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M(t) models the distance (in millions of km ) from Mars to the Sun t days after it's at its furthest point. M(t)=21 cos((2pi)/(687)t)+228 What does the solution set for 240=21 cos((2pi)/(687)t)+228 represent? Choose 1 answer: (A) The farthest distance, in millions of kilometers, that Mars reaches from the sun (B) The least number of days after when Mars is at its furthest point when it is 240 million kilometers from the sun (c) The distance, in millions of kilometers, that Mars is from the sun after 240 days

M(t) M(t) models the distance (in millions of km \mathrm{km} ) from Mars to the Sun t t days after it's at its furthest point.\newlineM(t)=21cos⁡(2π687t)+228 M(t)=21 \cos \left(\frac{2 \pi}{687} t\right)+228 \newlineWhat does the solution set for 240=21cos⁡(2π687t)+228 240=21 \cos \left(\frac{2 \pi}{687} t\right)+228 represent?\newlineChoose 11 answer:\newline(A) The farthest distance, in millions of kilometers, that Mars reaches from the sun\newline(B) The least number of days after when Mars is at its furthest point when it is 240240 million kilometers from the sun\newline(C) The distance, in millions of kilometers, that Mars is from the sun after 240240 days

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Q. M(t) M(t) models the distance (in millions of km \mathrm{km} ) from Mars to the Sun t t days after it's at its furthest point.\newlineM(t)=21cos⁡(2π687t)+228 M(t)=21 \cos \left(\frac{2 \pi}{687} t\right)+228 \newlineWhat does the solution set for 240=21cos⁡(2π687t)+228 240=21 \cos \left(\frac{2 \pi}{687} t\right)+228 represent?\newlineChoose 11 answer:\newline(A) The farthest distance, in millions of kilometers, that Mars reaches from the sun\newline(B) The least number of days after when Mars is at its furthest point when it is 240240 million kilometers from the sun\newline(C) The distance, in millions of kilometers, that Mars is from the sun after 240240 days
  1. Understanding the equation: Understand the given equation.\newlineThe equation M(t)=21cos⁡(2π687t)+228M(t) = 21 \cos\left(\frac{2\pi}{687}t\right) + 228 models the distance from Mars to the Sun in millions of kilometers as a function of time in days, where tt is the number of days after Mars is at its furthest point from the Sun.
  2. Setting up the equation: Set up the equation to find the solution set for when Mars is 240240 million kilometers from the Sun.\newlineWe need to solve the equation 240=21cos⁡(2π687t)+228240 = 21 \cos\left(\frac{2\pi}{687}t\right) + 228 for tt.
  3. Isolating the cosine term: Isolate the cosine term.\newlineSubtract 228228 from both sides of the equation to get:\newline240−228=21cos⁡(2π687t)240 - 228 = 21 \cos\left(\frac{2\pi}{687}t\right)\newline12=21cos⁡(2π687t)12 = 21 \cos\left(\frac{2\pi}{687}t\right)
  4. Solving for the cosine term: Divide both sides by 2121 to solve for the cosine term.\newline1221=cos⁡(2π687t)\frac{12}{21} = \cos\left(\frac{2\pi}{687}t\right)\newline47=cos⁡(2π687t)\frac{4}{7} = \cos\left(\frac{2\pi}{687}t\right)
  5. Finding the value of t t : Solve for t t .\newlineWe need to find the value of t t that satisfies the equation 47=cos⁡(2π687t) \frac{4}{7} = \cos\left(\frac{2\pi}{687}t\right) . This will give us the number of days after Mars is at its furthest point when it is 240 240 million kilometers from the Sun.
  6. Interpreting the solution set: Interpret the solution set.\newlineThe solution set for the equation represents the times (in days) when Mars is exactly 240240 million kilometers from the Sun. It does not represent the farthest distance Mars reaches from the Sun, nor does it represent the distance Mars is from the Sun after 240240 days. Therefore, the correct interpretation is:\newline(B) The least number of days after when Mars is at its furthest point when it is 240240 million kilometers from the sun.

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