9514 1404 393
Answer:
8000π mm^3/s ≈ 25,133 mm^3/s
Step-by-step explanation:
The rate of change of volume is found by differentiating the volume formula with respect to time.
V = 4/3πr^3
V' = 4πr^2·r'
For the given numbers, this is ...
V' = 4π(20 mm)^2·(5 mm/s) = 8000π mm^3/s ≈ 25,133 mm^3/s
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<em>Additional comment</em>
By comparing the derivative to the area formula for a sphere, you see that the rate of change of volume is the product of the area and the rate of change of radius. This sort of relationship will be seen for a number of different shapes.
You would have open circles at 3 and 6.
x < 3 so the line will go from 3 to the left.
x > 6 so the line will go from 6 to the right.
Answer: stretched by a factor of 2 and translated 8 units right and 5 units down
Explanation:
These is the set of choices that accompany with this question:
<span>a) stretched by a factor of 2 and translated 64 units right and 5 units down
b) stretched by a factor of 8 and translated 8 units right and 5 units down
c) stretched by a factor of 2 and translated 8 units right and 5 units down
d) stretched by a factor of 8 and translated 64 units right and 5 units down
Solution:
</span>Let's work a little the given function to compare it with the parent function.
1) The given function is y = ∛[8x - 64] - 5
2) Extract common factor 8 of the expression inside the square brackets:
y = ∛[ 8( x - 8) ] - 5
3) Extract 8 from the root:
y = 2∛(x - 8) - 5
4) The parent function is ∛x. Call the parent function g(x) => g(x) = ∛x
5) Compare: y is 2 * g(x - 8) - 5
6) Analyze the meaning of that:
g(x - 8) means that the graph of the function is translated 8 units to the right
scaling by 2 means that the graph is stretch vertically (by a scale factor of 2)
- 5 means that the entire graph is shifted 5 units downward.
So, the description of the graph y = ∛(8x - 64) - 5 compared to the parent cube root function is: stretched by a factor of 2 and translated 8 units right and 5 units down
Answer:
17
Step-by-step explanation:
42+x=5x
-5 - 5
=17
