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3 years ago

Simply your expression 4[(12-2) ²÷4]

Mathematics

1 answer:

lina2011 [118]3 years ago

8 0

Answer:

100

Step-by-step explanation:

Simplify the following:

4 (12 - 2)^2/4

Hint: | Express 4 (12 - 2)^2/4 as a single fraction.

4 (12 - 2)^2/4 = (4 (12 - 2)^2)/4:

(4 (12 - 2)^2)/4

Hint: | Cancel common terms in the numerator and denominator of (4 (12 - 2)^2)/4.

(4 (12 - 2)^2)/4 = 4/4×(12 - 2)^2 = (12 - 2)^2:

(12 - 2)^2

Hint: | Subtract 2 from 12.

| 1 | 2

- | | 2

| 1 | 0:

10^2

Hint: | Evaluate 10^2.

| 1 | 0

× | 1 | 0

| 0 | 0

1 | 0 | 0

1 | 0 | 0:

Answer: 100

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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

A bill from a plumber was $306 The plumber charged $150 for parts and $52 per hour for labor. How long did ths plumber work at h

ludmilkaskok [199]

We can make an equation from this.
Our intial value is 150 for parts, and he works for 52 dollars an hour.
We can define h for hours and c for total cost.
Therefore, we have:
c = 150 + 52h.
We can set this equal to 306 dollars, as that's the given total cost:
306 = 150 + 52h
Subtract 150 from both sides:
52h = 156
Divide both sides by 2:
h = 3
He worked 3 hours.
hope this helped!

6 0

3 years ago

What is the result of adding these two equations?

timofeeve [1]

Answer:

the result of adding these two equations is

3x = 14

Step-by-step explanation:

We are given two equations

5x − y = 6 eq. 1

−2x + y = 8 eq. 2

Add the like terms together

5x - 2x = 3x

− y + y = 0

6 + 8 = 14

So the result of adding these equations is

3x + 0 = 14

3x = 14

Bonus:

The value of x is

3x = 14

x = 14/3

6 0

3 years ago

John made 357$ for 17 hours of work.

yanalaym [24]

Answer: 14 hours

Step-by-step explanation: First I found the unit rate of how much money per hour. So, 357 divided by 17 = 21. So know I know that she earns 21$ per hour. Then, I did 237 divided by 17 which would be 13 remainder 16. Since he only get paid if he works for a full hour, I think the answer would be 14.

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2 years ago

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Estimate the square root of 75. a. 8.7 b. 4.2 c. 7.4 d. 9.5

SVEN [57.7K]

Answer: A.8.7

Step-by-step explanation:

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3 years ago

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