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4 years ago

Please help me simplify complex fractions 1/5/3/4

Mathematics

2 answers:

Inga [223]4 years ago

4 0

The answer is 4/15 decimal form is .26 and six repeates

Ne4ueva [31]4 years ago

3 0

1/5 reciprocal the second fraction to 4/3
1/5 ( 4/3) = 4/15

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Which postulate proves that the triangles below are similar?

Molodets [167]

Answer:

AA~

Step-by-step explanation:

These triangles are similar but not congruent. One triangle is bigger than the other, meaning none of the side lengths are the same. On the triangles, two angles are given, a 53 degree and a 90 meaning that you would us the AA rule to determine if they are similar. Which they are.

3 0

3 years ago

What is the intercept to this graph, please??

velikii [3]

Answer:

there is no intercept

Step-by-step explanation:

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4 years ago

A random sample (Sample 1) of the Mercedes's average driving speed (km/h) is: 120, 142, 142, 165, 132, 130, 156, 136, 167, 139,

ziro4ka [17]

The median of Mercedes' speed is 144 km/h.

The median of Audi's speed is ~133,6 km/h.

8 0

3 years ago

What is the answer for No.22 & 23 please

kondor19780726 [428]

Hello!

Number 22: We'd plot the first point at 0 since there is no stated y-intercept. Next, we'd use our slope to determine where to plot the next point, and that would create our line. According to the problem, our slope is $-\frac{1}{2}$ , which automatically tells us that the slope would be going downwards because it's negative.

To plot our point, use the slope while going down and across from our y-intercept, which is 0. Go down 1, and over 2.

Your points should be at (0, 0) and (-1, 2)

Number 23: This one will be a bit trickier since the equation is not in slope-intercept form. First, let's convert it to slope-intercept form.

$-2x + 3y = 6

-2x + 2x + 3y = 6 + 2x

3y = 6 + 2x

3y/3y = 6/3y + 2x/3y

y = 2 + 2/3x$

Flip some of those numbers around to get our equation in slope-intercept form:

$y = \frac{2}{3}x + 2$

Now to graph this, we do the same as we did for the last problem. Plot our first point at (0, 2), since 2 is our y-intercept. Afterwards, go up 2 and over 3, then plot the other point.

Your points should be at (0, 2) and (4, 3)

8 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

4 years ago