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2 years ago

HELP PLEASE HELP!!!!!

Mathematics

1 answer:

babunello [35]2 years ago

6 0

Answer:

(i): A triangle where all three sides are equal and the same.

(ii): A triangle where all three sides are unequal in length.

(iii): A triangle that has two sides of equal length.

(iv): A triangle where all three internal angles are acute(they measure less than 90 degrees.

(v): A triangle where all three internal angles are obtuse(measure above 90 degrees).

(vi): A triangle where one internal angle is a right angle(90 degrees).

Hope this helps

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

Describe how you would graph a figure that is translated by (x - 4,4+2).

atroni [7]

Answer:

see explanation

Step-by-step explanation:

Given the translation rule

(x, y ) → (x - 4, y + 2 )

This means subtract 4 from the original x- coordinate and add 2 to the original y- coordinate, that is

a point (4 , - 4 ) → (4 - 4, - 4 + 2 ) → (0, - 2 )

8 0

3 years ago

Find at least 3 numbers that are palindromes and have square roots that are palindromes

Artemon [7]

Hey there!

Palindromes are numbers that can be written the same way backwards, such as 101 and 12321. You're looking for some numbers which are palindromes, and so are their square numbers.

Alright, I'll give you four of those:

121 is a palindrome, and its square root is 11, both palindromes. 11 x 11 = 121
484 is a palindrome, and its square root is 22, both palindromes. 22 x 22 = 484
10201 is a palindrome, and its square root is 101, both palindromes. 101 x 101 = 10201
12321 is a palindrome, and its square root is 111, both palinromes. 111 x 111 = 12321

Hope this helps!

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2 years ago

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SSSSS [86.1K]

C’(500)=80 means at 500 pounds of documents, the cost is increasing at a rate of $80 dollars/pound

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2 years ago

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MArishka [77]

Answer: