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Citrus2011 [14]

2 years ago

6

material to build a rectangular box. The length is twice the width and there is no top. What values for W and L and H will creat

e a box that encloses the maximum volume using the material you have?

1 answer:

Gala2k [10]2 years ago

5 0

Answer:

5id4839y47f

Step-by-step explanation:

You might be interested in

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

2 years ago

Is 4 a solution of2=8

JulsSmile [24]

Answer:

Two doesn’t equal 8. Theoretically, eight is the solution...

Step-by-step explanation:

5 0

3 years ago

Y_Kistochka [10]

Answer:

A. 39,000.

Step-by-step explanation:

Volume of the lower prism = 30^3= 27,000

Volume of the pyramid = 1/3 area of the base * height

= 1/3 * 900 * 40

= 1200

Volume of the whole solid = 27000 + 12000

= 39,000,

5 0

2 years ago

<1 is a complement of <2, and m<1=66. find <2

Furkat [3]

Answer:

114

Step-by-step explanation:

that's supplementary

6 0

3 years ago

Write an equation in point slope form for a line that includes the origin and (9,-3)

aivan3 [116]

So we are given two points that the line crosses, the origin and (9, -3), we can calculate the slope m of the line with these data, dividing the y segment by the x segment:
m = (-3 - 0)/(9 - 0) = -3/9
m = -1/3
then we can use the point slope line equation to find the line equation, lets use the point origin (0,0) to do so:
y - y1 = m(x - x1), where x1, y1 are the coordinates of a point that the line crosses:
y - 0 = (-1/3)(x - 0)
y = <span>(-1/3)x
so this is the equation of the line, slope -1/3 and y intercept 0</span>

3 0

2 years ago