Please help and show work so I can understand how too alive this question please

A closed-top cylindrical container is to have a volume of 250 in2. 250 , in squared , . What dimensions (radius and height) will

miv72 [106K]

Answer:

radius r = 3.414 in

height h = 6.8275 in

Step-by-step explanation:

From the information given:

The volume V of a closed cylindrical container with its surface area can be expressed as follows:

$V = \pi r^2 h$

$S = 2 \pi rh + 2 \pi r^2$

Given that Volume V = 250 in²

Then;

$\pi r^2h = 250 \\ \\ h = \dfrac{250}{\pi r^2}$

We also know that the cylinder contains top and bottom circle and the area is equal to πr²,

Hence, if we incorporate these areas in the total area of the cylinder.

Then;

$S = 2\pi r h + 2 \pi r ^2$

$S = 2\pi r (\dfrac{250}{\pi r^2}) + 2 \pi r ^2$

$S = \dfrac{500}{r} + 2 \pi r ^2$

To find the minimum by determining the radius at which the surface by using the first-order derivative.

$S' = 0$

$- \dfrac{500}{r^2} + 4 \pi r = 0$

$r^3 = \dfrac{500 }{4 \pi}$

$r^3 = 39.789$

$r =\sqrt[3]{39.789}$

r = 3.414 in

Using the second-order derivative of S to determine the area is maximum or minimum at the radius, we have:

$S'' = - \dfrac{500(-2)}{r^3}+ 4 \pi$

$S'' = \dfrac{1000}{r^3}+ 4 \pi$

Thus, the minimum surface area will be used because the second-derivative shows that the area function is higher than zero.

Thus, from $h = \dfrac{250}{\pi r^2}$

$h = \dfrac{250}{\pi (3.414) ^2}$

h = 6.8275 in

7 0

3 years ago

A psychologist wants to see if a certain company has fair hiring practices in an industry where 60% of the workers are men and 4

makvit [3.9K]

Answer:

A) $H_{0}$ : p=0.5 (At least half of the workers are women,fair)

B) $H_{a}$ : p<0.5 (Less than half of the workers are women,unfair)

C) critical value of the test statistic is 1.64 (one tailed)

D) Test statistic is ≈ 0.29

E) Since 0.29<1.64, we fail to reject the null hypothesis. There is no significant evidence that the company has unfair hiring practices at 0.05 significance level.

Step-by-step explanation:

Let p be the proportion of women workers in the company. Null and alternative hypotheses are

$H_{0}$ : p=0.5 (At least half of the workers are women,fair)

$H_{a}$ : p<0.5 (Less than half of the workers are women,unfair)

Test statistic can be found using the equation:

z= $\frac{p(s)-p}{\sqrt{\frac{p*(1-p)}{N} } }$ where

p(s) is the sample proportion of women workers ( $\frac{55}{107} =0.514$ )

p is the proportion assumed under null hypothesis. (0.5)

N is the sample size (55+52=107)

Then z= $\frac{0.514-0.5}{\sqrt{\frac{0.5*0.5}{107} } }$ ≈ 0.29

For alpha 0.05, critical value of the test statistic is 1.64 (one tailed)

Since 0.29<1.64, we fail to reject the null hypothesis. There is no significant evidence that the company has unfair hiring practices at 0.05 significance level.

4 0

3 years ago

-1(t+8)=-7.1 solve for t

Darina [25.2K]

Answer:

t = -0.9

Step-by-step explanation:

-1(t+8) = -7.1

(t+8) = 7.1

t = -0.9

7 0

3 years ago

Read 2 more answers

a skateboard park is a shape of a trapezoid this area is 550 square meters the bases or 15 meters in 35 meters what is the Heigh

anyanavicka [17]

Hello,

( 550 m² × 2 ) ÷ ( 35 m + 15 m )
→ 1 100 m² ÷ 50 m
→ 22 m

Bye :)

4 0

3 years ago

How do you simplify slope?

mojhsa [17]

Answer:

Sometimes this fraction can be further simplified by dividing the numerator and the denominator by their greatest common factor. ... Divide the numerator by this number. If the result is zero, the simplified slope of the line is also zero.

Step-by-step explanation:

3 0

3 years ago