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2 years ago

17. Alex spent $125 to have a party. He

Mathematics

1 answer:

Mandarinka [93]2 years ago

7 0

Answer:

The answer is Coming because 125-35 is 90 and 90 divided by 10 is 9, so each pizza was 9.00

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Applying implicit differentiation, it is found that dy/dt when y=π/4 is of:

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<h3>What is implicit differentiation?</h3>

Implicit differentiation is when we find the derivative of a function relative to a variable that is not in the definition of the function.

In this problem, the function is:

xcos(y) = 2.

The derivative is relative to t, applying the product rule, as follows:

$\cos{y}\frac{dx}{dt} - x\sin{y}\frac{dy}{dt} = 0$

$\frac{dy}{dt} = \frac{\cos{y}\frac{dx}{dt}}{x\sin{y}}$

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$\frac{dy}{dt} = -2\frac{\cos{y}}{x\sin{y}}$

When y = π/4, x is given by:

xcos(y) = 2.

$x = \frac{2}{\cos{\frac{\pi}{4}}} = \frac{2}{\frac{\sqrt{2}}{2}} = \frac{4}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = 2\sqrt{2}$

Hence:

$\frac{dy}{dt} = -2\frac{\cos{y}}{x\sin{y}}$

$\frac{dy}{dt} = -\frac{1}{\sqrt{2}}\cot{y}$

Since cot(pi/4) = 1, we have that:

$\frac{dy}{dt} = -\frac{1}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = -\frac{\sqrt{2}}{2}$

Which means that option a is correct.

More can be learned about implicit differentiation at brainly.com/question/25608353

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