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2 years ago

The sum of the interior angles of an n-gon is 180° (n - 2). A) True B) False

Mathematics

2 answers:

garik1379 [7]2 years ago

7 0

True

hope it helps

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8_murik_8 [283]2 years ago

7 0

The answer is A

hope this helps

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Evaluate the integral by making an appropriate change of variables.

VARVARA [1.3K]

By inspecting the integrand, the "obvious" choice for substitution would be

u = y + x

v = y - x

Solving for x and y, we would have

x = (u - v)/2

y = (u + v)/2

in which case the Jacobian and its determinant are

$J=\begin{bmatrix}x_u&x_v\\y_u&y_v\end{bmatrix}=\dfrac12\begin{bmatrix}1&-1\\1&1\end{bmatrix}\implies|\det J|=\left|\dfrac12\right|=\dfrac12$

The trapezoid R has two of its edges on the lines x + y = 8 and x + y = 9, so right away, we have 8 ≤ u ≤ 9.

Then for v, we observe that when x = 0 (the lowest edge of R), v = y ; similarly, when y = 0 (the leftmost edge of R), v = -x. So

-x ≤ v ≤ y

-(u - v)/2 ≤ v ≤ (u + v)/2

-u + v ≤ 2v ≤ u + v

-u ≤ v ≤ u

So, the integral becomes

$\displaystyle\iint_R5\cos\left(7\frac{y-x}{y+x}\right)\,\mathrm dA=\int_8^9\int_{-u}^u\frac52\cos\left(\frac{7v}u\right)\,\mathrm dv\,\mathrm du$

$=\displaystyle\frac52\int_8^9\frac u7(\sin7-\sin(-7))\,\mathrm du$

$=\displaystyle\frac57\sin7\int_8^9u\,\mathrm du$

$=\displaystyle\frac5{14}\sin7(9^2-8^2)=\boxed{\frac{85}{14}\sin7}$

4 0

2 years ago

Question 2 of 5

andriy [413]

Answer:

Step-by-step explanation:

5 0

3 years ago

What is the greatest common factor for 200,205

bixtya [17]

$200|2\\100|2\\.\ 50|2\\.\ 25|5\\.\ \ 5|5\\.\ \ 1|\\\\200=2\times2\times2\times\fbox5\times5\\-----------------\\205|5\\.\ 41|41\\.\ \ 1|\\\\205=\fbox5\times41\\-------------------\\\\GCF(200;\ 205)=\fbox5$

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3 years ago

What are a) the ratio of the perimeters and b) the ratio of the ratio of the areas of the larger figure to the smaller figure

vfiekz [6]

Assuming that the figures given are square such that the scale factor between them is equal to 28/8 which can be further simplified into 7/2. The ratio of the perimeter is also equal to this value, 7/2. However, the ratio of the areas is equal to the square of this value giving us an answer of 49/4.

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2 years ago

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In a company's first year in operation, it made an annual profit of 169,500. The profit of the company increased at a constant 1

bixtya [17]

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3 years ago