As sum of money double in 20 years on simple interest . It will triple at the same rate in

A conical pile of road salt has a diameter of 112 feet and a slant height of 65 feet. After a storm, the linear dimensions of th

QveST [7]

we know that

the volume of a cone is equal to

$V= \frac{1}{3} \pi r^{2}h$

in this problem

the radius is equal to

$r= \frac{112}{2}= 56ft$

1) Find the height of the cone before the storm

Applying the Pythagorean Theorem find the height

$h^{2} = l^{2}-r^{2}$

$l=65 ft$

$h^{2} = 65^{2}-56^{2}$

$h^{2} = 1,089$

$h=33 ft$

2) Find the volume before the storm

$V= \frac{1}{3}*\pi* 56^{2}*33$

$V=34,496\pi\ ft^{3}$

3) Find the volume after the storm

After a storm, the linear dimensions of the pile are 1/3 of the original dimensions

so

r=(56/3) ft

h=(33/3)=11 ft

$V= \frac{1}{3}*\pi* (56/3)^{2}*11$

$V= 1,277.63\pi\ ft^{3}$

4) Find how this change affect the volume of the pile

Divide the volume after the storm by the volume before the storm

$\frac{1,277.63 \pi }{34,496 \pi } = \frac{1}{27}$

therefore

the answer part a) is

The volume of the pile after the storm is $\frac{1}{27}$ times the original volume

Part b) Estimate the number of lane miles that were covered with salt

5) Find the amount of salt that was used during the storm

$=34,496 \pi - 1,277.63 \pi \\= 33.218.37 \pi \\= 104,358.59\ ft^{3}$

6) Find the pounds of road salt used

$104,358.59*80=8,348,687.2\ pounds$

7) Find the number of lane miles that were covered with salt

$8,348,687.2/350=23,853.39 \ lane\ miles$

therefore

the answer part b) is

the number of lane miles that were covered with salt is $23,853.39 \ lane\ miles$

Part c) How many lane miles can be covered with the remaining salt? Round your answer to the nearest lane mile

the remaining salt is equal to $1,277.63\pi\ ft^{3}$

$1,277.63\pi\ ft^{3}=4,013.79\ ft^{3}$

8) Find the pounds of road salt

$4,013.79*80=321,103.20\ pounds$

9) Find the number of lane miles

$321,103.20/350=917.44 \ lane\ miles$

therefore

the answer part c) is

the number of lane miles is $917 \ lane\ miles$

7 0

4 years ago

Which of the following mathematical statements contains a quotient? A. 7 + 6 = 13 B. 7 × 6 = 42 C. 7 − 6 = 1 D. 42 ÷ 6 = 7

Black_prince [1.1K]

B: 7 x 6 = 42 and the only reason that B is the answer is because a quotient is the word used for a answer when you multiply c:

7 0

3 years ago

Read 2 more answers

For each exponential model indicate if the function represents growth or Decay, then identify initial value, growth/Decay factor

Dennis_Churaev [7]

Answer:

(g/d, initial, factor, rate)
(g, 45, 1.05, 5%)
(d, 50, 0.70, -30%)
(g, 90, 1.42, 42%)
(d, 120, 0.45, -55%)

Step-by-step explanation:

Exponential functions all have the form ...

f(x) = (initial value)(growth factor)^x

where (growth factor) is defined as ...

(growth factor) = (1 + growth rate) ⇒ growth rate = growth factor - 1

__

If the growth rate is negative (growth factor is less than 1), then it is decay, rather than growth. Growth rate is often expressed as a percentage. A growth rate of a negative amount may be reported as a decay rate of a positive amount. (Above, we have kept the decay rates negative to reinforce the fact that they are decay. Your grader may expect these values to be positive.)

_____

So, to fill in the table, compare the given functions to the form above. The results are listed in the answer section above.

4 0

4 years ago

If 2/3n = -6, then 1/3n =

Margarita [4]

Then 1/3 equals -3 because half of 2 is one

3 0

3 years ago

Find the difference and reduce to lowest terms: 3/7 - 2/1 =

kherson [118]

Answer:

0.43 - 2 = -1.57

Step-by-step explanation:

You can divide 3 by 7 and get 0.43. Then you can do 0.43 - 2 which equals -1.57

5 0

3 years ago

Read 2 more answers