Ted buys blocks
of spruce for 
dollars each, and 
blocks of mahogany for 
dollars each. In a given month, Ted spends a total of 
dollars, where 
. The price of a block of mahogany, given that a block of spruce costs 5/9 as much as a block of mahogany, and Ted has bought 12 blocks of spruce and 15 blocks of mahogany for a total cost of $9750. Write an equation whose solution is the given quantity.
1 answer:
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Answer:
OK, lets start by drawing a basic graph (the first one) so we can visualize.
We already know that the y coordinate of the circle's center is .
We know that the circle is tangent to the axis at
That means the x coordinate of the center has to be , as the tangent is a point on the edge of the circle that touches a line at exactly one point.
The radius is the distance from the center of the circle to its edge. We know the center's location now, it is and a point on the edge of the circle (the tangent point) which is
. so the distance between the points is 4 which is the radius (you can use the distance formula, but it's quite oblivious.)
We can imagine the circle should look like this (the second one):
Now we can piece together an equation
The equation of a circle is where
is the center and
is the radius. When we put the numbers in: we get
which can be simplified into
which is the answer.
Step-by-step explanation:
