If you're bored and want to help me with some Mathz

[Mr.GAW]

Hey so school's starting against soon and obviously I've procrastinated on my summer work.

If any of you would be so kind as to maybe choose a problem and help me with it I would be greatly appreciative. Of course, I want to actually understand the problems, so I don't want just answers otherwise I would just go copy one of my friends.

Hopefully this can be helpful to others going into Calc BC as well.

EDIT: Alright, it's updated.

Square= No idea how to get started
Circle= No answer yet
Triangle= I'm not sure about this answer.

Obviously square>circle>triangle in terms of importance, but obviously any help is appreciated.

Thanks,
GAW

 

[POKE40]

number 12 on paint:
(calculus ftw)

Number 26 on MS paint:
:3

 

[Fuelbi]

thank god Im not taking calculus. I understood nothing of that problem.....

 

[~Firefly~]

I'm lazy, so I'll just go through one of the easier ones.

32. There are two ways to have a restriction on the domain of a function; there cannot be division by 0 or the square root of a negative number. To satisfy the first condition, x =/= -2, since (-2) + 2 = 0. As for the square root, x must be greater than or equal to -5, or else the value under the radical sign will be negative. So we have x =/= -2 and x > -5. I'm assuming interval notation means the question is asking for a single interval, so when you combine the two, you'd be left with:

-5 < x < -2 < x

Or something like that. Use your own discretion to determine exactly how it should be expressed.

Hope that wasn't completely useless. >.<

 

[1048576]

Number 8.)

I'm calling the top Y

2X + Y = 240

XY = A A is area

Y = A/X (just divided both sides of above equation by X)

2X + A/X = 240 There's the answer to part 1

for A = 5500:

2x + 5500/X = 240

2X^2 -240X + 5500 = 0

that's easy to solve with quadratic formula. I don't have a calc to manipulate the large numbers offhand though.

Number 10.)

y = (3x+7)/(x-2)
for inverse, swap x and y, resolve for y
x = (3y+7)/(y-2)
xy-2x = 3y + 7
xy-3y = 2x + 7
y = (2x+7)/(x-3)

number 11.)

y = ax^2 + bx + c

-5 = 4a + 2b + c
7 = 16a + 4b +c
7 = 0a + 0b + c (vertex splits parabola in half, so 2 units to the left must also have y value of 7)
c=7
-12 = 4a + 2b
0 =16a + 4b

a = 3, b = -12
f(x) = 3x^2 -12x + 7

12 is obv B. I'd spend some time discerning why if you don't know already.

13.)

y = ax^3 + bx^2 + cx + d

0 = -8a + 4b -2c + d
0 = 125a + 25b + 5c + d

you see where that's going. Find the other two eqs. and solve the system.

14 is obv C. As X increases, y decreases.

 

[Mr.GAW]

I appreciate the help you guys keep them coming!

Firefly interval notation just means -5<(or equal to) x < -2 U x > -2

The U means and

 

[1048576]

I thought interval notation was like [-5, -2) U (-2, *infinity*)

 

[Mr.GAW]

^ This. Mind lapse. And thank you 1048576 for all the help so far.

 

[Mr.GAW]

I'm having a little bit of trouble solving the 3 equation system in problem 13...

 

[Mota]

Snap...what year is this? Way out of my league...Brainache.

 

[The Immortal Sir NZ]

you just reminded me of the Calc BC im taking this year. I would love to help, but seeing as how I'm going to go to bed soon, I can't sorry. good luck though.

 

[day-day]

God do I hate math with a passion, even more then the Kankers.
I'll try and help out by editing my post with answers though..

 

[1048576]

I'm having a little bit of trouble solving the 3 equation system in problem 13...

It's four equations with four unknowns. You have (-2,0) (1,0) (5,0) and (0,-3). You have to find A, B, C, and D.

Number 15.)

Uhh, shift left two, move it down by 3, and make it four times narrower. I don't remember the mathematical terms for these things.

Number 16)

This one's easy. For A plug in zero obv. For B plug in 750 for P(t) and solve for t. For C derive P(t) in terms of t and find the extrema by testing the values of t at which the derivative equals zero. You know how to determine whether it's a min or max, right? If not, you can just plug all the values of t back into the original equation and see what gives you the highest number.

Number 17.)

I don't remember the formula, but this should work.

4550 = 2700(1+0.09)^x

Solving for X gives you the number of quarters you need to keep the money in there. Convert to years.




Also, I need to find his bank. 9%!?

Number 18.)

cscxsinxcosx - tanxsinxcosx

cosx - sin^2(x)

Number 19.)

Is this a trick question? arcCos cancels out cos. It's like what's 17pi/5 + 8 - 8

Number 20.)

Find the roots and plug in one number between each root and one lower than the lowest root and one higher than the highest root. It's D. There's prolly a better way to do it than that though...

Number 21.)

You need the two sides + 1/12 of the outer circle. The sides are 8 obv, and the outer circle is 2*pi*8. You should have scanned your worksheet and completed the easy ones first. I know you could have done this by yourself.

Number 22.)

Use L'Hopital's rule. (cosx)/(2x-1) plug in zero gives -1.

 

[1048576]

Number 23.)

A = 4. R = 1/3 N = infininty

Sum = A(1-R^n)/(1-R)

4(1-0)/(2/3) which evaluates to 6.

24.)

Find the point of intersection. I'd just plug x/3 into the first equation to find the values of x and y where they are both equal. Graphing it shouldn't be too hard. One's an ellipse and the other is a line.

Sorry for double post. I didn't want to accidentally misclick and lose everything in the previous post.

 

[Mr.GAW]

I'm going to update the OP in a little bit with my work now as the packet has much progressed thanks to all of you and some more effort on my part. Circles will mean I don't have an answer and squares will mean I have no idea how to begin. Triangles will mean I'm unsure of my answer.

EDIT: Help with the "BC only" problems would be great.

For C derive P(t) in terms of t and find the extrema by testing the values of t at which the derivative equals zero.

err... how do I do this?

 

[Chronodiver Lokii]

...
...Im in Algebra 2 o__o|l|
That just scares me...so complicateddd @__@

 

[Mr.GAW]

alright its updated!

Help with questions 3, 4, 6, 34, and 40 is all I really need now. Maybe 28 too.

 

[victra♥]

I love this. Calculus <33333

Mr.GAW, why do you have summer work? ):

 

[Mr.GAW]

I guess since it's a "college level course" or whatever they have high expectations and weed out the people who don't really care by giving you a summer packet.

Anyways, school starts in less than 12 hours and I still cant figure those 5 problems out haha

 

[POKE40]

@ Mr. GAW:

Fix your 26 graph.
The line 3x+5 starts with a hole. You started with a dot.
:3

 

[Mr.GAW]

Thank you for that. Do you know how to do any of 3, 4, 6, 34, and 40 by chance?

 

[1048576]

Oooh, I should have checked this thread sooner..

Number 3.)
The min is -infinity, obv, and it occurs at +- infinity
To find the max, derive and set equal to zero.
-12x^3 -2x - 20 = 0
The max occurs at x ~=~ -1.14

You can show that it's a max by taking one value less than -1.14 and seeing that it is greater than zero, and one value more and showing that it is less than zero. This shows that the slope is positive, then zero, then negative around that point, which is indicative of a maximum.

The y value at -1.14 is found by plugging into the original equation (not the derivative). It is ~=~ 29.43. The range is (-infinity, 29.43]

Nvm, I can see you had class already. How was it?

 

[Crimson King]

Use the search - http://www.smashboards.com/showthread.php?t=113366&highlight=Math