Find the volume of the solid in the first octant bounded by the parabolic cylinder z = 4 − x2 and the plane y = 2.

We use triple integration to find volume of solid.

Volume of the solid in the first octant is 32/ 3

To solve this, it is important to set up the boundaries of double integral correctly.

First, notice that the cylinder we are given intersects the XY plane at the line given by the equation x = 2

Hence our boundaries of the integral with respect to x is the segment [0,2]. Since the other plane is y=2 . so,  boundaries of the integral with respect to y is the segment [0,2].

Now , integrate that

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i believe your answer is 99.7% of 7-year-old children are between 46.6 inches and 49.5 inches tall.

this is the formula: v = the value of investment at the end of the time period

p = the principal amount (the initial amount invested)

r = the annual interest rate

n = the annual frequency of compounding (how many times a year interest is added)

t = the number of years the money is invested

^ means raise to the power of