The volume of a cube decreases at a rate of 10 m3/s. Find the rate at which the side of the cube changes when the side of the cube is 2 m.

Name: Solved: The volume of a cube decreases at a rate of 10 m3/s. Find the rate at which the side of the cube changes when the side of the cube is 2 m. - MathMaster
Brand: MathMaster
Rating: 4.9 (242 reviews)

242

likes

1208 views

Answer to a math question The volume of a cube decreases at a rate of 10 m3/s. Find the rate at which the side of the cube changes when the side of the cube is 2 m.

$Expert avatar$

Velda

4.5

110 Answers

Solution: The formula for the volume of a cube is given by V=s^3 Taking the derivative of the equation with respect to t, \frac{\differentialD V}{\differentialD t}=3s^2\frac{\differentialD s}{\differentialD t} \frac{\differentialD s}{\differentialD t}=\frac{\frac{\differentialD V}{\differentialD t}}{3s^2} Substituting values, \frac{\differentialD s}{\differentialD t}=\frac{10}{3\left(2\right)^2}

\frac{\differentialD s}{\differentialD t}=\frac{5}{6}\operatorname{m/s}

Frequently asked questions (FAQs)

What is the equation for finding the length of the altitude of an isosceles triangle with a base of 12 units and congruent sides measuring 9 units each?

In a right triangle with an angle of 30°, if the opposite side measures 10 units, what is the length of the hypotenuse?

What is the equation of the perpendicular bisector of a triangle's hypotenuse?

New questions in Mathematics

Calculate to represent the function whose graph is a line that passes through the points (1,2) and (−3,4). What is your slope?

A circular park has a diameter of 150ft. A circular fence is to be placed on the edge of this park. Calculate the cost of fencing this park if the rate charged is $7 per foot. Use π = 3.14.

10.Silvana must knit a blanket in 9 days. Knitting 8 hours a day, at the end of the fifth day, only 2/5 of the blanket was done. To be able to finish on time, how many hours will Silvana have to knit per day?

(x^2+3x)/(x^2-9)=

A hotel in the Algarve had to offer 1 week of vacation to one of its employees as an Easter gift in a random choice. It is known that 80 people work in this hotel unit, 41 of whom are Portuguese and 39 are foreign nationals. There are 14 Portuguese men and 23 foreign women. Using what you know about conditional probability, check the probability that the gift was offered to a Portuguese citizen, knowing that it was a woman.

The director of a company must transfer 6 people from the human resources department to the sales department, in order to sustain sales during the month of December. What is the probability that he will transfer only 2 of them?

2.3/-71.32

Let r: x - y 5 = 0. Determine a general equation of the line s parallel to the line r, which forms an isosceles triangle with area 8 with the line x = 5 and the Ox axis.

Find all real numbers x that satisfy the equation \sqrt{x^2-2}=\sqrt{3-x}