What is the extracts volume of the largest cone that can fit into a cube with edges of 10 inches
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Hi!
<u>Your answer is 52.</u>
To start off, let's start with some facts that will help us solve this:
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<u><em>Supplementary angles</em></u> are two angles whose angle measures add up to 180 degrees. You can know that they are supplementary because they can be connected by a straight line.
<u><em>Triangles (all of them)</em></u> have angles that add up to 180 degrees.
We can start by using supplementary angles to solve. See where the angle of 67 degrees is? The one to the right of it is supplementary to it since they are on a straight line. That means their sum adds up to 180 degrees:
That angle is 113 degrees.
Now, we have 2 out of 3 angles in the triangle. Since we know that triangles' angles add up to 180 degrees, we can make an equation:
Therefore, x is equal to 52.
We can start from the given line's coefficients and translate the line from the origin to the given point.
4(x -(-2)) -(y -3) = 0
4x +8 -y +3 = 0
The equation of the desired line is ...
4x -y = -11
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For standard form line ax+by=c, any parallel line will have only a different value of c. For c=0, the line goes through the origin (0, 0). To make it go through point (h, k) we can write it as
a(x-h) +b(y-k) = 0
which is completely equivalent to
ax +by = ah +bk
4(x -(-2)) -(y -3) = 0
4x +8 -y +3 = 0
The equation of the desired line is ...
4x -y = -11
_____
For standard form line ax+by=c, any parallel line will have only a different value of c. For c=0, the line goes through the origin (0, 0). To make it go through point (h, k) we can write it as
a(x-h) +b(y-k) = 0
which is completely equivalent to
ax +by = ah +bk