Which number has a value between -8.423 and -8.395?

A. -8.1
B. -8.75
C. - 8 1/2
D. 8 2/5

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:

https://brainly.com/question/11952845

No change in area if sides of rectangle are equal.

Hope this helps.

Answer:

$1,815

Step-by-step explanation:

Use the simple interest formula, I = prt

Plug in the values we know:

I = prt

I = (1,500)(0.07)(3)

I = 315

Add this to the original amount:

1500 + 315

= 1,815

So, John will have $1,815 in his account after 3 years.

Answer:

I suppose that you want to find which gym will be cheaper for you.

We have two equations:

• Gym A: 30m + 50

• Gym B: 10m + 100

First, let's find the value of m such that both gyms cost exactly the same:

30*m + 50 = 10*m + 100

Let's solve this for m

30*m - 10*m = 100 - 50

20*m = 50

m = 50/20 = 2.5

now:

for m < 2.5, Gym A will be cheaper, because the y-intercept is smaller.

for m > 2.5, Gym B will be cheaper, because the slope is smaller,

Then depending on the number of months that Martin wants to go to the gym, he can se the info above to pick the one that is cheaper.

Answer: x=6/5

Step-by-step explanation:

Answer:

6/5

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

The percent error of the newspaper's estimate once the season is over will be 4%.

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

A school newspaper estimates that their academic team will win 25 out of 30 matches for the season.

Then the percentage will be given as,

P = (25 / 30) x 100

P = 0.8333 x 10

P = 83.33%

After 15 matches, they won 12. Then the percentage will be given as,

P = (12 / 15) x 100

P = 0.80 x 100

P = 80%

If the team continues winning at this rate. Then the percent error of the newspaper's estimate once the season is over will be

P = [(83.33 - 80) / (83.33)] x 100

P = 0.04 x 100

P = 4%

More about the percentage link is given below.

https://brainly.com/question/8011401

#SPJ5

Answer:

4y + 6x ≤ 96

12y + 2x ≤ 96

Step-by-step explanation:

Paper shredders produced :

Home :

Assembling time = 4 hours

Finishing work unit = 12

Office :

Assembling time = 6 hours

Finishing work unit = 2

Maximum number of assembly hours = 96 / day

Maximum number of finishing hours = 96/ day

Let

x = the number of office model shredders produced per day and

y = the number of home model shredders produced per day

(office Assembly hours x Number of office model) + (Assembly hours * number home models)

OFFICE MODEL:

Assembly operation :

Home + office ≤ 96

4y + 6x ≤ 96

Finishing operation :

Home + office ≤ 96

12y + 2x ≤ 96

Answer:

x=6

Step-by-step explanation:

Let X = Rob's weekly allowance

If he spent 1/2 of it on candy, then he had 1/2 of it left (1/2)X

After he earned $6 for cleaning the oven, he had $9.

So,

(1/2)X + 6 = 9

(1/2)X = 3

X = 6

Answer:

Daisy, Ivan, Patrick, Laura

Step-by-step explanation:

That's just the numbers biggest to smallest.

Answer:

4.

Step-by-step explanation:

(x^2 + 7x - 9) + (3x^2 - 2x) + (x^2 + 7x - 9) + (3x^2 - 2x)

x^2 + 7x - 9 + 3x^2 - 2x + x^2 + 7x - 9 + 3x^2 - 2x

Rearranging order:

3x^2 + 3x^2 + x^2 + x^2 + 7x + 7x - 2x - 2x - 9 - 9

Combine like terms

8x^2 + 10x - 18

Answer:43

Step-by-step explanation:

Answer:

69 miles per hour

Step-by-step explanation:

car travels 23 miles in 20 min

So 20 min=20/60hour

=1/3. hour

Speed of the car=23÷1/3

=69 miles/hour

So the final answer is 69miles/hour

Answer:

$69.21

Step-by-step explanation:

Since the box has a square base the length and breadth of the box will be equal. Let it be [tex]x[/tex]

Let h be the height of the box

V = Volume of the box = [tex]620\ \text{cm}^3[/tex]

[tex]x^2h=620\\\Rightarrow h=\dfrac{620}{x^2}[/tex]

Now surface area of the box with an open top is given

[tex]s=x^2+4xh\\\Rightarrow s=x^2+4x\dfrac{620}{x^2}\\\Rightarrow s=x^2+\dfrac{2480}{x}[/tex]

Differentiating with respect to x we get

[tex]\dfrac{ds}{dx}=2x-\dfrac{2480}{x^2}[/tex]

Equating with zero

[tex]0=2x-\dfrac{2480}{x^2}\\\Rightarrow 2x^3-2480=0\\\Rightarrow x^3=\dfrac{2480}{2}\\\Rightarrow x=(1240)^{\dfrac{1}{3}}\\\Rightarrow x=10.74[/tex]

Double derivative of the function

[tex]\dfrac{d^2s}{ds^2}=2+\dfrac{4960}{x^3}=2+\dfrac{4960}{1240}\\\Rightarrow \dfrac{d^2s}{ds^2}=6>0[/tex]

So, x at 10.74 is the minimum value of the function.

[tex]h=\dfrac{620}{x^2}\\\Rightarrow h=\dfrac{620}{10.74^2}\\\Rightarrow h=5.37[/tex]

So, minimum length and breadth of the box is 10.74 cm while the height of the box is 5.37 cm.

The total area of the sides is [tex]4xh=4\times 10.74\times 5.37=230.7\ \text{cm}^2[/tex]

The area of the base is [tex]x^2=10.74^2=115.35\ \text{cm}^2[/tex]

Cost of the base is $0.40 per square cm

Cost of the side is  $0.10 per square cm

Minimum cost would be

[tex]230.7\times 0.1+0.4\times 115.34=\$69.21[/tex]

The minimum cost of the box is 69.21 dollars.

