I’m pretty sure I know the answer but I just wanna check myself, thanks :)

Answer:

show me the choices

Step-by-step explanation:

so i qnswer ir

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

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Answer:

He has been saving for 41 weeks.

Step-by-step explanation:

492 is the total, we need to divide 492 by 12 to get how many weeks, 41 is the answer

Step-by-step explanation:

2vt= (ht²/2) - 2c - r

v= ((ht²/2) -2c -r) / 2t

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

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.

Answer:

more answers on wht

Step-by-step explanation:

Answer:

wdym more answers ? there isn't a question

Step-by-step explanation:

Answer:

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

largest 4 digit number : 9999

smallest 4 digit numbers : 1000

Difference = 9999 - 1000 = 8999

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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: does not

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

(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]

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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

===================================================

Explanation:

Choice B is one answer because -2 and 2 are additive inverses that add to -2+2 = 0

Choice D is a similar story. We have -5+5 = 0

In general, if x is some number then -x is its additive inverse. So we can say x+(-x) = 0 or -x+x = 0. In short, additive inverses add to 0.

Answer:

B and D

Step-by-step explanation:

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:

6 + 10v – 8w = 62

Step-by-step explanation:

Given the expression

6 + 10v – 8w

as

substituting the values in the expression

6 + 10v – 8w = 6 + 10(4) - 8(-2)

                      = 6 + 40 + 16

                      = 62

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

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:

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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:

-.1

Step-by-step explanation:

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:

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:

x=4

Step-by-step explanation:

9x-18 = x+14

9×-× = 14+18

8× = 32

X = 4

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:

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+9)-3

Step-by-step explanation:

Answer:

Step-by-step explanation:

Interest