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diamong [38]
3 years ago
14

You have been asked to design a can shaped like right circular cylinder that can hold a volume of 432π-cm3. What dimensions of t

he can (radius and height) will use the least amount of material?(Hint: The lightest can will be the can with the smallest surface area.)
Mathematics
1 answer:
rosijanka [135]3 years ago
3 0

Answer:

Height = 12cm

Radius = 6cm

Step-by-step explanation:

Given

Represent volume with v, height with h and radius with r

V = 432\pi

Required

Determine the values of h and r that uses the least amount of material

Volume is calculated as:

V = \pi r^2h\\

Substitute 432π for V

432\pi = \pi r^2h

Divide through by π

432 = r^2h

Make h the subject:

h = \frac{432}{r^2}

Surface Area (A) of a cylinder is calculated as thus:

A=2\pi rh+2\pi r^2

Substitute \frac{432}{r^2} for h in A=2\pi rh+2\pi r^2

A=2\pi r(\frac{432}{r^2})+2\pi r^2

A=2\pi (\frac{432}{r})+2\pi r^2

Factorize:

A=2\pi (\frac{432}{r} + r^2)

To minimize, we have to differentiate both sides and set A' = 0

A'=2\pi (-\frac{432}{r^2} + 2r)

Set A' = 0

0=2\pi (-\frac{432}{r^2} + 2r)

Divide through by 2\pi

0= -\frac{432}{r^2} + 2r

\frac{432}{r^2} = 2r

Cross Multiply

2r * r^2 = 432

2r^3 = 432

Divide through by 2

r^3 = 216

Take cube roots of both sides

r = \sqrt[3]{216}

r = 6

Recall that:

h = \frac{432}{r^2}

h = \frac{432}{6^2}

h = \frac{432}{36}

h = 12

Hence, the dimension that requires the least amount of material is when

Height = 12cm

Radius = 6cm

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Korvikt [17]

Answer:

g(15)=93.8\%

see the explanation

Step-by-step explanation:

Let

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g(x) ----> the percent of people 25 years and older who have completed at least high school

we know that

g(x)=0.008x^2+0.42x+87.5

so

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substitute

g(15)=0.008(15)^2+0.42(15)+87.5=93.8\%

That means

In the year 2023 (2008+15) the percent of people 25 and older completing at least high school will be 93.8%

5 0
3 years ago
Please help!! and please show the work and the answer!!
kumpel [21]

Company 1: (24 + 26 + 28 + 23 + 21) / 5 (this is how many numbers added together) = 24.4

Company 2: (6 + 32 + 9 + 31 + 21) / 5 = 19.8

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Company 4: (13 + 10 + 45 + 12 + 15) / 5 = 19

Company 1 has the longest average commute time per employee.

5 0
3 years ago
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Shalnov [3]
I hope this is the correct way to solve one of these.

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4 0
2 years ago
Please assist me with this problem. <br><br>​
Sladkaya [172]

Answer:

4

(We didn't even need to use (9,6) )

Step-by-step explanation:

The slope-intercept form a line is y=mx+b where m is the slope and b is the y-intercept.

We are given the line we are looking for has the same y-intercept as x+2y=8.

So if we put x+2y=8 into y=mx+b form we can actually easily determine the value for b.

So we are solving x+2y=8 for y:

x+2y=8

Subtract x on both sides:

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Divide both sides by 2:

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Separate the fraction:

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y=(-x/2)+4

Comparing this to y=mx+b we see that b is 4.

So the y-intercept is 4.

Again since we know that the line we are looking for has the same y-intercept, then the answer is 4 since the question is what is the y-intercept.

4

5 0
3 years ago
I don't understand how you do it
Alekssandra [29.7K]
Container A:
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container B:
y=-10x+1000
same thing with a container B
-6x+800=-10x+1000  =   800-6x=1000-10x
6 0
3 years ago
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