A cube of ice is melting and the volume is decreasing at a rate of 3 cubic m/s. How fast is the height decreasing when the cube is 6 inches in height?
By signing up, you agree to our Terms of Service and Privacy Policy
To find the rate at which the height is decreasing when the cube is 6 inches in height, you can use related rates. Since the cube is melting, its volume is decreasing at a rate of 3 cubic meters per second. Let ( V ) represent the volume of the cube and ( h ) represent its height. The volume of a cube is given by ( V = h^3 ). Differentiating both sides with respect to time ( t ), we get ( \frac{dV}{dt} = 3h^2 \frac{dh}{dt} ). Given that ( \frac{dV}{dt} = -3 ) (negative because the volume is decreasing) and when ( h = 6 ), you can solve for ( \frac{dh}{dt} ). Plugging in the values, you'll get ( \frac{dh}{dt} = -\frac{1}{4} ) meters per second.
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.
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.
- How do you find the linear approximation of #g(x)=sqrt(1+x)#?
- How do you estimate #(26.8)^(2/3)# using linear approximation?
- If a ball is thrown vertically upward from the ground with an initial velocity of 56 feet per second, for how long will the ball be going upward?
- How do you use linear approximation to the square root function to estimate square roots #sqrt 3.60#?
- How can I solve the mentioned problem?Please,help.

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