An orange cone has a exact volume of 120π ft³. What is the height of the cone if the radius is 6ft?
1 answer:
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Answer:
Length = 6
Width = 3/2
Step-by-step explanation:
You can choose to go about this question in lots of different ways, but this is how i did it. I drew a diagram of the rectangle and labeled it: the height/length as x and the width as x/4 (they told us the width is a quarter of the length). They also told us that the area is 9 square units.
We know that length x width = area
So: length x width = 9
I'm gonna bring in the variables i used in the diagram, so:
x
= 9
Keep solving:
= 9
Times both sides by 4:
= 36
Square root both sides for x:
<em>* remember that when you square root, its possible to have a positive or negative version of the value</em>
x = ±6
Since its impossible to have a negative length, we can say that x = 6.
X was just the variable we gave to the length of the rectangle, so now we know the length is 6. If you needed to find width as well, you can do 6/4, which simplifies to 3/2.
To double-check
- 6 x 3/2 should equal 9, since length x width = area
which it is, so we're correct!
Hope that helped : )
<u>ANSWER</u>
The zeros are
EXPLANATION
Given;
.
We can rewrite the function as
The zeros are found by equating the function to zero.
The multiplicity is 1, since it is odd the graph crosses at this intercept. which is
Or
The multiplicity is 1, since it is odd the graph crosses at this intercept. which is
Or
This last root has a multiplicity of 2.
That is
repeats two times.
Since the multiplicity is even, the graph touches the x-axis at the point .
See graph.
