Answer:
see explanation
Step-by-step explanation:
Given A is directly proportional to r² then the equation relating them is
A = kr² ← k is the constant of proportion
To find k use the condition when r = 5, A = 75 , then
75 = k × 5² = 25k ( divide both sides by 25 )
3 = k
A = 3r² ← equation of proportion
(a)
when r = 4, then
A = 3 × 4² = 3 × 16 = 48
(b)
when A = 147 , then
147 = 3r² ( divide both sides by 3 )
49 = r² ( take the square root of both sides )
r =
= 7
Method OneYour calculator might be able to do this. Mine does it like this.
6
nCr
2
=
15
Method 2You could simply set up 6C2
This gives you
Method ThreeYou only have to do this a couple of times to see how the cancellation works.

After all the cancellation takes place you have
6*5/2 = 15
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Answer:
The horizontal distance from the center is 49.3883 feet
Step-by-step explanation:
The equation of an ellipse is equal to:

Where a is the half of the wide, b is the high of the ellipse, x is the horizontal distance from the center and y is the height of the ellipse at that distance.
Then, replacing a by 106/2 and b by 33.9, we get:

Therefore, the horizontal distances from the center of the arch where the height is equal to 12.3 feet is calculated replacing y by 12.3 and solving for x as:

So, the horizontal distance from the center is 49.3883 feet
Answer:
I haven't done expressions in a while but I say the safest bet would be D.