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Evgen [1.6K]
2 years ago
5

I have a question that involves derivatives in the context of a triangle. Can someone confirm that the answer is 39/41?

Mathematics
1 answer:
astra-53 [7]2 years ago
5 0
X^2 + y^2 = z^2
d/dt[ x^2 + y^2 ] = d/dt[ z^2 ]
d/dt[ x^2 ] + d/dt[ y^2 ] = d/dt[ z^2 ]
2x*dx/dt + 2y*dy/dt = 2z*dz/dt
x*dx/dt + y*dy/dt = z*dz/dt
12*(3*dy/dt) + 5*dy/dt = z*1
12*(3*dy/dt) + 5*dy/dt = 13
12*(3*w) + 5*w = 13 ... letting w = dy/dt
36*w + 5*w = 13
41*w = 13
w = 13/41
dy/dt = 13/41
dx/dt = 3*(dy/dt)
dx/dt = 3*(13/41)
dx/dt = 39/41

You have the correct answer. Nice job.

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n T = 456 − 3 The equation above is used to model the relationship between the number of cups, n, of hot chocolate sold per day
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Answer:

3 represents: For every decrease of 1°F, three more cups of hot chocolate will be sold.

Step-by-step explanation:

Consider the provided equation.

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The relationship between the number of cups, n, of hot chocolate sold per day in a coffee shop and the average daily temperature, T, in degrees Fahrenheit.

The provided equation can be written as:

N= -3T+456

If we observe we can find that the above model is same as the slope intercept form y=mx+c. Where m is the slope.

Therefore, -3 represents the slope of the function.

The "minus" sign represents the slope of line is downward.

If we Substitute T=0 in provided equation we get N=456

That means when temperature is 0 degrees Fahrenheit the number of cups (N), of hot chocolate sold per day in a coffee shop is 456.

If we Substitute T=1 in provided equation we get N=453

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Therefore, If we increase temperature the number of cups decreases.

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