (b-a) The Pythagorean theorem relates the sides of a right sided triangle.

Alright, now I get it. The (b - a) thing only relates to the center square then.

All the question is asking of you is to find the roots of the quadratic equation. Just use the quadratic formula or factor it. The answers tells you the factors.

Okay, I'm gonna have to memorize this quadratic formula. Keeps coming up.

You use the distance formula. The distance formula is an extension of the Pythagorean theorem. d = Sqrt[(Change in x)^2 + (Change in y)^2] The answers shows you how to do this. Subtract the x components P1 from P2. Do the same with the y compononents and solve for a.

This makes a whole lot more sense now. Any other formulas I should be aware of for a test at this level?

I thought you said functions were easy...

f(g(x)) is a composition of functions. You need to replace the variable x in function f with function g(x) = x+1. Therefore, f(g(x)) = (x+1) + 1 which simplifies to x + 2

Turns out there's more to them than my middle-school drop-out ass thought

So basically, if f(x) = x + 2, and g(x) = x + 3, then f(g(x)) = x + 5?

All quadratic equations are parabolas

Alright, I'm basically never getting this wrong again haha. So then hyperbola/ellipse?

This problem has nothing to do with tangent lines. The answer tells you that it's just 4 times 5....which is the area of a parallelogram.

So AE is equal to AB? How's that possible? If they'd asked about the area of AECD this would make sense to me, but they're asking you to exclude triangle AEB.

Inverse functions gives you the original value of a function. Say g(x) is the inverse function of x for example. Then g(f(x) = x. For example. If f(x) = x^2 then g(x) = x^-2 and g(f(x)) = x. I learned this in Pre-Calculus personally

So if f(x) = x -1, then g(x) = x + 1, and g(f(x)) = just x?

24) All possible values of something. This one was pretty easy, but if I get a question asking me "all possible values", should I use some sort of trick to make it easier? Instead of, like, just using all provided values one by one.

Algebra 2. The answers explain this pretty well. There is no trick. You just have to have to mathematical intuition.

25) Ain't nobody got time fo dat. Sum of the first 40 even integers. This either needs some complex equation I don't know about or they for some reason want me to spend a lotta time on one question.

The answers explain how to do this. They factored out a 2 and then used the summation formula for everything inside the parenthesis 2[1+2+3+4...] This is from Algebra II

Alright, got these. I'm really glad you mentioned which branch of math these belong to cuz now I know which ones to take on Khan. Thank you very much.

*Last edited by ali.guitarkid7 at Jan 16, 2016,*

#9891

Alright, now I get it. The (b - a) thing only relates to the center square then.

No, the (b-a) indirectly tells you one of the sides of the right triangle has side lengths a.

This makes a whole lot more sense now. Any other formulas I should be aware of for a test at this level?

Midpoint formula, quadratic formula, distance formula, and summation formula should be it.

So basically, if f(x) = x + 2, and g(x) = x + 3, then f(g(x)) = x + 5?

Right

Alright, I'm basically never getting this wrong again haha. So then hyperbola/ellipse?

Look it up. Formujlas for hyperbolas and ellipses.

So AE is equal to AB? How's that possible? If they'd asked about the area of AECD this would make sense to me, but they're asking you to exclude triangle AEB.

No, AE =/= AB. The area of a parallelogram is the height of said parallelogram times the width.

So if f(x) = x -1, then g(x) = x + 1, and g(f(x)) = just x?

That is an example of an inverse function yes.

No, the (b-a) indirectly tells you one of the sides of the right triangle has side lengths a.

This makes a whole lot more sense now. Any other formulas I should be aware of for a test at this level?

Midpoint formula, quadratic formula, distance formula, and summation formula should be it.

So basically, if f(x) = x + 2, and g(x) = x + 3, then f(g(x)) = x + 5?

Right

Alright, I'm basically never getting this wrong again haha. So then hyperbola/ellipse?

Look it up. Formujlas for hyperbolas and ellipses.

So AE is equal to AB? How's that possible? If they'd asked about the area of AECD this would make sense to me, but they're asking you to exclude triangle AEB.

No, AE =/= AB. The area of a parallelogram is the height of said parallelogram times the width.

