So y=4x-5 so what would be the M= and the B=?
1 answer:
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Answer:
Part a) The equation for the volume of the film canister is
Part b) The radius of the film canister is
Step-by-step explanation:
<u><em>The complete question is</em></u>
A film canister in the shape of a cylinder has a height of 8 centimeters and a volume of 32π cubic centimeters.
a. Write an equation for the volume of the film canister.
b. What is the radius of the film canister?
Part a) Write an equation for the volume of the film canister
we know that
The volume of a cylinder is equal to
where
r is the radius of the circular base
h is the height of the cylinder
we have
substitute
----> equation for the volume of the film canister
Part b) What is the radius of the film canister?
we have
Simplify
Divide by 8π both sides
square root both sides
In the figure attached, red circle A and red point B are the circle and external point of interest. Note that we must know where the center of circle A is. If we don't know that, there are construction techniques for finding it, but that is beyond the scope of this answer.
Step 1. Set your compass to a radius greater than half the length of segment AB. Here, we have made the radius AD.
Step 2. Draw arcs above and below the center of segment AB centered at A and B using the radius of Step 1. Here the "arc" is shown a a full (green) circle. Only the points where the arcs intersect (E and F) are of interest, so it is not necessary to draw the full circle.
Step 3. Identify the points of interesection (E and F) of the arcs of Step 2, then draw a line segment between them. This segment (EF) is the perpendicular bisector of AB. Mark point G where it intersects segment AB. As with the green circles, it is not necessary to draw the whole line EF, since we are only interested in the location of the midpoint of AB, which is point G.
Step 4. Using G as the center, and GA or GB as the radius, draw semicircle AHB. The point of intersection H is the only part of that (blue) circle of interest, so it is not necessary to draw the whole thing.
Step 5. Finish the consruction by drawing tangent line BH.
Step 1. Set your compass to a radius greater than half the length of segment AB. Here, we have made the radius AD.
Step 2. Draw arcs above and below the center of segment AB centered at A and B using the radius of Step 1. Here the "arc" is shown a a full (green) circle. Only the points where the arcs intersect (E and F) are of interest, so it is not necessary to draw the full circle.
Step 3. Identify the points of interesection (E and F) of the arcs of Step 2, then draw a line segment between them. This segment (EF) is the perpendicular bisector of AB. Mark point G where it intersects segment AB. As with the green circles, it is not necessary to draw the whole line EF, since we are only interested in the location of the midpoint of AB, which is point G.
Step 4. Using G as the center, and GA or GB as the radius, draw semicircle AHB. The point of intersection H is the only part of that (blue) circle of interest, so it is not necessary to draw the whole thing.
Step 5. Finish the consruction by drawing tangent line BH.