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

step-by-step explanation:

20% of 120 is 24. if you subtract 24 from 120 you get 96

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.