Can anyone help me please I don’t understand this one can you please help me I appreciate it but don’t give me the wrong answer because I need my grade to go up I’m so sorry for being picky

Answer:

[tex]r = 1.34[/tex]

Step-by-step explanation:

Given

Solid = Cylinder + 2 hemisphere

[tex]Volume = 10cm^3[/tex]

Required

Determine the radius (r) that minimizes the surface area

First, we need to determine the volume of the shape.

Volume of Cylinder (V1) is:

[tex]V_1 = \pi r^2h[/tex]

Volume of 2 hemispheres (V2) is:

[tex]V_2 = \frac{2}{3}\pi r^3 +\frac{2}{3}\pi r^3[/tex]

[tex]V_2 = \frac{4}{3}\pi r^3[/tex]

Volume of the solid is:

[tex]V = V_1 + V_2[/tex]

[tex]V = \pi r^2h + \frac{4}{3}\pi r^3[/tex]

Substitute 10 for V

[tex]10 = \pi r^2h + \frac{4}{3}\pi r^3[/tex]

Next, we make h the subject

[tex]\pi r^2h = 10 - \frac{4}{3}\pi r^3[/tex]

Solve for h

[tex]h = \frac{10}{\pi r^2} - \frac{\frac{4}{3}\pi r^3 }{\pi r^2}[/tex]

[tex]h = \frac{10}{\pi r^2} - \frac{4\pi r^3 }{3\pi r^2}[/tex]

[tex]h = \frac{10}{\pi r^2} - \frac{4r }{3}[/tex]

Next, we determine the surface area

Surface area (A1) of the cylinder:

Note that the cylinder is covered by the 2 hemisphere.

So, we only calculate the surface area of the curved surface.

i.e.

[tex]A_1 = 2\pi rh[/tex]

Surface Area (A2) of 2 hemispheres is:

[tex]A_2 = 2\pi r^2+2\pi r^2[/tex]

[tex]A_2 = 4\pi r^2[/tex]

Surface Area (A) of solid is

[tex]A = A_1 + A_2[/tex]

[tex]A = 2\pi rh + 4\pi r^2[/tex]

Substitute [tex]h = \frac{10}{\pi r^2} - \frac{4r }{3}[/tex]

[tex]A = 2\pi r(\frac{10}{\pi r^2} - \frac{4r }{3}) + 4\pi r^2[/tex]

Open bracket

[tex]A = \frac{2\pi r*10}{\pi r^2} - \frac{2\pi r*4r }{3} + 4\pi r^2[/tex]

[tex]A = \frac{2*10}{r} - \frac{2\pi r*4r }{3} + 4\pi r^2[/tex]

[tex]A = \frac{20}{r} - \frac{8\pi r^2 }{3} + 4\pi r^2[/tex]

[tex]A = \frac{20}{r} + \frac{-8\pi r^2 }{3} + 4\pi r^2[/tex]

Take LCM

[tex]A = \frac{20}{r} + \frac{-8\pi r^2 + 12\pi r^2}{3}[/tex]

[tex]A = \frac{20}{r} + \frac{4\pi r^2}{3}[/tex]

Differentiate w.r.t r

[tex]A' = -\frac{20}{r^2} + \frac{8\pi r}{3}[/tex]

Equate A' to 0

[tex]-\frac{20}{r^2} + \frac{8\pi r}{3} = 0[/tex]

Solve for r

[tex]\frac{8\pi r}{3} = \frac{20}{r^2}[/tex]

Cross Multiply

[tex]8\pi r * r^2 = 20 * 3[/tex]

[tex]8\pi r^3 = 60[/tex]

Divide both sides by [tex]8\pi[/tex]

[tex]r^3 = \frac{60}{8\pi}[/tex]

[tex]r^3 = \frac{15}{2\pi}[/tex]

Take [tex]\pi = 22/7[/tex]

[tex]r^3 = \frac{15}{2 * 22/7}[/tex]

[tex]r^3 = \frac{15}{44/7}[/tex]

[tex]r^3 = \frac{15*7}{44}[/tex]

[tex]r^3 = \frac{105}{44}[/tex]

Take cube roots of both sides

[tex]r = \sqrt[3]{\frac{105}{44}}[/tex]

[tex]r = \sqrt[3]{2.38636363636}[/tex]

[tex]r = 1.33632535155[/tex]

[tex]r = 1.34[/tex] (approximated)

Hence, the radius is 1.34cm

The radius of the cylinder that produces the minimum surface area is 1.34cm and this can be determined by using the formula area and volume of cylinder and hemisphere.

