1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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

You might be interested in
How many times bigger is a group of 18 coins than a group of 3 coins?
Jlenok [28]

Answer:

6 times

Step-by-step explanation:

18 / 3 = 6

5 0
3 years ago
Read 2 more answers
PLEASE HELP
Ludmilka [50]

Answer:

C.

Step-by-step explanation:

The slope intercept form is:

y= mx +b

so you first want to start off by looking for the equation with y being the sum. In this case, there is only one, so you don't have to do anymore work.

5 0
3 years ago
According to the U.S. Department of Agriculture, the average American consumed 54.3 pounds (ap- proximately seven gallons) of sa
sladkih [1.3K]

Answer:

a) 0.11%

b) 55.99%

c) 0.25%

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Normally distributed with a mean of 54.3 pounds and a standard deviation of 14.5 pounds.

This means that \mu = 54.3, \sigma = 14.5

1. What percentage of Americans' annual salad and cooking oil consumption is less than 10 pounds?

The proportion is the pvalue of Z when X = 10. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{10 - 54.3}{14.5}

Z = -3.06

Z = -3.06 has a pvalue of 0.0011

0.0011*100% = 0.11%.

2. What percentage of Americans' annual salad and cooking oil consumption is between 35 and 60?

The proportion is the value of Z when X = 60 subtracted by the pvalue of Z when X = 35.

X = 60

Z = \frac{X - \mu}{\sigma}

Z = \frac{60 - 54.3}{14.5}

Z = 0.39

Z = 0.39 has a pvalue of 0.6517

X = 35

Z = \frac{X - \mu}{\sigma}

Z = \frac{35 - 54.3}{14.5}

Z = -1.33

Z = -1.33 has a pvalue of 0.0918

0.6517 - 0.0918 = 0.5599

0.5599*100% = 55.99%

3. What percentage of Americans' annual salad and cooking oil consumption is more than 95 pounds?

The proportion is 1 subtracted by the pvalue of Z when X = 95.

Z = \frac{X - \mu}{\sigma}

Z = \frac{95 - 54.3}{14.5}

Z = 2.81

Z = 2.81 has a pvalue of 0.9975

1 - 0.9975 = 0.0025

0.0025*100% = 0.25%

8 0
3 years ago
A population of beetles are growing according to a linear growth model. The initial population (week 0) is p0=6 and the populati
wel

Answer:

P(n)= p0 + 11(n)

Where p0= population of week 0

P(n) = population of n weeks

n= number of weeks

Step-by-step explanation:

Population of beetles in Week 0= 6

Population of beetles in Week 7= 83

From week 0 to week 7 there are 8 weeks.

But subtracting population of week 0 from population of week 7 gives

= 83-6

= 77

After the subtraction, we have 7 weeks remaining.

Dividing the remaining population by the number of weeks remaining

=77/7

= 11

For n number of weeks, population p of beetles

P(n)= p0 + 11(n)

Where p0= population of week 0

P(n) = population of n weeks

n= number of weeks

3 0
3 years ago
What is the nth term rule of the quadratic sequence below? 7, 14, 23, 34, 47, 62, 79
Julli [10]

Answer:

Tn = Tn-1 + 2(n-1) + 5

Kindly note that Tn-1 means T subscript n-1

Step-by-step explanation:

Here, we want an expression for the nth term.

First term is 7

Then first common difference is 7

second common difference is 7 + 2

Third common difference is 9 + 2

So within the common differences, the nth term is 7 + (n-1) 2

Now, the nth term of the series would be;

Tn = Tn-1 + 7 + 2(n-1)

Tn = Tn-1 + 7 + 2n -2

Tn = Tn-1 + 2n + 5

Now there is a fix to this,

n for the term is not the same n for the common difference.

the 7th term works with the 6th common. difference, while the 8th term work for the 7th common difference.

So we might need to rewrite the final expression as follows;

Tn = Tn-1 + 2(n-1) + 5

6 0
3 years ago
Other questions:
  • Write a program that prompts the user to read two integers and displays their sum . if anything but an integer is passed as inpu
    9·1 answer
  • TIME REMAINING
    13·2 answers
  • I need help with how to find 2 equations for thy problem
    5·1 answer
  • What is the product of (3x-9) and 6x↑2-2x+5 Write your answer in standard form.
    8·1 answer
  • Determine each unknown addend ___ + 41=-18
    11·1 answer
  • Approximate 5.824 to the nearest whole​
    11·1 answer
  • How does dating violence affect health? Click all that apply. ​
    13·2 answers
  • Find the product 1 1/4 x 5 3/5
    14·1 answer
  • Please help me! I will give brainly!
    8·2 answers
  • A person is connecting heat trace cable on pipe at the jobsite. The cable he or she is using is rated 2.5 watts/foot. How many f
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!