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3 years ago

Perpendicular lines are two coplanar lines that intersect to form what type of angle?

Mathematics

1 answer:

Jobisdone [24]3 years ago

7 0

Answer:

Perpendicular Line Theorems

Step-by-step explanation:

If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular. If two sides of two adjacent angles are perpendicular, then the angles are complementary. If two lines are perpendicular, then they intersect to form four right angles.

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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

3 years ago

Please help me! Given (x+a)(x+b) = x^2+x-12, what is the value of a^2+b^2

Sonja [21]

(x + 4) (x - 3)
a = 4
b = -3

a^2 + b^2 = ...
= 4^2 + (-3)^2
= 16 + 9
= 25

4 0

3 years ago

On her way to visit her parents,jennifer drives 265 miles in 5 hours. What is her average rate of speed in miles per hour?

Nutka1998 [239]

Her total distance (so 265 miles) over the number of hours she drives will give miles per hour.
265miles/5hours=53 miles/hour

5 0

3 years ago

Read 2 more answers

Look at the histograms of real estate data and decide whether you think the standard deviation of home prices in City A was larg

Kruka [31]

Answer:

The description according to the framework in question is illustrated in the portion below.

Step-by-step explanation:

These same 2 histograms are quite dissimilar or separate, for City A, each information collected has always been largely focused at 400, although for City B, these same results are interpreted at 400.
The price increases including its households throughout City B have quite a higher SD than those of the exchange rates throughout City A, also because documentation from City A generate a lot of price levels close to the middle of the bar chart, as well as the wages throughout City B, require a high amount of rates farther from the midpoint of the

7 0

3 years ago

Enter the solutions from least to greatest. (2x +4)(3x -2)=0

morpeh [17]

Answer:

From least to greatest: -2, 2/3

Step-by-step explanation:

Set each factor equal to 0 and solve

2x + 4 =0

2x = -4

x = -2

3x - 2 = 0

3x = 2

x = 2/3

The solutions are -2 and 2/3

7 0

3 years ago