Problem 1
Answer: Choice A
[tex]f(n) = 59,000\left(1.08^{n-1}\right)[/tex]
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Explanation:
The right hand side for choice A is in the form [tex]a(r)^{n-1}[/tex] which is the nth term of a geometric sequence.
- a = first term = 59,000 = starting salary
- r = common ratio = 1.08 = tells us how the salary increases year to year
The 1.08 represents an increase of 8% because,
1.08 = 1 + 0.08 = 100% + 8% = 108%
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Problem 2
Answer: Choice C
[tex]\frac{(y-60)^2}{144} + \frac{x^2}{100} = 1[/tex]
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Explanation:
The ellipse is 20 inches wide, which cuts in half to 10 inches. This is the corresponding value plugged into the denominator of the 'x' fraction, as x deals with the horizontal component. So we'll have a^2 = 10^2 = 100 in the denominator under the x term. Only choice C has this, so this is the answer we go for. For the vertical component, we cut 24 in half to get 12, then square it to get 144, which explains the denominator for the y term.
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Problem 3
Answer: Choice C
30 feet; major axis
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Explanation:
Pick the larger denominator 225. Apply the square root to get 15. Then double this value to land on 30. This is the length of the major axis which is the longer axis through the center of the ellipse. The major axis also passes through both foci.
Let's say points P and Q are any two random points on the ellipse. The longest segment PQ can get is 30 feet.
