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rosijanka [135]

2 years ago

11

A recipe for sparkling grape juice calls for 1/2 quarts of sparkling water and 3/4 quarts of grape juice how much sparkling wate

r would you need to mix with 9 quarts of grape juice

1 answer:

dimaraw [331]2 years ago

6 0

Answer: 6

Step-by-step explanation:

3/4 x 12 =36/4

12 x 1/2=6

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A sphere and a cylinder have the same radius and height. The volume of the cylinder is 21m. what is the volume of the sphere.

Goshia [24]

Answer:

The volume of the sphere is 14m³

Step-by-step explanation:

Given

Volume of the cylinder = $21m^3$

Required

Volume of the sphere

Given that the volume of the cylinder is 21, the first step is to solve for the radius of the cylinder;

<em>Using the volume formula of a cylinder</em>

The formula goes thus

$V = \pi r^2h$

Substitute 21 for V; this gives

$21 = \pi r^2h$

Divide both sides by h

$\frac{21}{h} = \frac{\pi r^2h}{h}$

$\frac{21}{h} = \pi r^2$

The next step is to solve for the volume of the sphere using the following formula;

$V = \frac{4}{3}\pi r^3$

Divide both sides by r

$\frac{V}{r} = \frac{4}{3r}\pi r^3$

Expand Expression

$\frac{V}{r} = \frac{4}{3}\pi r^2$

Substitute $\frac{21}{h} = \pi r^2$

$\frac{V}{r} = \frac{4}{3} * \frac{21}{h}$

$\frac{V}{r} = \frac{84}{3h}$

$\frac{V}{r} = \frac{28}{h}$

Multiply both sided by r

$r * \frac{V}{r} = \frac{28}{h} * r$

$V = \frac{28r}{h}$ ------ equation 1

From the question, we were given that the height of the cylinder and the sphere have equal value;

This implies that the height of the cylinder equals the diameter of the sphere. In other words

$h = D$ , where D represents diameter of the sphere

Recall that $D = 2r$

So, $h = D = 2r$

$h = 2r$

Substitute 2r for h in equation 1

$V = \frac{28r}{2r}$

$V = \frac{28}{2}$

$V = 14$

Hence, the volume of the sphere is 14m³

4 0

3 years ago

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What is a equation for line with a slope o 2/3 and a y-intercept of (0,0)

Lerok [7]

Answer:

y= 2/3 x

Step-by-step explanation:

point slope form

y-y1 = m(x-x1)

y-0 = 2/3 (x-0)

y = 2/3(x)

y= 2/3 x

3 0

2 years ago

Write 31/11 as a decimal. If necessary, use a bar to indicate with digit or group of digits repeats

Andrews [41]

Answer:

2.81

Step-by-step explanation:

.81 has a bar over it.

5 0

2 years ago

Solve the inequality. -6b>42 or 4b>-4

goldfiish [28.3K]

- 6b > 42 or 4b > - 4
Divide by - 6. Divide by 4.
b < - 7 Or b > - 1

7 0

2 years ago

Find the surface area of the prism.

8_murik_8 [283]

Answer:

148^2

Step-by-step explanation:

2(lb+bh+lh) = 2(4*5+5*6+4*6)=148 in^2

6 0

2 years ago

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