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3 years ago

11

Given cos x=0.4762,find the degree measure of x.round your answer to the nearest tenth

1 answer:

alex41 [277]3 years ago

5 0

If you have a calculator, you can use the inverse cos " cos⁻¹ " key. Many upper level books write that as Arccos so as not to confuse you with a negative exponent. We do that because if you take the cosine of any angle, and then the inverse cosine of any angle, it leads you back to the original angle. Think of it as a big "UNDO" button.

To one decimal place, that result is 61.6 degrees.

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If f(x, y) = esin(x + y) and D = [−π, π] × [−π, π], show the following. 1 e ≤ 1 4π2 D f(x, y) dA ≤ e The area of the region D is

Digiron [165]

I'm guessing the purpose of this exercise is to find the average value of $f(x,y)=e^{\sin(x+y)}$ over the region $D$ ,

$D=\left\{(x,y)\mid (x,y)\in[-\pi,\pi]^2\right\}$

which is

$\displaystyle\frac{\displaystyle\iint_Df(x,y)\,\mathrm dx\,\mathrm dy}{\displaystyle\iint_D\mathrm dx\,\mathrm dy}$

The denominator is the measure (area) of $D$ , which is easy to compute:

$\displaystyle\iint_D\mathrm dx\,\mathrm dy=\int_{-\pi}^\pi\int_{-\pi}^\pi\mathrm dx\,\mathrm dy=(2\pi)^2=4\pi^2$

Not to be confused with the integral in the numerator:

$\displaystyle\iint_Df(x,y)\,\mathrm dx\,\mathrm dy=\int_{-\pi}^\pi\int_{-\pi}^\pi e^{\sin(x+y)}\,\mathrm dx\,\mathrm dy$

but this integral is difficult to compute, hence the inequalities. We have

$-1\le\sin(x+y)\le1$

$\implies\dfrac1e\le e^{\sin(x+y)}\le e$

$\implies\displaystyle\iint_D\frac{\mathrm dx\,\mathrm dy}e\le\iint_De^{\sin(x+y)}\,\mathrm dx\,\mathrm dy\le\iint_De\,\mathrm dx\,\mathrm dy$

$\implies\displaystyle\frac{4\pi^2}e\le\iint_De^{\sin(x+y)}\,\mathrm dx\,\mathrm dy\le4\pi^2e$

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3 years ago

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erik [133]

The answer is 1.6
or 1 and 3/5

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3 years ago

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Answer is D.

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3 years ago

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3 years ago

The area of Chile is approximately 2*10^6 square kilometers the area Bosnia is approximately 9*10^4 square kilometers what is th

Eddi Din [679]

Answer:

2,090,000

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Area = Area of Chile + Area of Bosnia

Area of Chile = 2*1000000

Area of Bosnia = 9*10000

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Area = 2,090,000

6 0

2 years ago

Read 2 more answers