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3 years ago

13

Can someone please help me solve 3 and 4!? Im stuck. Their short too(:

1 answer:

stepan [7]3 years ago

8 0

What r u takeing i have not did this in a while tbh

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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

your friend deposits $9500 in an investment account that earns 2.1% annual interest. what is the balance after 11 years when the

solmaris [256]

Answer:

The answer is "$ 11,961.43"

Step-by-step explanation:

Given values:

P = $ 9500

r= 2.1 %

time (t)= 11 year

total quarterly year =4

Formula:

$A= P (1+\frac{r}{n})^{nt}\\\\$

quarterly time = $4 \times 11$

$= 44$

$A= P (1+\frac{r}{n})^{nt}\\\\$

$A = 9500 ( 1+ \frac{0.021}{4})^{44}\\\\A = 9500(\frac{4+ 0.021}{4} )^{44} \\\\A = 9500(\frac{4.021}{4} )^{44} \\\\A= 9500 (1.00525)^{44}\\\\A= 9500(1.25909819)\\\\A= 11,961. 43\\$

8 0

3 years ago

Which statement is true about the underlined digit in the number 65,888?

Ghella [55]

Sixty five thousand eight hundred and eighty eight

8 0

3 years ago

Applicants for the University of Statland take two tests, one for writing ability and the other on critical thinking, and normal

bezimeni [28]

Answer:

hello your question is incomplete attached below is the complete question

<em>answer</em> : 1

Step-by-step explanation:

Given Function:

F(x,y)= $\left \{ {{1/4(2x+y)} \atop {0}} \right.$ for 0<x<1, 0<y<2

elsewhere.

Evaluating the marginal density of the writing test score at point

X = 1/2 = 1/4 ( 4x + 2 ) = 1/4 ( 4 * 1/2 + 2 ) = 1

attached below is the detailed solution

7 0

2 years ago

Degree Of Length Degree Of Width Degree Of Height Degree Of Volume

Andrew [12]

Answer: length = 1, width = 1, height = 3, volume = 5

<u>Step-by-step explanation:</u>

Degree is the biggest exponent for the variables in the expression

Length = 4x - 1. The exponent for x is 1 --> degree = 1

Width = x The exponent for x is 1 --> degree = 1

Height = x³ The exponent for x³ is 3 --> degree = 3

Volume = 4x⁵ - x⁴. The biggest exponent for x is 5 --> degree = 5

4 0

3 years ago