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3 years ago

Plot the solution set of |-x|=3.5

Mathematics

1 answer:

lutik1710 [3]3 years ago

5 0

It is 3.5, because anything inside an absolute is always positive.

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Help please! Could you explain it too?

Olegator [25]

Answer:

a. Not proportional

b. Proportional;

k = ⅞

Step-by-step explanation:

A proportional relationship is usually represented in the format, y = kx. k here represents constant of proportionality. This shows that x and y are directly proportional.

a. y = -2x + 9 is not a proportional equation.

b. y = ⅞x is a proportional equation.

Constant of proportionality: k = ⅞

8 0

2 years ago

Divide completely for the question below

juin [17]

Answer:

B) 5x^2

Step-by-step explanation:

$\sqrt{\frac{50x^5}{2x} }$

We can divide 50 by 2, we get 25 and we can cancel out x from x^5.

Therefore, we get

$\sqrt{\frac{25x^4}{1} }$

= √25x^4

When we take the square root of 25, we get 5 and √x^4 = x^2.

Taking the square root, we get

= 5x^2

Answer: B) 5x^2

Thank you.

3 0

3 years ago

Calculate s f(x, y, z) ds for the given surface and function. g(r, θ) = (r cos θ, r sin θ, θ), 0 ≤ r ≤ 4, 0 ≤ θ ≤ 2π; f(x, y, z)

Triss [41]

$g(r,\theta)=(r\cos\theta,r\sin\theta,\theta)\implies\begin{cases}g_r=(\cos\theta,\sin\theta,0)\\g_\theta=(-r\sin\theta,r\cos\theta,1)\end{cases}$

The surface element is

$\mathrm dS=\|g_r\times g_\theta\|\,\mathrm dr\,\mathrm d\theta=\sqrt{1+r^2}\,\mathrm dr\,\mathrm d\theta$

and the integral is

$\displaystyle\iint_Sx^2+y^2\,\mathrm dS=\int_0^{2\pi}\int_0^4((r\cos\theta)^2+(r\sin\theta)^2)\sqrt{1+r^2}\,\mathrm dr\,\mathrm d\theta$

$=\displaystyle2\pi\int_0^4r^2\sqrt{1+r^2}\,\mathrm dr=\frac\pi4(132\sqrt{17}-\sinh^{-1}4)$

###

To compute the last integral, you can integrate by parts:

$u=r\implies\mathrm du=\mathrm dr$

$\mathrm dv=r\sqrt{1+r^2}\,\mathrm dr\implies v=\dfrac13(1+r^2)^{3/2}$

$\displaystyle\int_0^4r^2\sqrt{1+r^2}\,\mathrm dr=\frac r3(1+r^2)^{3/2}\bigg|_0^4-\frac13\int_0^4(1+r^2)^{3/2}\,\mathrm dr$

For this integral, consider a substitution of

$r=\sinh s\implies\mathrm dr=\cosh s\,\mathrm ds$

$\displaystyle\int_0^4(1+r^2)^{3/2}\,\mathrm dr=\int_0^{\sinh^{-1}4}(1+\sinh^2s)^{3/2}\cosh s\,\mathrm ds$

$\displaystyle=\int_0^{\sinh^{-1}4}\cosh^4s\,\mathrm ds$

$=\displaystyle\frac18\int_0^{\sinh^{-1}4}(3+4\cosh2s+\cosh4s)\,\mathrm ds$

and the result above follows.

4 0

3 years ago

What is the cube root of 27a12

Mice21 [21]

3a4

that should be your answer

4 0

3 years ago

Read 2 more answers

Find three consecutive integers whose sum is 21

stira [4]

Answer:

6 + 7 + 8 = 21

Step-by-step explanation:

6, 7, and 8 are consecutive integers.

6 + 7 is 13. 13 + 8 = 21. So, 6 + 7 + 8 are consecutive integers that equal 21.

5 0

3 years ago

Read 2 more answers