Because of the symmetry, we can just go from x=0 to x=2 to find the area between
<span>y = x^2 and y = 4 </span>
<span>that area = ∫4-x^2 dx from 0 to 2 </span>
<span>= [4x - (1/3)x^3] from 0 to 2 </span>
<span>= 8 - 8/3 - 0 </span>
<span>= 16/3 </span>
<span>so when y = b </span>
<span>x= √b </span>
<span>and we have the area as </span>
<span>∫(b - x^2) dx from 0 to √b </span>
<span>= [b x - (1/3)x^3] from 0 to √b </span>
<span>= b√b - (1/3)b√b - 0 </span>
<span>(2/3)b√b = 8/3 </span>
<span>b√b =4 </span>
<span>square both sides </span>
<span>b^3 = 16 </span>
<span>b = 16^(1/3) = 2 cuberoot(2) </span>
<span>or appr 2.52</span>
Answer:
The equations represent circles that result in the same graph.
Step-by-step explanation:
we have

Divide by -10 both sides
-----> equation A
This is the equation of a circle centered at origin with radius 
and
Divide by 5 both sides
-----> equation B
This is the equation of a circle centered at origin with radius 
equation A and equation B are equal
therefore
The system has infinite solutions, because the equations represent circles that result in the same graph.
Parallel lines need the same slope, and for y = 1/2x + 4, it is 1/2.
Let's solve for b.
2 = 1/2(-6) + b
2 = -3 + b
Add 3 on both sides.
5 = b
y = 1/2x + 5
We want to know how many 1/8's are in 3/4, so we divide.

Flip the 2nd fraction and multiply:

Multiply the numerators and denominators together:

Divide:
<span>First, subtract 132 from 145, then divide 145 by that answer (13) and you will get : 11.1538461538</span>