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2 years ago

13

If the ratio of the edges of two cubes is 3:2, what is the ratio of the volume of the larger cube to the volume of the smaller o

ne?

1 answer:

natulia [17]2 years ago

6 0

Answer:

81 : 8

Step-by-step explanation:

Cube 1 has side lengths of 3, so it's volume is 3³ = 81

Cube 2 has side lengths of 2, so it's volume is 2³ = 8

So the ration of volume of the larger cube to the smaller cube is 81 : 8

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An oil refinery is located on the north bank of a straight river that is 2 km wide. A pipeline is to be constructed from the ref

hichkok12 [17]

Answer:

P is exactly 3km east from the oil refinery.

Step-by-step explanation:

Let's d be the distance in km from the oil refinery to point P. So the horizontal distance from P to the storage is 3 - d and the vertical distance is 2. Hence the diagonal distance is:

$\sqrt{(3 - d)^2 + 2^2} = \sqrt{(3 - d)^2 + 4}$

So the cost of laying pipe under water with this distance is

$800000\sqrt{(3 - d)^2 + 4}$

And the cost of laying pipe over land from the refinery to point P is 400000d. Hence the total cost:

$800000\sqrt{(3 - d)^2 + 4} + 400000d$

We can find the minimum value of this by taking the 1st derivative and set it to 0

$800000\frac{2*0.5*(3-d)(-1)}{\sqrt{(3 - d)^2 + 4}} + 400000 = 0$

We can move the first term over to the right hand side and divide both sides by 400000

$1 = 2\frac{3 - d}{\sqrt{(3 - d)^2 + 4}}$

$\sqrt{(3 - d)^2 + 4} = 6 - 2d$

From here we can square up both sides

$(3 - d)^2 + 4 = (6 - 2d)^2$

$9 - 6d + d^2 + 4 = 36 - 24d + 4d^2$

$3d^2-18d+27 = 0$

$d^2 - 6d + 9 = 0$

$(d - 3)^2 = 0$

$d -3 = 0$

d = 3

So the cost of pipeline is minimum when P is exactly 3km east from the oil refinery.

3 0

2 years ago

an equilateral triangle has a perimeter of 8 3/4cm. what is the side length of the triangl? show your work please

Elina [12.6K]

Equilateral = all sides are same

side length = 8 3/4 ÷ 3
= 35/4 ÷ 3
= 35/4 × 1/3
= 35/12

3 0

2 years ago

Landon is going to invest in an account paying an interest rate of 4.3%

andrezito [222]

Answer:

$6,100

Step-by-step explanation:

So to solve this problem, let's give the amount of money the variable "x". We just need to do x - 0.043 × x. Then we replace x with our answer and repeat the process 13 more times.

7 0

2 years ago

Read 2 more answers

PLEASE HELP TIMED

ivolga24 [154]

Answer:

D. 1, 5, 7, 9, 11, 14, 16

Step-by-step explanation:

Your welcome ;)

6 0

2 years ago

A cars gas mileage refers to its rate in miles traveled per gallon of gas. Kara's family is thinking about renting a camper that

kifflom [539]

Answer: 10 ¹/₂ miles per gallon

Step-by-step explanation:

The gas mileage of the camper refers to the distance (in miles for this question) that the camper can travel on 1 gallon of gas.

The camper can travel 3¹/₂ miles on ¹/₃ gallons so the mileage is:

= Distance traveled/ Gallons used

= 3¹/₂ ÷ ¹/₃

= 7/2 * 3/1

= 21 / 2

= 10 ¹/₂ miles per gallon

8 0

2 years ago