Answer:
4/9
Step-by-step explanation:
The scale factor for the linear dimensions of the ball bearings will be the cube root of the volume scale factor:
k = ∛(1.6/5.4) = 2/3
Then the scale factor for the areas will be the square of this scale factor:
ratio of surface area = (2/3)² = 4/9
_____
The area is the product of two linear dimensions, so its scale factor is the product of the linear dimension scale factors. That is, the scale factor for area is the square of the linear dimension scale factor.
Similarly, volume is the product of three linear dimensions, so its scale factor is the cube of the linear dimension scale factor.
Answer: Absolute minimum: f(-1) = -2
Absolute maximum: f(
) = 12.5
Step-by-step explanation: To determine minimum and maximum values in a function, take the first derivative of it and then calculate the points this new function equals 0:
f(t) = 
f'(t) = 
f'(t) = 
f'(t) = 
= 0
For this function to be zero, only denominator must be zero:
t = ±
≠ 0
t = ± 5
Now, evaluate critical points in the given interval.
t = 
and t = - 5 don't exist in the given interval, so their f(x) don't count.
f(t) =
f(-1) = 
f(-1) = 
f(-1) = 
f() = 
f() = 12.5
f(5) = 
f(5) = 0
Therefore, absolute maximum is f() = 12.5 and absolute minimum is
f(-1) = .
Considering the scatter plot, the function that best fits the data is given by:
f(x) = 3x².
<h3>What is the function that best fits the data?</h3>
To find the function that best fits the data, we have to look at the scatter plot, which gives a series of points (x,y).
We have that:
- When x increases, y also increases, hence the function is increasing, which removes the option f(x) = -3x.
- The increase looks "faster" than a linear increase, hence a quadratic model should be used, thus removing option f(x) = 3x.
Hence the function that best fits the data is given by:
f(x) = 3x².
More can be learned about scatter plots at brainly.com/question/22968877
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