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Mazyrski [523]
3 years ago
11

A conical container can hold 120π cubic centimeters of water. The diameter of the base of the container is 12 centimeters.

Mathematics
1 answer:
timofeeve [1]3 years ago
3 0

Answer:

cone volume=(1/3)hpir^2

d/2=r

d=12

d/2=12/2=6=r

V=120pi

120pi=(1/3)hpi6^2

120pi=(1/3)hpi36

120pi=12hpi

divide both sides by pi

120=12h

divide 12

10=h cm

if height and diameter is doubled aka height and radius are doubled

V=(1/3)(2h)pi(2r^2)

we want to see how it compares to V=(1/3)hpir^2

V=(1/3)(2h)pi(2r^2)

V=2(1/3)(h)pi4r^2

V=8((1/3)hpir^2)

the volume is increased by 8 times

blanks are

10

8

Step-by-step explanation:

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Answer:

1) The linear equation in point and slope form is y - 67 = -4 × (x - 14)

2) The variables are;

a) The number of candies available = y

b) The number of days Jennifer eats the candies =

c) The slope, m = -4

3) Jennifer received 123 pieces of candies on Halloween

Step-by-step explanation:

The given parameters are;

The number of candies Jennifer eats everyday = 4 pieces

The number of days for which Jennifer eats the daily 4 candies = 14

The number of candies left at the end of the 14th day = 67 candies

1) We note that the rate of decrease in the number of candies = 4 candies/day

Therefore, the slope of the linear equation is m = -4

The y-intercept = The initial amount of candies Jennifer has = c = 67 + 14× 4 = 123 candies

The linear equation in point and slope form is given as follows;

y - 67 = -4 × (x - 14)

2) The variables are;

a) The y-value represents the number of candies available on a specific day

b) The x value represents the number of days Jennifer eats the candies'

c) The slope = The rate of decrease in the number of candies per day = -4

3) The number of candies Jennifer receives on Halloween is given by the y-intercept of the straight line equation as follows;

y - 67 = -4 × (x - 14)

y - 67 = -4·x + 56

y = -4·x + 56 + 67 = -4·x + 123

y = -4·x + 123

Comparing the above equation, with the general form of the straight line equation, y = m·x + c, where, the constant term, c = The y-intercept, we have;

The y-intercept of the equation y = -4·x + 123 = 123 = The initial amount of candies Jennifer received on Halloween.

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