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3 years ago

Find the area of the composite figure.

Mathematics

1 answer:

larisa86 [58]3 years ago

8 0

Find the area of all the separate figures and add them together
area of rectangle = length x width
11 x 3 = 33 ft
area of square = a^2
3^2 = 9ft
area of triangle = base x height over 2
11 x 3 = 33
33 over 2 = 16.5 ft
33 + 9 + 16.5 = 58.5 ft ^ 2

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If = and x > 0 what is the value of x ?

Masteriza [31]

O valor de x é 45º

Explicação:Confia no pai

8 0

2 years ago

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

1 year ago

Find the degree of the term -5x to the power of 4

marysya [2.9K]

Answer:

4 or -625x^4 (Just in case I misunderstood)

Step-by-step explanation:

The degree is always the power of something. Since -5x has a power of 4, its degree is 4.

Just in case I misunderstood the question, I will solve it another way that I think you meant. (-5x)^4 is -5^4 times x^4.

-625 times x^4 is -625x^4.

5 0

2 years ago

Evaluate the expression:<br> 3x + 2y when X=10 and y=4

sveta [45]

Answer:

Step-by-step explanation:

3x + 2y when X=10 and y=4

3(10) + 2(4)

30 + 8

5 0

2 years ago

Read 2 more answers

If EFGH is a parallelogram, what is the value of x?

Leokris [45]

To be a parallogram the 2 angles shown need to equal 180 degrees

so we have: 34 + (4x-2) = 180

now we can solve for x

34 + 4x -2 = 180

simplify the left side by subtracting 2 from 34

32+4x =180

subtract 32 from each side:

4x = 148

divide both sides by 4 to get x

x = 148 / 4

x = 37

The answer is B

5 0

3 years ago