Find the number b such that the line y = b divides the region bounded by the curves y = x2 and y = 4 into two regions with equal area. give your answer correct to 3 decimal places.

  b = ∛16 ≈ 2.520

Step-by-step explanation:

The area bounded by y=x^2 and y=b is given by the integral ...

For b = 4,

  A(4) = (4/3)4^(3/2) = 32/3

We want to find b such that the area is half that, or ...

  A(b) = (1/2)(32/3) = 16/3

So, we're solving the equation ...

  16/3 = 4/3b^(3/2)

  4 = b^(3/2) . . . . . . . . . . . . . . multiply by 3/4

  4^(2/3) = b = ∛16 . . . . . . . . raise to the 3/2 power

1. x> -5

2. x< 8

step-by-step explanation:

1. 2x> -10

divide by 2 from both sides of equation.

2x/2> -10/2

simplify, to find the answer.

-10/2=-5

x> -5 is the correct answer.

2. 3x< 24

divide by 3 from both sides of equation.

3x/3< 24/3

simplify, to find the answer.

24/3=8

x< 8 is the correct answer.

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