Answer:
3pi
Step-by-step explanation:
First find the area of the entire circle
A = pi r^2
A = pi * 2^2
A = 4 pi
We know that this is 3/4 of a circle so multiply the area by the fraction of the circle
3/4 * 4 pi
3 pi
We can find this using the formula: L= ∫√1+ (y')² dx
First we want to solve for y by taking the 1/2 power of both sides:
y=(4(x+1)³)^1/2
y=2(x+1)^3/2
Now, we can take the derivative using the chain rule:
y'=3(x+1)^1/2
We can then square this, so it can be plugged directly into the formula:
(y')²=(3√x+1)²
<span>(y')²=9(x+1)
</span>(y')²=9x+9
We can then plug this into the formula:
L= ∫√1+9x+9 dx *I can't type in the bounds directly on the integral, but the upper bound is 1 and the lower bound is 0
L= ∫(9x+10)^1/2 dx *use u-substitution to solve
L= ∫u^1/2 (du/9)
L= 1/9 ∫u^1/2 du
L= 1/9[(2/3)u^3/2]
L= 2/27 [(9x+10)^3/2] *upper bound is 1 and lower bound is 0
L= 2/27 [19^3/2-10^3/2]
L= 2/27 [√6859 - √1000]
L=3.792318765
The length of the curve is 2/27 [√6859 - √1000] or <span>3.792318765 </span>units.
Answer:
D : [-2,0) U (0, infinity) ; -2<=x<0 U x>0
Pretty sure it's D. When you have a fractional exponent, the root number is always on the bottom, while the exponent on the top. Since x and y are not grouped together in a parentheses, we can assume that only "y" is being raised to the 2/9 power. That means "x "will stay out in front and y will be in the 9th root being raised to the 2nd power.
Step-by-step explanation:
given f(x) = 2/x and g(x) = 2/x
f(g(x)) = 2/(g(x)) = 2/2/x = x/2 × 2 = x
g(f(x)) = 2/(f(x)) = 2/2/x = x/2 × 2 = x
therefore they are inverses
since f(g(x)) = g(f(x)) = x.
