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2 years ago

What is the standard form of the equation 2(3x + 2y) - 13 = 0?

Mathematics

1 answer:

Lerok [7]2 years ago

4 0

Answer:

6x+4y-13=0

Step-by-step explanation:

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Sketch the domain D bounded by y = x^2, y = (1/2)x^2, and y=6x. Use a change of variables with the map x = uv, y = u^2 (for u ?

cluponka [151]

Under the given transformation, the Jacobian and its determinant are

$\begin{cases}x=uv\\y=u^2\end{cases}\implies J=\begin{bmatrix}v&u\\2u&0\end{bmatrix}\implies|\det J|=2u^2$

so that

$\displaystyle\iint_D\frac{\mathrm dx\,\mathrm dy}y=\iint_{D'}\frac{2u^2}{u^2}\,\mathrm du\,\mathrm dv=2\iint_{D'}\mathrm du\,\mathrm dv$

where $D'$ is the region $D$ transformed into the $u$ - $v$ plane. The remaining integral is the twice the area of $D'$ .

Now, the integral over $D$ is

$\displaystyle\iint_D\frac{\mathrm dx\,\mathrm dy}y=\left\{\int_0^6\int_{x^2/2}^{x^2}+\int_6^{12}\int_{x^2/2}^{6x}\right\}\frac{\mathrm dx\,\mathrm dy}y$

but through the given transformation, the boundary of $D'$ is the set of equations,

$\begin{array}{l}y=x^2\implies u^2=u^2v^2\implies v^2=1\implies v=\pm1\\y=\frac{x^2}2\implies u^2=\frac{u^2v^2}2\implies v^2=2\implies v=\pm\sqrt2\\y=6x\implies u^2=6uv\implies u=6v\end{array}$

We require that $u>0$ , and the last equation tells us that we would also need $v>0$ . This means $1\le v\le\sqrt2$ and $0$ , so that the integral over $D'$ is

$\displaystyle2\iint_{D'}\mathrm du\,\mathrm dv=2\int_1^{\sqrt2}\int_0^{6v}\mathrm du\,\mathrm dv=\boxed6$

4 0

2 years ago

Please Help Asap!!! I hate integers!!!

sveta [45]

5 times (-17)= -85 so you should have said -85

8 0

2 years ago

Read 2 more answers

Uh can someone please help? please get it right and try to explain how

Anestetic [448]

Answer:

From least likely to most likely:

Colorado Bronze wins

I Am Pat wins

Good Legs Lance wins

Step-by-step explanation:

Converting all probabilities to the same type may be easier to visualize and see the chances. Let's convert each chance to percentage:

P(I Am Pat wins) = 3/10 = 30%

P(Good Legs Lance wins) = 0.6 = 60%

P(Colorado Bronze wins) = 10%= 10%

Thus, the desired order is:

Colorado Bronze wins

I Am Pat wins

Good Legs Lance wins

4 0

2 years ago

Read 2 more answers

12. How much do 21 bushels of sweet

lesantik [10]

Answer:

21 bushels of sweet corm weight 735 pounds.

Step-by-step explanation:

Given:

Weight of 21 bushels of sweet corn is obtained by multiplying the unit weight to the number of bushels required.

Unit weight of sweet corn is the weight of 1 bushel of sweet corn.

Weight of 1 bushel of sweet corn = 35 pounds

So, weight of 21 bushels of sweet corns = $35\times 21=735$ pounds.

Therefore, 21 bushels of sweet corn weigh 735 pounds.

8 0

3 years ago

In ABC,if sin A=4/5 and tan A=4/3, then what I s cos A?

Svet_ta [14]

Cos(A) will be 3/5 Cos(A) is adjacent/hypotenuse. So here we have sin(A)=opp/hyp which is 4/5 and tan(A)=opp/adj which is 4/3. So cos(A) is adj./hyp and knowing the previous 2 terms of sin(A) and cos(A), you can go ahead and find Cos(A). So cos(A) is 3/5

5 0

3 years ago