Answer:
Step-by-step explanation:
Water is being pumped into an inflated rubber sphere at a constant rate of 0.03 cubic meters per second.
So, dV/dt = 0.03.
We want to show that dS/dt is directly proportional to 1/r.
In other words, we want to establish the relationship that dS/dt = k(1/r), where k is some constant.
First, the volume of a sphere V is given by:
Therefore:
Next, the surface area of a sphere S is given by:
Therefore:
We can divide both sides by 2:
We can substitute this into dV/dt. Rewriting:
So:
Since dV/dt = 0.03 or 3/100:
Therefore:
Where k = 3/50.
And we have shown that dS/dt is directly proportional to 1/r.
9514 1404 393
Answer:
8√3 ≈ 13.86 ft
Step-by-step explanation:
The light source is usually placed at the focus, so the focus-vertex distance is p=3 ft. The equation for the parabola with its vertex at the origin is ...
y = 1/(4p)x^2
y = 1/12x^2
The opening for some y-value extends ±x from the axis of symmetry, so is a total of 2x in width.
For y=4, the corresponding value of x is ...
4 = 1/12x^2
48 = x^2
√48 = x = 4√3
Then the width of the searchlight opening is ...
2(4√3 ft) = 8√3 ft ≈ 13.86 ft
It should be 7.97 decigrams, since you want to convert 3 milligrams to decigrams (0.03), it is asking "How much more" which means you subtract. 8 subtracted from 0.03 is 7.97.
Hope this helps :)
The simplest form would be x
The rule for power to a power is 'keep the base and multiply the powers'.
3 * (1/3) = 1
So it would be x^1 or just x
Given a function in a table or in algebraic or graphical form, identify key features such as x- and y-intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; and end behavior. Use key features of an algebraic function to graph the function.
