# Determine how fast the length of an edge of a cube is changing at the moment when the length of the edge is #5 cm# and the volume of the cube is decreasing at a rate of #100 (cm^3)/sec#?

By signing up, you agree to our Terms of Service and Privacy Policy

To determine how fast the length of an edge of a cube is changing when the length of the edge is 5 cm and the volume of the cube is decreasing at a rate of (100 , \text{cm}^3/\text{sec}), follow these steps:

- Given that the volume (V) of a cube is (V = s^3), where (s) is the length of one edge.
- Differentiate both sides of the volume formula with respect to time (t), using the chain rule: [\frac{dV}{dt} = \frac{d}{dt}(s^3)]
- Given that the volume is decreasing at a rate of (-100 , \text{cm}^3/\text{sec}), (\frac{dV}{dt} = -100 , \text{cm}^3/\text{sec}).
- To find (\frac{ds}{dt}), differentiate (s^3) with respect to (t) using the chain rule: [\frac{d}{dt}(s^3) = 3s^2 \frac{ds}{dt}]
- Substitute the given values and solve for (\frac{ds}{dt}): [-100 = 3(5^2)\frac{ds}{dt}] [-100 = 3(25)\frac{ds}{dt}] [-100 = 75\frac{ds}{dt}] [\frac{ds}{dt} = \frac{-100}{75} , \text{cm/sec}] [\frac{ds}{dt} = -\frac{4}{3} , \text{cm/sec}]
- So, the length of an edge of the cube is changing at a rate of (-\frac{4}{3} , \text{cm/sec}) when the length of the edge is (5 , \text{cm}) and the volume of the cube is decreasing at a rate of (100 , \text{cm}^3/\text{sec}).

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- Solve this problem? It's so hard for me
- A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola #y=6-x^2#. What are the dimensions of such a rectangle with the greatest possible area? thanks for any help!?
- How do you find the rate at which water is pumped into an inverted conical tank that has a height of 6m and a diameter of 4m if water is leaking out at the rate of #10,000(cm)^3/min# and the water level is rising #20 (cm)/min#?
- How do you minimize and maximize #f(x,y)=ye^(2x)-ln(y/x)# constrained to #0<xy-y+x<1#?
- Bases are located on the field 90 feet away from one another Jimmy is running at a speed of 10 ft/sec from second to third base. When Jimmy is halfway to third base, how quickly is the distance between him and home plate decreasing?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7