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Simora [160]
3 years ago
13

(04.02 MC) If f(x) = 2x2 − 10, find f(5).

Mathematics
1 answer:
KIM [24]3 years ago
4 0
F(x)=2x^2-10

f(5)=2(5^2)-10

f(5)=2(25)-10

f(5)=50-10

f(5)=40
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Suppose that the derivable functions x=x(t) and y=y(t) satisfy xcosy=2.
ololo11 [35]

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

a-) -√2 / 2.

<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}}

Since dx/dt=−2, we have that:

\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

#SPJ1

4 0
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Please help me, I promise I will give brainliest to the first answer, I dont care if there is no explanation, please just give t
Sergeeva-Olga [200]

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Answer:

No

Step-by-step explanation:

(x,y)=(4,-1)

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73*4+5*(-1)=287

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____________________________

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175*4-3*(-1)=703

17\neq 703

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Answer:

X = 13

Step-by-step explanation:

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