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kotykmax [81]
3 years ago
7

Use the given transformation to evaluate the integral.

Mathematics
1 answer:
GuDViN [60]3 years ago
3 0

For the transformation

\begin{cases}x=7u+v\\y=u+7v\end{cases}

the Jacobian is

\dfrac{\partial(x,y)}{\partial(u,v)}=\begin{bmatrix}7&1\\1&7\end{bmatrix}

with determinant

\det\left(\begin{bmatrix}7&1\\1&7\end{bmatrix}\right)=48

The vertices of the triangle in the u,v-plane are

(x,y)=(0,0)\implies(u,v)=(0,0)

(x,y)=(7,1)\implies(u,v)=(1,0)

(x,y)=(1,7)\implies(u,v)=(0,1)

Then the integral is

\displaystyle\iint_R(x-8y)\,\mathrm dA=-48\int_0^1\int_0^{1-v}(u+55v)\,\mathrm du\,\mathrm dv=\boxed{-448}

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Find the LCM of 6 and 8 and list the multiples <br>​
Hitman42 [59]

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8 0
3 years ago
PLEASE HELPPPP(BRAINLIEST FOR RIGHT ANSWER)
Thepotemich [5.8K]

Answer:

The relation between polar and Cartesian coordinates are

r2=x2+y2

tan

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y

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sin

θ

r

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or

r

2

=

8

r

sin

θ

∴

x

2

+

y

2

=

8

y

or

x

2

+

y

2

−

8

y

=

0

or

x

2

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y

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−

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graph{x^2+(y-4)^2=16 [-20, 20, -10, 10

Step-by-step explanation:

i created it that way so yall will take a longer time to answer

8 0
3 years ago
Read 2 more answers
Which relation is a function?
xz_007 [3.2K]

Answer:

I see this

"Which relation is a function?

A {(-3,4),(-3,8),(6,8)}

B {(6,4),(-3,8),(6,8)}

C {(-3,4),(3,-8),(3,8)}

D {(-3,4),(3,5),(-3,8)}"

So the answer is none of these.

Please make sure you have the correct problem.

Step-by-step explanation:

A set of points is a function if you have all your x's are different.  That is, all the x's must be distinct. There can be no value of x that appears more than once.

If you look at choice A, this is not a function because the first two points share the same x, which is -3.

Choice B is not a function because the first and last point share the same x, which is 6.

Choice C is not a function because the last two points share the same x, which is 3.

Choice D is not a function because the first and last choice share the same x, which is -3.

None of your choices show a function.

If you don't have that choice you might want to verify you written the problem correctly.

This is what I see:

"Which relation is a function?

A {(-3,4),(-3,8),(6,8)}

B {(6,4),(-3,8),(6,8)}

C {(-3,4),(3,-8),(3,8)}

D {(-3,4),(3,5),(-3,8)}"

7 0
3 years ago
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