Answer:

The first one

Answer:

146.5619<x<153.4381

Step-by-step explanation:

The formula for calculating the confidence interval is expressed as:

CI =  xbar±(z*s/√n)

xbar is the mean = 150

s is the standard deviation = 15.50

n is the sample size = 55

z is the z score at 90% CI = 1.645

Substitute and get CI

CI = 150±(1.645*15.50/√55)

CI = 150±(1.645*15.50/7.4162)

CI = 150±(1.645*2.09)

CI = 150±(3.4381)

CI = (150-3.4381, 150+3.4381)

CI = (146.5619, 153.4381)

CI = 146.5619<x<153.4381

Hence a 90% confidence interval for the population mean repair cost 146.5619<x<153.4381

The minimum cost is approximately $147 while the maximum cost of the refrigerator is $153

Answer:

7) y = -2

8) x = 4

Step-by-step explanation:

Any straight horizontal/vertical line you find will be x= or y=. The vertical lines are always x= because they only touch the x axis. It's the opposite for horizontal lines. For example, on number 7, the line touches -2 on the y axis. That's why it's "y=-2". Same goes for 8. the line only touches 4.

I hope this helped and wasn't confusing!

Answer:

See below.

Step-by-step explanation:

What you wrote means:

[tex] r = \dfrac{n}{2}(b + H) [/tex]

If that is what you meant, then the answer is:

[tex] \dfrac{2r}{n} = b + H [/tex]

[tex] H = \dfrac{2r}{n} - b [/tex]

On the other hand, if this is what you meant:

[tex] r = \dfrac{n}{2(b + H)} [/tex]

then the answer is:

[tex] 2r(b + H) = n [/tex]

[tex] 2rb + 2rH = n [/tex]

[tex] 2rH = n - 2rb [/tex]

[tex] H = \dfrac{n - 2rb}{2r} [/tex]

Answer:

Step-by-step explanation:

[tex]\frac{n}{2}(b + H) = r\\\\b +H = r * \frac{2}{n}\\\\b + H = \frac{2r}{n}\\\\H = \frac{2r}{n} - b[/tex]

Answer:

50 golf balls

Step-by-step explanation:

200/4 is 50. I did that because it says the golf balls are DIVIDED into 4 smaller buckets.

To check the answer you do 50 times four.

Answer:

50 in each small bucket

Answer:

the answer is c

Step-by-step explanation:hope this helps

Answer:

C or the third option, 3/4 x + 10

Step-by-step explanation:

100% correct please mark brainlist. HAVE A GREAT DAY

The given expression is

=ab+cd+ef+gh

The meaning of expression is equal to terms which contains variables and constants and operation between them is Addition, Subtraction,  Multiplication and Division.

→The expression consists of four terms which are, ab, cd, ef, and gh.

→Each term contains

Two factors.

plz mark as brainliest

Answer:

3/5

Step-by-step explanation:

Both can be divided by 5. So, 15 divided by 5 is 3, and 25 divided by 5 is 5! Hoped this helped :)

Answer:

65

Step-by-step explanation:

just took the quiz.com

Answer:

y = -2x - 3

Step-by-step explanation:

Given:

Equation of -x +2y =4

Point of (-2,1)

-x + 2y = 4

y = x/2 + 2 or y = 1/2x + 2

Which means the equation's slope is m = 1/2.

The slope of the perpendicular line is negative inverse which is m = -2.

Now we have an equation of y = -2x + a.

Use (-2, 1) to find a:

1 = (-2)(-2) + a

a = -3

y = - 2x - 3

Answer:

Step-by-step explanation:

From the given information:

[tex]R_{in} = ( \dfrac{1}{2} \ lb/gal) (6)\ gal /min \\ \\R_{in} = 3 \ lb/min[/tex]

Given that the solution is pumped at a slower rate of 4gal/min

Then:

[tex]R_{out} = \dfrac{4A}{100+(6-4)t}[/tex]

[tex]R_{out}= \dfrac{2A}{50+t}[/tex]

The differential equation can be expressed as:

[tex]\dfrac{dA}{dt}+ \dfrac{2}{50+t}A = 3 \ \ \ ... (1)[/tex]

Integrating the linear differential equation; we have::

[tex]\int_c \dfrac{2}{50 +t}dt = e^{2In |50+t|[/tex]

[tex]\int_c \dfrac{2}{50 +t}dt = (50+t)^2[/tex]

multiplying above integrating factor fields; we have:

[tex](50 +t)^2 \dfrac{dA}{dt} + 2 (50 + t)A = 3 (50 +t)^2[/tex]

[tex]\dfrac{d}{dt}\bigg [ (50 +t)^2 A \bigg ] = 3 (50 +t)^2[/tex]

[tex](50 + t)^2 A = (50 + t)^3+c[/tex]

A = (50 + t) + c(50 + t)²

Using the given conditions:

A(0) = 20

⇒ 20 = 50 + c (50)⁻²

-30 = c(50) ⁻²

c = -30 × 2500

c =  -75000

A = (50+t) - 75000(50 + t)⁻²

The no. of pounds of salt in the tank after 35 minutes is:

A(35) = (50 + 35) - 75000(50 + 35)⁻²

A(35) = 85 - [tex]\dfrac{75000}{7225}[/tex]

A(35) =69.6193 pounds

A(35) [tex]\simeq[/tex] 70 pounds

Thus; the number of pounds of salt in the tank after 35 minutes is 70 pounds.

Report that other guy smh... but im not quite too sure but i believe the answer you were looking for was C. The total cost will increase by 4$ every 3 games bowled :D