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yaroslaw [1]
3 years ago
11

A cylindrical can is to have volume 1500 cubic centimeters. determine the radius and the height which will minimize the amount o

f material to be used. note that the surface area of a closed cylinder is s=2rh+2r2 and the volume of a cylindrical can is v=r2h.
Mathematics
1 answer:
Degger [83]3 years ago
8 0
Assuming R and H:
So volume is pir^2 * H = 1500 and H = 1500/(pir^2)  while surface area is A= 2pir*H + 2pir^2 
A = 2pir(r+h)= 2piR^2 + 2pir*1500/(pir^2)= 2piR^2 + 3000/r
For A to take minimum, get the derivative 4pir - 3000/R^2 and let it be 0 
4pir^3 - 3000 = 0 
r = cbrt(3000/(4pi)) ≈ 6.20
h = 1500/(pi(6.20)^2) ≈ 12.42
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A car travels at an avarage speed of 52 miles per hour how many miles does it travel in 4 hours and 15 minutes
vichka [17]

Answer:221 miles

Step-by-step explanation:

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8 0
4 years ago
Yesterday, Carmen went on a bike ride. Her average speed was 8 miles per hour. Today, she went on another ride, this time averag
Ilya [14]

Answer: the expression for the combined total number of miles she biked in the two days is

117 - 5x miles

Step-by-step explanation:

Let x be the number of hours she biked yesterday.

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Yesterday, Carmen went on a bike ride. Her average speed was 8 miles per hour. This means that the distance that she covered yesterday is 8x miles

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6 0
3 years ago
The data show the chest size and weight of several bears. Find the regression​ equation, letting chest size be the independent​
Ipatiy [6.2K]

Answer:

y = 16.3216X - 330.3904

322 pounds;

Result is significant

Step-by-step explanation:

Given the data:

Chest size, x : 41,54,44,55,39,51

Weight, Y : 328,528,418,580,296,503

Using technology, the prediction model obtained by fitting the data is :

y = 16.3216X - 330.3904

Where, x = chest size ; y = weight

The best predicted weight of a bear with chest size of 40 is

Put x = 40 in the equation :

y = 16.3216(40) - 330.3904

Y = 322.4736

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At α = 0.05

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Pvalue(0.986, 5) = 0.00198

Since, Pvalue < α ; result is significant at α = 0.05

8 0
3 years ago
PLEASE HELP I HAVE AN HOUR LEFT!!
Yuki888 [10]

The statement that correctly describes the horizontal asymptote of g(x) is:

Limit of g (x) as x approaches plus-or-minus infinity = 6, so g(x) has an asymptote at y = 6.

<h3>What are the asymptotes of a function f(x)?</h3>

  • The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.
  • The horizontal asymptote is the limit of f(x) as x goes to infinity, as long as this value is different of infinity.

In this problem, the function is:

g(x) = \frac{42x^3 - 15}{7x^3 - 4x^2 - 3}

The horizontal asymptote is given as follows:

y = \lim_{x \rightarrow \infty} g(x) = \lim_{x \rightarrow \infty} \frac{42x^3 - 15}{7x^3 - 4x^2 - 3} = \lim_{x \rightarrow \infty} \frac{42x^3}{7x^3} = \lim_{x \rightarrow \infty} 6 = 6

Hence the correct statement is:

Limit of g (x) as x approaches plus-or-minus infinity = 6, so g(x) has an asymptote at y = 6.

More can be learned about asymptotes at brainly.com/question/16948935

#SPJ1

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2 years ago
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