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3 years ago

Which step is included in the construction of parallel lines?

Mathematics

1 answer:

tekilochka [14]3 years ago

6 0

Copy an angle by creating arcs with a compass.

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The distance from the library to the park is 0.7 km how many meters is this

givi [52]

1000 meters are 1km so 700 meters

3 0

3 years ago

Read 2 more answers

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

3 years ago

The table shows the results of a survey of college students. Find the probability that a student’s first class of the day is a h

Mariana [72]

Answer is B..............:)

6 0

3 years ago

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Which expression gives the distance between the points (5, 1) and (9, -6)?

Vesna [10]

So the distance formula: d = rad (x2 - x1)^2 + (y2 - y1)^2
it doesn't matter what order you do, you just have to make sure it's a y coordinate for y and an x coordinate for x.
rad (9-5)^2 + ((-6)-1)^2
rad 4^2 + (-7)^2
rad 16 + 49
rad 65

4 0

3 years ago

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Find the missing number so that the equation has infinitely many solutions.

Alex17521 [72]

equation has infinitely many solutions has the same number on both sides of the equal sign

-3x -21 + x + 5 = -20x -16

-2x -16 = -20x -16

so either you have -18x on the left or +18x in the right

5 0

2 years ago