Jen

In the answer below, I am having trouble getting from here:

= 8(1 + 4x)⁵(1 - 2x)(3 + x - x²)⁷ + 20(3 + x - x²)⁸ (1 + 4x)⁴

To here:

= 4(1 + 4x)⁴(3 + x - x²)⁷( (2)(1 + 4x)(1 - 2x) + (5)(3 + x - x²) )

Can someone explain the above step? See below for the original answer.

g(x) = (1 + 4x)⁵ (3 + x - x²)⁸

is in the form of g(x) = uv

u = (1 + 4x)⁵

du/dx = 5(4)(1 + 4x)⁴ = 20(1 + 4x)⁴

v = (3 + x - x²)⁸

dv/dx = 8(1 - 2x)(3 + x - x²)⁷

if g(x) = uv

then, g ' (x) = u dv/dx + v du/dx

g ' (x)

= (1 + 4x)⁵ (8)(1 - 2x)(3 + x - x²)⁷ + (3 + x - x²)⁸ (20)(1 + 4x)⁴

= 8(1 + 4x)⁵(1 - 2x)(3 + x - x²)⁷ + 20(3 + x - x²)⁸ (1 + 4x)⁴

= 4(1 + 4x)⁴(3 + x - x²)⁷( (2)(1 + 4x)(1 - 2x) + (5)(3 + x - x²) )

= 4(1 + 4x)⁴(3 + x - x²)⁷( (-16x² + 4x + 2) + (15 + 5x - 5x²) )

= 4(1 + 4x)⁴(3 + x - x²)⁷ (-21x² + 9x + 17)

This is in the chapter before introducing the product rule, so I guess you're not suppose to do it that way. Why wouldn't you need to use the product rule here?

I already have the answer, but I'm having a hard time understanding the steps. Here they are:

ΔV(r) = V(r+1)−V(r)

= 4/3π(r+1)^3 − 4/3πr^3

= 4/3π((r+1)3−r3)

= 4π(3r^2+3r+1)

My problem is on this step:

= 4/3π(r+1)^3 − 4/3πr^3

= 4/3π((r+1)^3−r3)

QUESTION: Where does the 4/3pi go?

If the radius of a circle increases at a rate of 1 in/min, find the rate at which the area of the circle increases when the radius is 2 in?

As of right now my answer is 1/4pi, but I'm pretty sure I'm incorrect. Please help me understand this problem!

Does sinx/cos^2x = tan x or does that only work for sinx/cosx? Trying to study for an exam that I have in a few hours and I am really not understanding these types of problems.

Here is a picture of the problem which is easier to see: http://tinypic.com/r/2yv8hl1/6

Determine the degree measure of an arc with the given length, L, in a circle with the given radius, r. L=20, r=100

Please explain how to solve this. Not HW, need to understand.

My answer is -2 (plus or minus) 2 sqrt5 / -2 and the answer is supposed to be 1 (plus or minus) sqrt 5. I don't understand how to simplify this. Can anyone help? I have attached a picture of the question using symbols because it's a little confusing above.

http://tinypic.com/r/205v2uq/5

The angles are EFGH

E= 8x-10

F= x^2+10

G= 2x+30

H= x^2+2x+10

I have the answers, I just don't know how to solve it. Can't seem to remember this at all.

Write the equation of a line in Standard Form to 2/3x - 5/2y=1 through (-3/4, -1/7).

Need help on the steps. Very confused.

h(x) = √(4-x) + √(x^2-1)

Need help understanding.. thought of maybe trying to square each side, but having a lot of trouble.

-6 l 5-2y l = -9

I'm not sure if this is no solution or not. Can you please explain why?

Please explain to me how to simplify the following expression. The answer = x / 9y^7

( [ 3 x^(3/2) y^(3) ] / [ x^(2) y^(- 1/2) ] ) ^-2

Clicking here to see a picture of it may be easier to understand:

http://tinypic.com/r/2vlws9i/7

Please explain to me how to simplify the following expression:

( [ 3 x^(3/2) y^(3) ] / [ x^(2) y^(- 1/2) ] ) ^-2

Clicking here to see a picture of it may be easier to understand:

http://tinypic.com/r/2vlws9i/7

Reaction: Mg(s) + 2HCl(aq) --> MgCl2(aq) + H2 (g)

Assume the reaction is carried out in a calorimeter containing 100 mL H20

Initial Temp: 21.0 C

Final Temp: 31.8 C

Wt of Mg Ribbon: 0.2481g

More than than the answer I need the formula to answer problems like this one. I have a quiz in about 20 minutes!

EEK!

In the titration of 10mL of an unknown weak acid (HX) with a strong base that has a molarity of 0.1002 M, the equivalence volume was found to be 19.20 mL.

a) Calculate the concentration of HX

b) If the initial pH of the solution was recorded as 3.12, what is the Ka and pKa of HX.

Please explain how to arrive at answers. I don't need the answers so much as I need to know how to do it.

Ok so I know the equation should look like this:

(1-f)(34.97) + f (36.97) = 35.45

where f = the fraction of the smaller isotope, but I'm having a little bit of algebraic difficulty! How do I solve for f here? The answer is f = .24

My I know how to do the rest but the main question is how do I solve for f (algebraically)