We will have the following:
First, we can see that the volume of the sphere and the regular cone are given by:
And:
Now, since the volume of the cone is inscribed by a maximum stablished by the sphere, we know that the maximum height for the cone will be equal to the radius of the sphere, so, we re-write the volume of the cone:
i. Now, we determine the ratio of both volumes as follows:
[Cone to sphere]
So, the ratio of the volumes of the cone to the sphere will be of 1:4.
ii. And the expression in terms of r for the volume inside the sphere but outside the cone will be:
So, the expression is:
Answers:
Describing the Error:
Choice B) The function is nonlinear and the increase in y is not constant.
Correcting the Error:
As x increases by a constant amount, <u> y </u> needs to increase or decrease by <u>the same amount</u> for the function to be linear.
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Explanation:
Each time x goes up by 2, y is being multiplied by 4.
It may appear y is increasing at a constant rate, but this is not true. The jump from y = 4 to y = 16 is +12; while the jump from y = 16 to y = 64 is +48. The increase in y is not the same each time. This is just a rephrasing of what is discussed in the "correcting the error" section above.
So this is why the function is nonlinear. It turns out that this function is an exponential. Specifically, this is the function y = 2^x. For instance, if x = 8, then y = 2^x = 2^8 = 256. Graphing this function produces a curve that isn't a straight line, which is visual confirmation the function is nonlinear.
Answer:
20x + 2
Step-by-step explanation:
Using the quadratic formula the 2 zeros of the function (there have to be 2 cuz it's a quadratic) are x = -1/2 and -5 1/2
Answer:
y = -x -3
Step-by-step explanation:
The slope intercept form is
y = mx+b where m is the slope and b is the y intercept
3x+3y = -9
Subtract 3x from each side
3x-3x+3y = -3x-9
3y = -3x-9
Divide each side by 3
3y/3 = -3x/3 -9/3
y = -x -3