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3 years ago

Does anyone know how to convert meters per second into miles per hour? if possible, plz post the exact equation

Mathematics

1 answer:

igomit [66]3 years ago

5 0

One meter would equal 2.23694 miles per hour.

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Use trigonometric substitution to evaluate the integral 13 + 12x − x2 dx . First, write the expression under the radical in an a

SCORPION-xisa [38]

I don't see a square root sign anywhere, so I'll assume the integral is

$\displaystyle\int\sqrt{13+12x-x^2}\,\mathrm dx$

First complete the square:

$13+12x-x^2=49-(6-x)^2=7^2-(6-x)^2$

Now in the integral, substitute

$6-x=7\sin t\implies\mathrm dx=-7\cos t\,\mathrm dt$

so that

$t=\sin^{-1}\left(\dfrac{6-x}7\right)$

Under this change of variables, we have

$7^2-(6-x)^2=7^2-7^2\sin^2t=7^2(1-\sin^2t)=7^2\cos^2t$

so that

$\displaystyle\int\sqrt{13+12x-x^2}\,\mathrm dx=-7\int\sqrt{7^2\cos^2t}\,\cos t\,\mathrm dt=-49\int|\cos t|\cos t\,\mathrm dt$

Under the right conditions, namely that cos(<em>t</em>) > 0, we can further reduce the integrand to

$|\cos t|\cos t=\cos^2t=\dfrac{1+\cos(2t)}2$

$\displaystyle-49\int|\cos t|\cos t\,\mathrm dt=-\frac{49}2\int(1+\cos(2t))\,\mathrm dt=-\frac{49}2\left(t+\frac12\sin(2t)\right)+C$

Expand the sine term as

$\dfrac12\sin(2t)}=\sin t\cos t$

Then

$t=\sin^{-1}\left(\dfrac{6-x}7\right)\implies \sin t=\dfrac{6-x}7$

$t=\sin^{-1}\left(\dfrac{6-x}7\right)\implies \cos t=\sqrt{7^2-(6-x)^2}=\sqrt{13+12x-x^2}$

So the integral is

$\displaystyle-\frac{49}2\left(\sin^{-1}\left(\dfrac{6-x}7\right)+\dfrac{6-x}7\sqrt{13+12x-x^2}\right)+C$

3 0

3 years ago

Help me !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Goshia [24]

Answer = -3/2

Explanation:

Slope = rise/run

Rise = vertical
Run= horizontal

The slope is negative because it goes from right to left.

6 0

3 years ago

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I need help :( :( :( :( :(

sertanlavr [38]

Ok. With what may I ask?

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3 years ago

Determine the ordered pair that lies on the unit circle corresponding to startfraction 5 pi over 4 endfraction .

viktelen [127]

(negative square root two)/2, (negative square root two)/2

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3 years ago

How many x-intercepts appear on the graph of this polynomial function? f (x) = x Superscript 4 Baseline minus 5 x squared 1 x-in

Brut [27]

Answer:

3 x-intercepts

Step-by-step explanation:

f(x) = x⁴ - 5x²

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3 years ago

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