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3 years ago

Factorize,m

}^{2} - 40 + 6m" alt=" {m }^{2} - 40 + 6m" align="absmiddle" class="latex-formula">

Mathematics

1 answer:

aev [14]3 years ago

6 0

Answer:

Step-by-step explanation:

m^2-40+6m

=m^2+6m-40

=m^2-(10-4)m-40

=m^2-10m+4m-40

=m(m-10)+4(m-10)

=(m+4)(m-10)

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Assuming you mean the US election a problem with our electron is the person who wins the most popular vote doesn't always win.

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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:

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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:

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

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

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.

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

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

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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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