So if f(x) = x -1, then g(x) = x + 1, and g(f(x)) = just x?

That is an example of an inverse function yes.

#9892

Alright, I just wanna confirm something about composite functions:

f(x) = x^2 + 2x + 4

g(x) = x^2 + 3x + 2

f(g(x)) = x^4 + 5x + 6

Would that be correct? As for inverse functions, if g(x) is inverse:

f(x) = x^2 + 2x + 4

g(x) = sqrt(x) - (1/2)x - 4

f(g(x)) = 3.5x

?

f(x) = x^2 + 2x + 4

g(x) = x^2 + 3x + 2

f(g(x)) = x^4 + 5x + 6

Would that be correct? As for inverse functions, if g(x) is inverse:

f(x) = x^2 + 2x + 4

g(x) = sqrt(x) - (1/2)x - 4

f(g(x)) = 3.5x

?

*Last edited by ali.guitarkid7 at Jan 16, 2016,*

#9893

Alright, I just wanna confirm something about composite functions:

f(x) = x^2 + 2x + 4

g(x) = x^2 + 3x + 2

f(g(x)) = x^4 + 5x + 6

Would that be correct? As for inverse functions, if g(x) is inverse:

f(x) = x^2 + 2x + 4

g(x) = sqrt(x) - (1/2)x - 4

f(g(x)) = 3.5x

?

No, what you're doing is adding the two functions together. f(g(x)) is not f(x) + g(x).

I don't even know what you did on the latter case but no, that's not an inverse function. The f(x) you chose has no inverse function.

#9894

So what is it?

Also, I thought the composite of a function with its inverse would just cancel each other out. So like if f(x) = x^3 + 2, then g(x) = 3Sqrt(x) - 2, and f(g(x)) = x - 1

Also, I thought the composite of a function with its inverse would just cancel each other out. So like if f(x) = x^3 + 2, then g(x) = 3Sqrt(x) - 2, and f(g(x)) = x - 1

#9895

The first one:

f(g(x))

= f(x^2 + 3x + 2)

= (x^2 + 3x + 2)^2 + 2(x^2 + 3x + 2) + 4

= x^4 + 6x^3 + 13x^2 + 12x + 4 + 2x^2 + 6x + 4 + 4

= x^4 + 6x^3 + 15x^2 + 18x + 12

So basically anywhere there is x in f(x) we put instead g(x).

f(g(x))

= f(x^2 + 3x + 2)

= (x^2 + 3x + 2)^2 + 2(x^2 + 3x + 2) + 4

= x^4 + 6x^3 + 13x^2 + 12x + 4 + 2x^2 + 6x + 4 + 4

= x^4 + 6x^3 + 15x^2 + 18x + 12

So basically anywhere there is x in f(x) we put instead g(x).

#9896

So, I don't know math but gotta know: Couldn't you just simplify that last line as = 40x^9 + 12 ?

#9897

No, you can't add terms of different exponents. x^4 + x^3 is just that, there's no simplifying it further.

E. I mean of course you can add them but you can't SIMPLIFY them further...sorry if I'm confusing you just more

E. I mean of course you can add them but you can't SIMPLIFY them further...sorry if I'm confusing you just more

*Last edited by ElMaco at Jan 16, 2016,*

#9898

However, for example x^3 + x^3 = 2x^3, as they have the same exponent, which is 3.

#9899

Nah I got that one haha. You add the values of the numbers resulting from the exponent, you can't combine them.

So could you say that (x^3)(x^3) is the simplest possible form? You wouldn't be able to make it x^6?

So could you say that (x^3)(x^3) is the simplest possible form? You wouldn't be able to make it x^6?

*Last edited by ali.guitarkid7 at Jan 16, 2016,*

#9900

Multiplying exponents is fine, even when they are not the same, so x^3*x^3 = x^6. Another example: x^4*x^5 = x^9

#9901

#9902

Yeas I've drank a couple of beers but I think stuff's right!

#9903

Alright, back again with something I don't understand.

