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3 years ago

The volume of a sphere is 36π in³. What is the radius of the sphere?

Mathematics

2 answers:

Inessa05 [86]3 years ago

7 0

36pi = 4/3 * pi * r^3
27 = r^3
r = 3 in

vlada-n [284]3 years ago

3 0

The equation for volume of a sphere is (4/3)πr^3, and you want to solve for r, so:
(4/3)πr^3 = 36π
÷ 4/3
πr^3 = 27π
÷ π
r^3 = 27
(cube root)
r = 3

So the radius is 3, I hope this helps!

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An explosion causes debris to rise vertically with an initial speed of 120 feet per second. The formula h equals negative 16 t s

Novay_Z [31]

Answer:

The debris will be at a height of 56 ft when time is <u>0.5 s and 7 s.</u>

Step-by-step explanation:

Given:

Initial speed of debris is, $s=120\ ft/s$

The height 'h' of the debris above the ground is given as:

$h(t)=-16t^2+120t$

As per question, $h(t)=56\ ft$ . Therefore,

$56=-16t^2+120t$

Rewriting the above equation into a standard quadratic equation and solving for 't', we get:

$-16t^2+120t-56=0\\\textrm{Dividing by -8 throughout, we get}\\\frac{-16}{-8}t^2+\frac{120}{-8}t-\frac{56}{-8}=0\\2t^2-15t+7=0$

Using quadratic formula to solve for 't', we get:

$t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\t=\frac{-(-15)\pm \sqrt{(-15)^2-4(2)(7)}}{2(2)}\\\\t=\frac{15\pm \sqrt{225-56}}{4}\\\\t=\frac{15\pm\sqrt{169}}{4}\\\\t=\frac{15\pm 13}{4}\\\\t=\frac{15-13}{4}\ or\ t=\frac{15+13}{4}\\\\t=\frac{2}{4}\ or\ t=\frac{28}{4}\\\\t=0.5\ s\ or\ t=7\ s$

Therefore, the debris will reach a height of 56 ft twice.

When time $t=0.5\ s$ during the upward journey, the debris is at height of 56 ft.

Again after reaching maximum height, the debris falls back and at $t=7\ s$ , the height is 56 ft.

5 0

3 years ago

1.6 - 1.3 mathematics

elena-14-01-66 [18.8K]

Answer: 0.3 :) :) :) :)

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3 years ago

Find the equation of a line parallel to y=-10x-5 passing through the coordinate (-3,5)

Allushta [10]

With a given parallel line and a given point on the line
we can use the point-line method: y-y0=m(x-x0)
where
y=mx+k is the given line, and
(x0,y0) is the given point.

Here
m=-10, k=-5, (x0,y0)=(-3,5)

=> the required line L is given by:
L: y-5=-10(x-(-3))

on simplification
L: y=-10x-30+5
L: y=-10x-25

4 0

3 years ago

Lorinda can walk 1.8 miles in 30 minutes. Which proportion can be used to find how many miles she can walk in 45 minutes?

KonstantinChe [14]

Maybe this is the answer 1.8/30 = x/45

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3 years ago

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I am stuck on |x+3|<5. Can someone help?

NeTakaya

the answer would be -8<x<2

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3 years ago