Given :

The volume of a cylinder is given by:

[tex]\rm V = \pi r^2 h[/tex]

The total volume of the two hemispheres is given by:

[tex]\rm V' = 2\times \dfrac{2}{3}\pi r^3[/tex]

[tex]\rm V' = \dfrac{4}{3}\pi r^3[/tex]

Now, the total volume of the solid is given by:

[tex]\rm V_T = \pi r^2 h+\dfrac{4}{3}\pi r^3[/tex]

Now, substitute the value of the total volume in the above expression and then solve for h.

[tex]\rm 10 = \pi r^2 h+\dfrac{4}{3}\pi r^3[/tex]

[tex]\rm h = \dfrac{10}{\pi r^2}-\dfrac{4r}{3}[/tex]

Now, the surface area of the curved surface is given by:

[tex]\rm A = 2\pi r h[/tex]

Now, the surface area of the two hemispheres is given by:

[tex]\rm A'=2\times (2\pi r^2)[/tex]

[tex]\rm A'=4\pi r^2[/tex]

Now, the total area is given by:

[tex]\rm A_T = 2\pi rh+4\pi r^2[/tex]

Now, substitute the value of 'h' in the above expression.

[tex]\rm A_T = 2\pi r\left(\dfrac{10}{\pi r^2}-\dfrac{4r}{3}\right)+4\pi r^2[/tex]

Simplify the above expression.

[tex]\rm A_T = \dfrac{20}{r} + \dfrac{4\pi r^2}{3}[/tex]

Now, differentiate the total area with respect to 'r'.

[tex]\rm \dfrac{dA_T}{dr} = -\dfrac{20}{r^2} + \dfrac{8\pi r}{3}[/tex]

Now, equate the above expression to zero.

[tex]\rm 0= -\dfrac{20}{r^2} + \dfrac{8\pi r}{3}[/tex]

Simplify the above expression in order to determine the value of 'r'.

[tex]8\pi r^3=60[/tex]

r = 1.34 cm

For more information, refer to the link given below:

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Answer:

the perm will cost $60

Step-by-step explanation:

take away $5 from the total because Its a set amount that's already known

which leaves 90 which if you  take 30 away you are left with 60 its twice the amount of the haircut, I didn't really do any math techniques so I'm sorry that my explanation is weird, I hope this helped

Answer:

v = 1808,64cm³

Step-by-step explanation:

big cone:

a = pi.r²

a = 3,14x12²

a = 452,16cm²

v = a.h/3

v = 452,16x12/3

v = 1808,64cm³ (that's a three)

you got the point, now you can do the others... kinda of

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[tex]y = f(x) = 2x + 5[/tex]

[tex]f(2) = 2(2) + 5[/tex]

[tex]f(2) = 4 + 5[/tex]

[tex]f(2) = 9[/tex]

Thus ;

[tex]( \: 2 \: , \: 9 \: )[/tex]

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Answer:

9

Step-by-step explanation:

Answer:

The result when 65 is increased by 53% is 34.45

Step-by-step explanation:

Answer:

34.45

Step-by-step explanation:

i hope you get it right

Answer:

more answers on wht

Step-by-step explanation:

Answer:

wdym more answers ? there isn't a question

Step-by-step explanation:

Step-by-step explanation:

2vt= (ht²/2) - 2c - r

v= ((ht²/2) -2c -r) / 2t

v= ht/4 - c/t - r/2t

Answer:

a

 [tex]z = - 2.12[/tex]

b

 [tex]p- value = 0.017003[/tex]

c

There is sufficient evidence to show that the population mean is less than 20

d

 [tex]z_{0.05} =- 1.645[/tex]

e

   The decision rule is  

Reject the null hypothesis

f

The conclusion is  

  There is sufficient evidence to show that the population mean is less than 20.

