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3 years ago

Name two acute angles

Mathematics

2 answers:

tatiyna3 years ago

6 0

A because they are less than 90 degrees

Lerok [7]3 years ago

6 0

The answer is A i promise you

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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

8. Solve for x. Round your answer to the nearest tenth. 8.6 4 x 0176

earnstyle [38]

Answer:

C. 9.5

Step-by-step explanation:

The Pythagorean Theorem: a^2 + b^2 = c^2.

4^2 + 8.6^2 = c^2

16 + 73.96 = c^2

c^2 = 89.96

c = 9.4847....

8 0

3 years ago

Simplify a^n*a^-n Thank you! :)

irakobra [83]

Yy^2 I'm pretty sure is the answer!

6 0

3 years ago

Read 2 more answers

Izzie recently took a math test where each correct answer (a) on the main part of the test was worth 8.3 points. She also correc

Temka [501]

Answer:

12 correct answers

Step-by-step explanation:

Since in the main part she scores 8.3 points for each question she answers correctly, we can assume that the number of questions she answers correctly=a

Therefor, the total number of points she achieved in the math test in the main part alone can be expressed as:

Total score(main part)=8.3×a=8.3a points

She also solved a bonus question worth=11 points

Consider expression 1 below

The total score in the whole test=Total score in the main part+Bonus points, where;

Total score in the whole test=110.6 points

Total score in the main part=8.3a points

Bonus points=11 points

Substituting the values in expression 1:

8.3a+11=110.6

8.3a=110.6-11

8.3a/8.3=99.6/8.3

a=12

Number of correct answers in the main part=a=12

4 0

4 years ago

64 ft of rope weighs 20 pounds 28 ft of rope weighs x pounds

castortr0y [4]

Answer

89.6

Step-by-step explanation:

Each foot of rope weighs 3.2 so then mutiplied 3.2 by 28 and got that

4 0

3 years ago