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2 years ago

Brain is skateboarding at 8 kilometers per hour. How long will it take Brain to travel 12 kilometers?

Mathematics

1 answer:

Vladimir [108]2 years ago

8 0

Answer:

1.5 hours

Step-by-step explanation:

All you do is divide the speed by the distance 12/8=1.5 simple as that

Would be amazing if you marked me brainliest :)

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The surface area of a right circular cone of radius r and height h is S = πr√ r 2 + h 2 , and its volume is V = 1 3 πr2h. What i

kirill115 [55]

Answer:

Required largest volume is 0.407114 unit.

Step-by-step explanation:

Given surface area of a right circular cone of radious r and height h is,

$S=\pi r\sqrt{r^2+h^2}$

and volume,

$V=\frac{1}{3}\pi r^2 h$

To find the largest volume if the surface area is S=8 (say), then applying Lagranges multipliers,

$f(r,h)=\frac{1}{3}\pi r^2 h$

subject to,

$g(r,h)=\pi r\sqrt{r^2+h^2}=8\hfill (1)$

We know for maximum volume $r\neq 0$ . So let $\lambda$ be the Lagranges multipliers be such that,

$f_r=\lambda g_r$

$\implies \frac{2}{3}\pi r h=\lambda (\pi \sqrt{r^2+h^2}+\frac{\pi r^2}{\sqrt{r^2+h^2}})$

$\implies \frac{2}{3}r h= \lambda (\sqrt{r^2+h^2}+\frac{ r^2}{\sqrt{r^2+h^2}})\hfill (2)$

And,

$f_h=\lambda g_h$

$\implies \frac{1}{3}\pi r^2=\lambda \frac{\pi rh}{\sqrt{r^2+h^2}}$

$\implies \lambda=\frac{r\sqrt{r^2+h^2}}{3h}\hfill (3)$

Substitute (3) in (2) we get,

$\frac{2}{3}rh=\frac{r\sqrt{R^2+h^2}}{3h}(\sqrt{R^2+h^2+}+\frac{r^2}{\sqrt{r^2+h^2}})$

$\implies \frac{2}{3}rh=\frac{r}{3h}(2r^2+h^2)$

$\implies h^2=2r^2$

Substitute this value in (1) we get,

$\pi r\sqrt{h^2+r^2}=8$

$\implies \pi r \sqrt{2r^2+r^2}=8$

$\implies r=\sqrt{\frac{8}{\pi\sqrt{3}}}\equiv 1.21252$

Then,

$h=\sqrt{2}(1.21252)\equiv 1.71476$

Hence largest volume,

$V=\frac{1}{3}\times \pi \times\frac{\pi}{8\sqrt{3}}\times 1.71476=0.407114$

3 0

3 years ago

Question 13 y-5x= -4

Julli [10]

Which variable are we solving for?

For y:

y= 5x-4/ 13

For x:

x= 13y+4/ 5

5 0

3 years ago

Suppose that many large samples are taken from a population and that the sample proportions are normally distributed, with a mea

Taya2010 [7]

Answer:

[0.16316 , 0.27684]

Step-by-step explanation:

0.22 +/- 1.96(0.029)

0.22 +/- 0.05684

[0.16316 , 0.27684]

8 0

3 years ago

After the strand of measurement why do you think that graphing and data analysis are easier? Please help ASAP!!! :(

Vikki [24]

It’s organized and you can see it more visually , gives you a way to double check and write down the data properly.

8 0

3 years ago

Find a vector equation and parametric equations for the line. (Use the parameter t.) The line through the point (1, 0, 9) and pe

pogonyaev

Answer:

vector equation and parametric equations for the line are;

r(t) = < 1, 0, 9 > + t< 1, 3, 1 >

x(t),y(t),z(t) = < 1 + t, 3t, 9 + t >

Step-by-step explanation:

Given the data in the question;

Plane = x + 3y + z = 5

Normal of pane ⇒ <a> = < 1, 3, 1 >

As line is perpendicular to pane, Line is parallel to normal of plane.

⇒ Direction ratio of line < 1, 3, 1 >

Also line passes through < 1, 0, 9 >

r(t) = < 1, 0, 9 > + t< 1, 3, 1 >

Also,

(x-1)/1 = (y-0)/3 = (z-9)/1 = t

⇒ (x-1)/1 =t, (y-0)/3 = t, (z-9)/1 = t

⇒ x = 1 + t, y = 3t, z = 9 + t

⇒ x(t),y(t),z(t) = < 1 + t, 3t, 9 + t >

Therefore, vector equation and parametric equations for the line are;

r(t) = < 1, 0, 9 > + t< 1, 3, 1 >

x(t),y(t),z(t) = < 1 + t, 3t, 9 + t >

5 0

3 years ago