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3 years ago

The volume of the sphere is 500/3pi cubic units. What is the value of x

Mathematics

1 answer:

Sphinxa [80]3 years ago

5 0

Answer:

Step-by-step explanation:

Formula for the volume of a sphere is V = (4/3) (π) r³

3V 4²

and so the cube of the radius, "r," is r³ = ------------- * -----

4 4²

Taking the cube root of both sides, we get

∛[3V / 4²] 3V

and so the radius, "r," is r = ------------------ = ∛ ( --------- ) = (1/4)*∛(3*v)

∛[4³] 4³

Then

r = (1/4)*∛(3*V), after substituting 500/(3π) for V, becomes:

r = (1/4)*∛[ 3*500/3π ] = (1/4)*∛[ 500/π ]

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3 years ago

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A 3-gallon tub of ice cream yields about 90 scoops of ice cream. There are roughly 3785 cubic centimeters in 1 gallon. Determine

ASHA 777 [7]

Answer:

The radius of the scoop is r = 3.1 cm

Step-by-step explanation:

Since 3 gallons yields 90 scoops, and 1 gallon = 3785 cm³.

3 gallons = 3 × 3785 cm³ = 11355 cm³

So we have 11355 cm³ in 3 gallons which is also the volume of 90 scoops.

Since 90 scoops = 11355 cm³, then

1 scoop = 11355 cm³/90 = 126.2 cm³

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Substituting V = 126.2 cm³, we have

r = ∛(3× 126.2 cm³/4π)

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= 3.1 cm

So, the radius of the scoop is r = 3.1 cm

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3 years ago

What is the reason for each step in the solution of the equation?

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3 years ago

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The coordinates of AB are A(-5, -1) and B(-2, -6). If AC : CB = 3 : 7, what are the coordinates of point C?

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$\text{Let the coordinates of AB are }A(-5,-1), \text{ and }B(-2, -6)\\
\\
\text{let the coordinate of th point C be (x, y), such that}\\
\\
AC:CB=3:7\\
\\
\text{By the section formula, we know that if P(x,y) lies on a line segment AB}\\
\text{where, }A(x_1,y_1), \ B(x_2,y_2)\text{ and satisfy the ratio, }AP:PB=m:n, \text{ then}$

$P=\left ( \frac{mx_2+nx_1}{m+n}, \ \frac{my_2+ny_1}{m+n} \right ).\\
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\text{So using this formula, we get for the given problem}\\
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C=\left ( \frac{3(-2)+7(-5)}{3+7}, \ \frac{3(-6)+7(-1)}{3+7} \right )\\
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4 years ago

Debra has a job transporting soft drinks by truck. Her truck is filled with cans that weigh 14 ounces each and bottles that weig

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Answer:

14C + 70B

Step-by-step explanation:

Let us represent:

The number of cans = C

The number of bottles = B

Her truck is filled with cans that weigh 14 ounces each and bottles that weigh 70 ounces each. There is a combined total of 880 cans and bottles in her truck.

The expression for the combined total weight (in ounces) of the cans and bottles in her truck is given as

Total weight in out = 14 × C + 70 × B

= 14C + 70B

When:

C + B = 880

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