Answer:
<u><em>y = -190 cos(π t / 120) + 195</em></u>
Step-by-step explanation:
<em>General form of a sinusoidal function: y = A cos(Bt - C) + D
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<em>Now generally a cosine function starts at the maximum value, so to start at the minimum value, flip the cosine function by making it negative.
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<em>A is the amplitude of the curve and will be the radius of the ferris wheel. Therefore, A = 380 / 2 = 190 feet.
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2π / B is the period of the curve and will be the time to complete one full rotation. The time to complete one full rotation is given as 4 minutes. Convert this into seconds to get period = 4 minutes * (60 seconds / minute) = 240 seconds. Therefore, B = 2π / period = 2π / 240 seconds = π / 120.
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C/B is the phase shift, or horizontal shift of the graph. Since the negative cosine function already starts at the minimum value, there is no phase shift so C/B = 0, meaning C = 0.
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D is the vertical shift and will be the height of the center of the ferris wheel. Therefore, D = 195 feet.
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Your final function will be:</em>
<u><em>y = -190 cos(π t / 120) + 195</em></u>
Answer:
1.46666666667
Step-by-step explanation:
calculator
1. By the chain rule,
I'm going to switch up the notation to save space, so for example, 
is shorthand for 
.
We have
Similarly,
where
To capture all the partial derivatives of 
, compute its gradient:
2. The problem is asking for and 
. But 
is already a function of 
, so the chain rule isn't needed here. I suspect it's supposed to say "find 
and 
" instead.
If that's the case, then
as the hint suggests. We have
Putting everything together, we get
Closing parenthesis is misplaced. Should be:
<span>A = h(b₁ + b₂)/2 </span>
<span>h = 75 ft </span>
<span>b₁ = 125 ft </span>
<span>b₂ = 81 ft </span>
<span>Then it's just plug & grind: </span>
<span>A = 75(125 + 81)/2 ft² = 75·206/2 ft² = 75·103 ft² = (7500 + 225) ft² = 7725 ft² </span>
<span>If you follow that, it will guide you through any other, similar p</span>
Answer:
266
Step-by-step explanation:
if a 45 minute workout is 1000 calories, at the same rate, a 12 minute workout would be 266 calories and 2 thirds. 
x 1000 = 266