1. Now the explanation is (x = num. of tickets)

3x + 5(50 - x) = 230

2. I get that. Simple enough. Now this is where they lost me:

3x + 250 - 5x = 230

I get that they may have multiplied the cost of 5 dollar tickets by the total amount sold, but why? What does this actually represent? If you had to explain this through English, what would you say? And why subtract 5x from it?

3. This ends up being

2x = 20

and I get why this happens from the preceding line. It's just 5x - 3x = 250 - 230. What I don't understand, however, is what happens in step two. I understand that they're multiplying cost of tix * total sold, I just don't get what that means in logical terms.

Tickets for a show cost 3 dollars or 5 dollars. If 50 tickets were sold for a total of 230 dollars, how many tickets were sold for 3 dollars?

1. Now the explanation is (x = num. of tickets)

3x + 5(50 - x) = 230

2. I get that. Simple enough. Now this is where they lost me:

3x + 250 - 5x = 230

I get that they may have multiplied the cost of 5 dollar tickets by the total amount sold, but why? What does this actually represent? If you had to explain this through English, what would you say? And why subtract 5x from it?

3. This ends up being

2x = 20

and I get why this happens from the preceding line. It's just 5x - 3x = 250 - 230. What I don't understand, however, is what happens in step two. I understand that they're multiplying cost of tix * total sold, I just don't get what that means in logical terms.

#9904

From the moment you've got the equation, you don't have to think in terms of "real world logic" anymore, all the real world logic has been incorporated into the equation.

They're using the distributive property of multiplication.

a*(b+c) = a*b + a*c

To be able to add things together in equations, you usually need to "break down" everything that's inside brackets. So that happened because

5(50 - x) = 5*50 + 5*(-x) = 250 - 5x

and now you can solve the rest of the equation.

They're using the distributive property of multiplication.

a*(b+c) = a*b + a*c

To be able to add things together in equations, you usually need to "break down" everything that's inside brackets. So that happened because

5(50 - x) = 5*50 + 5*(-x) = 250 - 5x

and now you can solve the rest of the equation.

#9905

Ah alright, yeah that sorta makes sense. I really have to start thinking in those terms come Saturday. Thanks, once again.

#9906

Alright, I don't expect to get an answer on this before tomorrow, if ever, but I've got a fucked up problem here.

Consider the cap of thickness h that has been sliced from a sphere of radius r. Verify that the volume of the cap is pi(h^2)((3r-h)/3) using the washer method, the shell method, and the general slicing method.

I can figure out how to do this with washer method (which doesn't seem at all different from the slicing method in this case?), but the shell method just comes out to a bunch of gibberish.

Lower limit: r-h

Upper limit: r

Integrand: 2(pi)(y)(squareroot(r^2-y^2) dy

After doing a u substitution I eventually get

pi((2/3)(2rh-h^2)^3/2-0)

Expanding the 3/2 exponent just gets me a bunch of fucking nonsense. It doesn't simplify out to be pi(h^2)((3r-h)/3). Chances are I'm just setting it up all wrong.

Consider the cap of thickness h that has been sliced from a sphere of radius r. Verify that the volume of the cap is pi(h^2)((3r-h)/3) using the washer method, the shell method, and the general slicing method.

I can figure out how to do this with washer method (which doesn't seem at all different from the slicing method in this case?), but the shell method just comes out to a bunch of gibberish.

Lower limit: r-h

Upper limit: r

Integrand: 2(pi)(y)(squareroot(r^2-y^2) dy

After doing a u substitution I eventually get

pi((2/3)(2rh-h^2)^3/2-0)

Expanding the 3/2 exponent just gets me a bunch of fucking nonsense. It doesn't simplify out to be pi(h^2)((3r-h)/3). Chances are I'm just setting it up all wrong.

#9907

Quick question:

Would I count the 27 values in the "25.5 up to 27" box or the "27 to 28.5" box?

Would I count the 27 values in the "25.5 up to 27" box or the "27 to 28.5" box?

#9908

Quick question:

Would I count the 27 values in the "25.5 up to 27" box or the "27 to 28.5" box?

I read that as up to 27 but not including 27.....I would say the 27-28.5 box

#9909

That was correct, good lookin out

#9910

glad to help...but yeah they could make it a little clearer

*Last edited by mattedbird at Feb 7, 2016,*