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.

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 global maximum and minimum of the function f(x) = x^3 - 4x^2 + 5x - 2 on the interval [-2, 3]?

What is the value of x in the equation 2x - 5 = 13?

What is the standard deviation for a data set with values 5, 10, 15, and 20?

New questions in Mathematics

Solution of the equation y'' - y' -6y = 0

Let the vectors be u=(-1,0,2) , v=(0,2,-3) , w=(2,2,3) Calculate the following expressions a)<u,w> b) <2u- 5v,3w>

A circle with a 12-inch diameter is folded in half and then folded in half again. What is the area of the resulting shape?

two particles start at the origin and move along the x axis. for 0 <= t <= 10, their respective position functions are given by x1 = cos(t) and x2 = (e^-3t) + 1. for how many values of t do the particles have the same velocity?

You have been hired to estimate the average weight of quarters in circulation. Based on the sample of quarters you collect (below), create a 90% confidence interval for the weight of quarters in circulation. Quarter Weights (grams) 5.631 5.714 5.719 5.689 5.551 5.723 5.705 5.627 5.627 5.715 5.576 5.632 5.641 5.676 5.660 5.699 5.609 5.634 5.713 5.591 5.674 5.675 5.684 5.694 5.655 5.632 5.598 5.675 5.628 5.562 5.636 5.583 5.567 5.551 5.649 5.708 5.696 5.614 5.637 5.601 5.628 5.711 5.566 5.653 5.653 5.597 5.687 5.717 5.678 5.654 5.556 5.707 5.563 5.628 5.679 5.714 5.555 5.719 5.634 5.647 5.717 5.612 5.705 5.657 5.670 5.607 5.687 5.666 5.612 5.718 5.714 5.713 5.663 5.641 5.589 5.656 5.712 5.639 5.577 5.580 5.674 5.636 5.625 5.597 5.616 5.591 5.616 5.700 5.706 5.695 5.562 5.699 5.607 5.573 5.659 5.632 5.654 5.568 5.628 5.687 5.605 5.689 5.687 5.554 5.618 5.701 5.681 5.645 5.714 5.665 5.661 5.634 5.714 5.586 5.656 5.673 5.657 5.717 5.611 5.578 5.579 5.614 5.644 5.724 5.647 5.566 5.697 5.558 5.586 5.586 5.611 5.573 5.573 5.709 5.629 5.649 5.552 5.615 5.645 5.611 5.686 5.588 5.641 5.704 5.703 5.696 5.557 5.551 5.725 5.608 5.725 5.603 5.677 5.638 5.573 5.640 5.561 5.631 5.563 5.671 5.662 5.569 5.648 5.680 5.681 5.551 5.555 5.578 5.701 5.645 5.670 5.574 5.594 5.705 5.633 5.719 5.680 5.647 5.641 5.553 5.616 5.698 5.552 5.566 5.559 5.697 5.686 5.560 5.629 5.701 5.622 5.615 5.553 5.608 5.637 5.663 5.696 5.714 5.675 5.613 5.594 5.669 5.569 5.716 5.705 5.603 5.709 5.717 5.606 5.581 5.575 5.601 5.600 5.664 5.715 5.705 5.583 5.586 5.592 5.550 5.628 5.662 5.603 5.559 5.676 5.558 5.678 5.671 5.642 5.581 5.568 5.706 5.665 5.712 5.574 5.602 5.699 5.716 5.693 5.711 5.635 5.612 BLANK #1: Is this a question involving mean or proportion? ***ANSWER "MEAN" OR "PROPORTION" (WITHOUT THE QUOTATION MARKS)*** BLANK #2: What is the LOW end of the estimate ***ANSWER TO 3 DECIMALS*** BLANK #3: What is the HIGH end of the estimate ***ANSWER TO 3 DECIMALS***

Estimate the fifth term if the first term is 8 and the common ratio is -1/2