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3 years ago

Draw a line representing the "rise" and a line representing the "run" of the line. State

Mathematics

2 answers:

AleksAgata [21]3 years ago

3 0

The answer would be -3/5. The slope is the rise over run. It goes up 3 and over 5. Hope this helps!

Bumek [7]3 years ago

3 0

Answer: The slope of the line is 3/5 or 0.6

Step-by-step explanation: The line you drew was run of 4 and -1 and the rise was 7 and 4.

y=y1-y2/x1-x2

7-4/4-(-1)

7-4/4+1

3/5 or 0.6

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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

katie bought 12 roses she gave some a way and now has 4 roses left.how many roses did katie give away

Firlakuza [10]

Rosie gave away 8 roses

8 0

3 years ago

Read 2 more answers

A value of a car is $24,000. You pay it off by making payments of $6200 a year. Write and equation for when the car would be pay

Damm [24]

Answer: 24,000 / 6,200 = x years

Step-by-step explanation:

The car is valued at $24,000.

Yearly payments are $6,200.

The year that it will be paid off can be dtermined by calculating how long it would take $6,200 to get to $24,000.

You can do that by dividing $24,000 by $6,200.

Assume the number of years for the car to be paid off is x:

24,000 / 6,200 = x years

When solved:

= 24,000 / 6,200

= 3.87 years

4 0

3 years ago

According to a recent Catalyst Census, 16% of executive officers were women with companies that have company headquarters in the

Elanso [62]

Answer: 0.0885

Step-by-step explanation:

Given : According to a recent Catalyst Census, 16% of executive officers were women with companies that have company headquarters in the Midwest.

i.e. p= 0.16

Sample size : n= 154

Now, the probability that more than 20% of this sample is comprised of female employees is given by :-

$P(p>0.20)=P(z>\dfrac{0.20-0.16}{\sqrt{\dfrac{0.16(1-0.16)}{154}}})$

[∵ $z=\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}$ ]

$=P(z>1.35)\approx1-P(z\leq1.35)=1-0.9115=0.0885$ [Using the standard z-value table]

Hence, the required probability = 0.0885

6 0

3 years ago

Whut is the soluton of when multiplying by 3

saveliy_v [14]

The answer of this is 3,6,9,12,15,18,21,24,27,30,33,36,39,...

4 0

3 years ago