We know that:
x=rcosθ and y=rsinθ with 0≤r≤2 and 0≤θ≤pi.
Also we need the Jacobian Determinant ∂(x,y)/∂(r,θ) = r (in this case).
Therefore the double integral becomes int_{θ=0→pi}int_{r=0→2}(rcosθ)^2+(rsinθ)^2 r drdθ.
This turns out to be int_{θ=0→pi}int_{r=0→2}r^3drdθ=pi/4(2)^4=4pi...

In order to graph you need to get all the y's to one side of the equation and everything else on the opposite side.
You want it in this form: y = mx + b, where m = slope (rise over run) and b = the y-intercept
Part (a).
x + y = -6 (subtract...

The two pages you were reading were pages: 99 and 100.
9 + 9 + 1 + 0 + 0 = 19
The next page is: 101.
1 + 0 + 1 = 2
Therefore you were reading page 100 because the NEXT page must be page 101.

9t+6/t(t+3) = 7/(t+3)
(9t+6)(t+3)=7t(t+3) (Cross multiply the proportion)
9t+6=7t (divide (t+3) from both sides)
2t+6=0 (subtract 7t from both sides)
2t=-6...

x6 - 9x4 - x2 + 9 = 0
= x4(x2-9) - (x2-9) factor out x4 in the first two terms and a (-1) in the last two terms.
= (x4-1)(x2-9) collect like terms. Ex. a(x2-c)...

-4(2-3x)=7-2(x-3) *first use the distributive property Ex. a(b+c)=ab+ac
-8+12x=7-2x+6 *get all the terms with "x's" on each side.
12x+2x=7+6+8 *Collect like terms. Ex. 3x+5x=8x...