Marc solves the equation Latex: (\sqrt[4]{x})^3=5\textsf{.} His work is shown below. Step 1: Latex: (\sqrt[4]{x})^3=5
(
√
[
4
]
x
)
3
=
5

Step 2: Latex: x^{\frac{3}{4} }=5
x
3
4
=
5

Step 3: Latex: x^{\frac{3}{4} \cdot \frac{4}{3} }=5^{\frac{4}{3} }
x
3
4
⋅
4
3
=
5
4
3

Step 4: Latex: x=\sqrt[3]{5 \cdot 5 \cdot 5 \cdot 5}
x
=
√
[
3
]
5
⋅
5
⋅
5
⋅
5

Step 5: Latex: \require{cancel}x=5\sqrt[3]{\cancel {5} \cdot \cancel{5} \cdot \cancel{5} \cdot 5}

Step 6: Latex: x=5\sqrt[3]{5}
x
=
5
√
[
3
]
5

Explain what Marc did in steps 4 and 5.

Why did he do this?

Create your own radical equation and explain how to solve it.

Is there an extraneous solution to your equation?

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

10.416 meters per second

step-by-step explanation:

distance=1 00 meters

time= 9.6 seconds in decimal form or 9 3/5 as a mixed number

average speed= 100/9.6

=10.416 meters per second or 10 52/125 as a mixed number.