Pls help I’m almost done and I’ll give the branliest thing if that’s what it’s called

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

Ksju [112]

Answer:

We conclude that the mean contents of cola bottles is more than or equal to the advertised 300 ml.

Step-by-step explanation:

We are given that Bottles of a popular cola drink are supposed to contain 300 ml of cola. The distribution of the contents is normal with standard deviation of 3 ml.

A student who suspects that the bottler is under-filling measures the contents of six bottles. The results are: 299.4, 297.7, 301.0, 298.9, 300.2, 297.0

Let $\mu$ = mean contents of cola bottles.

SO, Null Hypothesis, $H_0$ : $\mu \geq$ 300 ml {means that the mean contents of cola bottles is more than or equal to the advertised 300 ml}

Alternate Hypothesis, $H_A$ : $\mu$ < 300 ml {means that the mean contents of cola bottles is less than the advertised 300 ml}

The test statistics that will be used here is One-sample z test statistics as we know about the population standard deviation;

T.S. = $\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean contents of cola bottle = $\frac{\sum X}{n}$ = 299.03 ml

$\sigma$ = population standard deviation = 3 ml

n = sample of bottles = 6

So, test statistics = $\frac{299.03-300}{\frac{3}{\sqrt{6} } }$

= -0.792

Now at 5% significance level, the z table gives critical value of -1.6449 for left-tailed test. Since our test statistics is more than the critical value of z as -0.792 > -1.6449, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the mean contents of cola bottles is more than or equal to the advertised 300 ml.

8 0

3 years ago

£150 is invested at 5% compound interest for 2 years. How much will be in the account at the end of the investment?

morpeh [17]

Answer:

165

Step-by-step explanation:

5% of 150 british pounds = 7.5 British pounds

2 years = 7.5 BS per year

7.5 + 7.5

= 15 british pounds

15 british pounds + 150 british pounds =

165 british pounds

7 0

1 year ago

NEED HELP BEING TIMED !!! Which is the value of this expression when

Kruka [31]

The answer is 4
I used the Safari calculator, so I really hope this is right. Best of luck to you

7 0

2 years ago

Read 2 more answers

Can you relly much help me do this

slava [35]

Hey!
So It would be set up as .75n -2 = 10
.75 is the same as 3/4
Now add 2 to both sides
.75n = 12
now we want to get n alone so that we know what the number is, so divide .75 to both sides since it's multiplied to n
n=16
The answer is D!
Hope this helps!

5 0

3 years ago