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3 years ago

What is the slope of the line that passes through the points (8,8) and (20, -2)?

Mathematics

1 answer:

Sindrei [870]3 years ago

3 0

Answer:

-5/6

Step-by-step explanation:

Use slope intercept form: $\frac{y_2-y_1}{x_2-x_1}$

$\frac{-2-8}{20-8}$ = $\frac{-10}{12}$ = -5/6

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Use the given transformation x=4u, y=3v to evaluate the integral. ∬r4x2 da, where r is the region bounded by the ellipse x216 y2

exis [7]

The Jacobian for this transformation is

$J = \begin{bmatrix} x_u & x_v \\ y_u & y_v \end{bmatrix} = \begin{bmatrix} 4 & 0 \\ 0 & 3 \end{bmatrix}$

with determinant $|J| = 12$ , hence the area element becomes

$dA = dx\,dy = 12 \, du\,dv$

Then the integral becomes

$\displaystyle \iint_{R'} 4x^2 \, dA = 768 \iint_R u^2 \, du \, dv$

where $R'$ is the unit circle,

$\dfrac{x^2}{16} + \dfrac{y^2}9 = \dfrac{(4u^2)}{16} + \dfrac{(3v)^2}9 = u^2 + v^2 = 1$

so that

$\displaystyle 768 \iint_R u^2 \, du \, dv = 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2 \, du \, dv$

Now you could evaluate the integral as-is, but it's really much easier to do if we convert to polar coordinates.

$\begin{cases} u = r\cos(\theta) \\ v = r\sin(\theta) \\ u^2+v^2 = r^2\\ du\,dv = r\,dr\,d\theta\end{cases}$

Then

$\displaystyle 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2\,du\,dv = 768 \int_0^{2\pi} \int_0^1 (r\cos(\theta))^2 r\,dr\,d\theta \\\\ ~~~~~~~~~~~~ = 768 \left(\int_0^{2\pi} \cos^2(\theta)\,d\theta\right) \left(\int_0^1 r^3\,dr\right) = \boxed{192\pi}$

3 0

2 years ago

What is 6 1/4 x 3 3/5

aliya0001 [1]

Answer:

Step-by-step explanation:

Change mixed fraction to improper fraction. Then reduce to lowest term if possible.

6 1/4 x 3 3/5 = 25/4 * 18/5 = 25* 18 /4*5

= 5 * 18 / 4 {giving by 5th table}

= 5* 9 /2 { giving by 2nd tables}

= 45/2

8 0

3 years ago

Help !!!

ivann1987 [24]

7.5 gallons. (5x60)/40 5x60 being the equation to find the total miles driven

3 0

3 years ago

Plz help ASAP!!!!!!!!

lilavasa [31]

Answer:

The answer is 95.03

Step-by-step explanation

The formula that I used

A=πr^2

Area = π·5.5^2 ≈ 95.03318

Hope that helps :)

4 0

3 years ago

At the fall festival, a booth is selling $5 meals and $10 meals. They sell 1000 meals in all and collect $3500. Which system of

Tamiku [17]

The system of equation that can be used to represent the number of meals sold is

x + y = 1000

5x + 10y = 3,500

Given:

Number of $5 meals sold = x

Number of $10 meals sold = y

Total number of meals = 1000

Total amount of meals = $3,500

The equations:

Quantity

x + y = 1000

Price

5x + 10y = 3,500

Therefore, the system of equation that can be used to represent the number of meals sold is

x + y = 1000

x + y = 10005x + 10y = 3,500

Learn more about equation:

brainly.com/question/15165519

5 0

2 years ago