Step-by-step explanation:

From the question we are told that

   The null hypothesis  is  [tex]H_o: \mu = 20[/tex]

    The alternative hypothesis is  Ha: µ < 20

    The sample size is  n  =  50  

    The sample mean is  [tex]\= x = 19.4[/tex]

    The level of significance is  [tex]\alpha = 0.05[/tex]

      The population standard deviation is  [tex]\sigma = 2[/tex]

Generally the test statistics is mathematically represented as

       [tex]z = \frac{\= x - \mu }{ \frac{\sigma }{ \sqrt{n} } }[/tex]

=>    [tex]z = \frac{19.4 - 20 }{ \frac{2}{ \sqrt{50 } } }[/tex]

=>    [tex]z = - 2.12[/tex]

From the z table  the area under the normal curve to the left corresponding to  -2.12  is  

       [tex](P< -2.12) = 0.017003[/tex]

Generally the p-value is  

        [tex]p- value = 0.017003[/tex]

From values obtained we see that [tex]p-value < \alpha[/tex] hence  

   The decision rule is  

Reject the null hypothesis

   The conclusion is  

  There is sufficient evidence to show that the population mean is less than 20.

Generally form the normal distribution table the critical value at a level of significance of  [tex]\alpha = 0.05[/tex] is

        [tex]z_{0.05} =- 1.645[/tex]

Generally given that  [tex]z < z_{0.05}[/tex]

   The decision rule is  

Reject the null hypothesis

   The conclusion is  

  There is sufficient evidence to show that the population mean is less than 20.

Answer:

(x+9)-3

Step-by-step explanation:

Answer:

The remainder is...

7

Hope this helps!!

Step-by-step explanation:

Answer: it’s c

Step-by-step explanation:

Answer:

x = 30

Step-by-step explanation:

Since this is a right triangle,

90 = (x + 20) + (x + 10)

90 = x + x + 20 + 10

90 = 2x + 30

90 - 30 = 2x

60 = 2x

60/2 = 2x/2

30 = x

Check:

x + 20

30 + 20 = 50

x + 10

30 + 10 = 40

50 + 40 = 90

Hope this helps!

Answer:

show me the choices

Step-by-step explanation:

so i qnswer ir

Answer:

Step-by-step explanation:

Interest

Answer:

Yes! (it’s making me write 20 letters so yes is ur answer ok cool)

Answer:

x=22

Step-by-step explanation:

3x+3+27+x+3+2x+18=180

6x+48=180

6x=132

x=22

Answer:

Step-by-step explanation

Given

a snail moves through a garden and travels 1 1/8 meters in 1 1/2 Minutes.

Solution

So

the snails rate =11/8÷11/2

= 1/4Minutes per Meters

So the answer is 1/4 minute per meter

It is the quantity of an amount of something at a rate of one of another quantity.

If a snail moves through a garden and travels 1 1/8 meters in 1 1/2 Minutes.

The snail's rate in minutes per meter is 4/3 minutes.

It is the quantity of an amount of something at a rate of one of another quantity.

Example:

3 miles in 60 minutes.

1 mile in 20 minutes.

We have,

Snail travels:

[tex]1\frac{1}{8}[/tex] meters = [tex]1\frac{1}{2}[/tex] minutes

9/8 meters = 3/2 minutes

Multiplying 8/9 on both sides.

1 meters = 8/9 x 3/2 minutes

1 meter = 4/3 minutes

This means that the snail's rate in minutes per meter is 4/3 minutes.

Thus,

If a snail moves through a garden and travels 1 1/8 meters in 1 1/2 Minutes.

The snail's rate in minutes per meter is 4/3 minutes.

Learn more about unit rates here:

https://brainly.com/question/11258929

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Answer:

Slope= -0.5

Step-by-step explanation:

Answer:

1/2x

Step-by-step explanation:

You go down one step and run 2 steps

Answer:

x=4

Step-by-step explanation:

9x-18 = x+14

9×-× = 14+18

8× = 32

X = 4

(13−0)

           = 10/13

(10−0)

​13,10

Slope of the given line is [tex]\frac{10}{13}[/tex] and the equation of the line is [tex]10x - 13y = 0[/tex].

