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alex41 [277]
3 years ago
7

4. Find the total surface area.5.1 in.3 in.8.3 in.​

Mathematics
1 answer:
maw [93]3 years ago
6 0

Answer:

Surface Area  = 165.06 inches 2

Step-by-step explanation:

5.1 in.

3 in.

8.3 in.​

Surface Area = 2×(5.1×3 + 5.1×8.3 + 3×8.3)

                      = 165.06 inches 2

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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

3 0
3 years ago
341÷5 what's the remander​
Maksim231197 [3]

Answer:

its 1

Step-by-step explanation: 341/5= 68 r1

6 0
3 years ago
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4. True or false: Lines, colors, and textures are often used to create shapes.
ioda

Answer:

true!

Step-by-step explanation:

because if we havent got lines, colors ,  and textures

how could shapes be created?

8 0
1 year ago
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What is the domain, range, and function? {(-3, 3), (1, 1), (0, -2), (1,4), (5, -1)}
wolverine [178]

The domain are all the inputs, that is; the x-values

Domain = { -3, 0, 1, 5}

The range are all the output, that is the y-values

Range = { 3, 1, -2, 4, -1}

This is just a relation and not a function, as we have more than 2 same value of x

8 0
11 months ago
The slope formula can be used to prove that a triangle has
OverLord2011 [107]

Answer:

The slope formula can be used to prove that a triangle has

A. Congruent Sides

<u>B. A right angle </u>

C. Parallel sides

D.Congruent angles

Step-by-step explanation:

The formula for finding the slope of a line on a coordinate plane is (y2 - y1) / (x2 - x1), where (x2, y2) and (x1, y1) represent two distinct points on the line. This is also known as "change in y over change in x" or "rise over run."

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3 years ago
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