A solid lies between planes perpendicular to the x-axis at xequals=0 and xequals=1212. The cross-sections perpendicular to the axis on the interval 0less than or equals≤xless than or equals≤1212 are squares with diagonals that run from the parabola y equals negative 2 StartRoot x EndRooty=−2x to the parabola y equals 2 StartRoot x EndRooty=2x. Find the volume of the solid.

Question:

A solid lies between planes perpendicular to the x-axis at x=0 and x=12. The cross-sections perpendicular to the axis on the interval 0≤x≤12 are squares with diagonals that run from the parabola y=-2√x to the parabola y=2√x. Find the volume of the solid.

576

Step-by-step explanation:

Given:

Length of diagonal square:

Here, the diagonal is the hypotenus of a right angle triangle, with leg S, where the square has a side of length S.

Using Pythagoras theorem:

Divide both sides by 2

Thus,

Area, A = S² = 8x

Take differential volume, dx =

dV = Axdx

dV = 8xdx

Where limit of solid= 0≤x≤12

Volume of solid, V:

V =∫₀¹² dV

V = 8 ∫₀¹² xdx

V = [4x²]₀¹²

V = 4 (12)²

V = 12 * 144

= 576

Volume of solid = 576

29 is the correct answer

step-by-step explanation:

42%

step-by-step explanation:

we know,

total people = 60

total males = 25

percentage of males

= 25/60 × 100

= 25/6 × 10

= 25/3 × 5

= 125 / 3

= 41.

rounding of = 42%

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