The slope of a line(m) that passes through points (x, y) and (x, y) is

[tex]m = \frac{y_{2} - x_{1}}{x_{2} - x_{1}}[/tex]

The given line passes through points (0, 1.3) and (0, 1).

Therefore, slope of the line is

[tex]m = \frac{y_{2} - x_{1}}{x_{2} - x_{1}} = \frac{1 - 0}{1.3 - 0} = \frac{10}{13}[/tex]

Now, the line passes through the point (2.6, 2).

Putting this equation in slope-intercept form, we get:

[tex]2 = \frac{10}{13}(2.6) + c\\c = 2 - 2\\c = 0[/tex]

The equation of the line will be:

[tex]y = \frac{10}{13}x\\10x - 13y = 0[/tex]

Learn more about slope of a line here: https://brainly.com/question/21504186

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Answer:

A) f(x) = 0.85x

B) g(x) = x - 1500

C) g(f(x)) = $14650

D) f(g(x)) = $14875

Step-by-step explanation:

A) The list price is x and a 15% discount is applied.

Thus;

f(x) = x - 15%x

f(x) = 0.85x

B) We are told that the manufacturer offers a $1500 rebate for each purchase of a car.

Thus, the function g(x) to represent the price after the rebate is applied is;

g(x) = x - 1500

C)if the discount is applied before the rebate, the function is;

g(f(x))

Now,

f(x) = 0.85(19000)

f(x) = 16150

g(x) = x - 1500

Thus;

g(x) = 16150 - 1500

g(x) = $14650

D) If discount after rebate, then we have; f(g(x))

g(x) = 19000 - 1500

g(x) = 17500

f(g(x)) = 0.85(17500)

f(g(x)) = $14875

Answer:

b

Step-by-step explanation:

absoulute value is never negative.

Answer:

Step-by-step explanation:

holdup im gonna help

Answer:

x = 2

Step-by-step explanation:

2[3(3x - 1)] = 5(2x + 2)

18x - 6 = 10x + 10

8x = 16

x = 2

Answer:

b c and a

Step-by-step explanation:

Answer:

A, B, C

Step-by-step explanation:

Answer:

his remarkable mathematical flow continued without interruption – in fact, it increased.

Step-by-step explanation:

Answer: does not

Step-by-step explanation: I think a linear equation is y=mx+b

Answer:

y=5/3x-3.4

Step-by-step explanation:

slope is 5/3

Answer:

[tex]\frac{3}{5}[/tex]

Step-by-step explanation:

In slope-intercept form of linear equation y = mx + b , "m" is the slope

3x - 5y = 17

- 5y = - 3x + 17

y = [tex]\frac{3}{5}[/tex] x - [tex]\frac{17}{5}[/tex]  

m = [tex]\frac{3}{5}[/tex]

Answer:

[tex] y = 3x - 2 [/tex]

Step-by-step explanation:

The equation that describes how x

and y are related is given in the slope-intercept form, [tex] y = mx + b [/tex]

Where, m = slope, and b = y-intercept.

Let's find the value of m and b using the table of values given.

Using two of the pairs given, (-2, -8) and (-1, -5),

[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-5 -(-8)}{-1 -(-2)} = \frac{3}{1} = 3 [/tex]

Substitute x = -2, y = -8, and m = 3 in [tex] y = mx + b [/tex] to find the value of b.

Thus:

[tex] -8 = (3)(-2) + b [/tex]

[tex] -8 = -6 + b [/tex]

Add 6 to both sides

[tex] -8 + 6 = b [/tex]

[tex] -2 = b [/tex]

Substitute m = 3 and b = -2 in [tex] y = mx + b [/tex].

The equation that describes how x

and y are related would be:

[tex] y = 3x - 2 [/tex]

Answer:

Step-by-step explanation:

The rate of change for the line that goes through the points (8,14) and (11, 19.25)​ is known as the slope expressed as;

slope m = y2-y1/x2-x1

Substitute the coordinate pairs into the formula;

m = 19.25-14/11-8

m = 5.25/3

m = 1.75

Hence the rate of change for the line is 1.75.