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2 years ago

For 15, the answer is b correct?

Mathematics

2 answers:

den301095 [7]2 years ago

7 0

Answer:

a. C = (0,0), r = 3

Step-by-step explanation:

No, the 9 is squared. The square root of 9 is ±3. Therefore, the only possible answer is a.

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vaieri [72.5K]2 years ago

5 0

Answer:

a C= (0, 0), r = 3

Step-by-step explanation:

For 15th question: a Is the correct answer

${x}^{2} + {y}^{2} = 9 \\ {(x - 0)}^{2} + {(y - 0)}^{2} = {3}^{2} \\ equating \: it \: with \\ {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} \\h = 0 \\ k = 0 \\c = (h, \: \: k) \\ c= (0, \: \: 0) \\ {r}^{2} = {3}^{2} \\ r = 3$

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Answer:

See below for answers and explanations (along with a graph attached)

Step-by-step explanation:

Part A

The amplitude of a sinusoidal function is half the distance between the maximum and the minimum. It is given to us that the distance from the highest and lowest point is 6 feet, so our amplitude is 6/2 = 3 feet

Part B

The graph's function would be in the form of $y=acos(bx+c)+d$ where $a$ is the amplitude, $\frac{2\pi}{b}$ is the period, $-\frac{c}{b}$ is the phase/horizontal shift, and $d$ is the average/midline.

We already know our amplitude of $a=3$ from part A.

Since our period is given to us as 26 seconds, then we can use the equation $\frac{2\pi}{b}=26$ to find $b$ , which happens to be $b=\frac{\pi}{13}$ .

Since the cosine function starts at its maximum and we want it to start at the average where the bottle travels up, we would need to use the cofunction identity $sin(x)=cos(x-\frac{\pi}{2})$ which shifts the cosine graph $\frac{\pi}{2}$ units to the right. This means that $c=-\frac{\pi}{2}$ , making our phase shift $-\frac{c}{b}=-\frac{-\frac{\pi}{2}}{\frac{\pi}{13}}=6.5$ , or 6.5 feet to the right

Our average/midline would be $d=12$ as given as the average height by the problem.

Therefore, the function is $f(x)=3cos(\frac{\pi}{13}x-\frac{\pi}{2})+12$

Part C

Using our determined function from Part B, by looking at its graph, we see that the bottle will reach its lowest height of 9 feet after 19.5 seconds (see attached graph).

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