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3 years ago

I dont know how to do geometry like that and i need help on my assignment

Mathematics

2 answers:

bearhunter [10]3 years ago

8 0

Answer:

Step-by-step explanation: Can you ask your teacher? Or no?

shusha [124]3 years ago

6 0

I’m going from left to right on answers, just so you know.
Alternate interior, vertical, alternate exterior, same side interior, same side exterior, same side interior, corresponding.

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A cylinder shaped can needs to be constructed to hold 500 cubic centimeters of soup. The material for the sides of the can costs

iogann1982 [59]

Answer:

r=3.628cm

h=12.093cm

Step-by-step explanation:

For this problem we are going to use principles, concepts and calculations from multivariable calculus; mainly we are going to use the Lagrange multipliers method. This method is thought to help us to find a extreme value of a multivariable function 'F' given a restriction 'G'. F represents the function that we want to optimize and G is just a relation between the variables of which F depends. The Lagrange method for just one restriction is:

$\nabla F=\lambda \nabla G$

First, let's build the function that we want to optimize, that is the cost. The cost is a function that must sum the cost of the sides material and the cost of the top and bottom material. The cost of the sides material is the unitary cost (0.03) multiplied by the sides area, which is $A_s=2\pi rh$ for a cylinder; while the cost of the top and bottom material is the unitary cost (0.05) multiplied by the area of this faces, which is $A_{TyB}=2\pi r^2$ for a cylinder.

So, the cost function 'C' is:

$C=2\pi rh*0.03+2\pi r^2*0.05\\C=0.06\pi rh+0.1\pi r^2$

The restriction is the volume, which has to be of 500 cubic centimeters:

$V=500=\pi r^2h\\500=\pi hr^2$

So, let's apply the Lagrange multiplier method:

$\nabla C=\lambda \nabla V\\\frac{\partial C}{\partial r}=0.06\pi h+0.2\pi r\\\frac{\partial C}{\partial h}=0.06\pi r\\\frac{\partial V}{\partial r}=2\pi rh\\\frac{\partial V}{\partial h}=\pi r^2\\(0.06\pi h+0.2\pi r,0.06\pi r)=\lambda (2\pi rh,\pi r^2)$

At this point we have a three variable (h,r, λ)-three equation system, which solution will be the optimum point for the cost (the minimum). Let's write the system:

$0.06\pi h+0.2\pi r=2\lambda \pi rh\\0.06\pi r=\lambda \pi r^2\\500=\pi hr^2$

(In this kind of problems always the additional equation is the restricion, in this case, V=500).

Let's divide the first and second equations by π:

$0.06h+0.2r=2\lambda rh\\0.06r=\lambda r^2\\500=\pi hr^2$

Isolate λ from the second equation:

$\lambda =\frac{0.06}{r}$

Isolate h from the third equation:

$h=\frac{500}{\pi r^2}$

And then, replace λ and h in the first equation:

$0.06*\frac{500}{\pi r^2} +0.2r=2*(\frac{0.06}{r})r\frac{500}{\pi r^2} \\\frac{30}{\pi r^2}+0.2r= \frac{60}{\pi r^2}$

Multiply all the resultant equation by $\pi r^{2}$ :

$30+0.2\pi r^3=60\\0.2\pi r^3=30\\r^3=\frac{30}{0.2\pi } =\frac{150}{\pi}\\r=\sqrt[3]{\frac{150}{\pi}}\approx 3.628cm$

Then, find h by the equation $h=\frac{500}{\pi r^2}$ founded above:

$h=\frac{500}{\pi r^2}\\h=\frac{500}{\pi (3.628)^2}=12.093cm$

4 0

3 years ago

If f(x) = x2 and g(x) =1/ 2x+3, find g(f(-1)).

Dvinal [7]

-1=1/2x+3
2=1/2x
(2)2=1/2x(2)
4=x
Answer: x=4

5 0

3 years ago

The Jacksons went on a 700 mile trip. On the first day they drove 6 and 2/3 hours and on the second day the drove 5 and 3/4 hour

likoan [24]

Answer:

Step-by-step explanation:

Total number of miles is 700.

On the first day, they drove 6 and 2/3 hours. We would convert 6 and 2/3 hours to improper fraction. It becomes 20/3 hours. On the second day, they drove 5 and 3/4 hours. Converting to improper fraction, it becomes 23/4 hours. Total number of hours that they drove during the first two days is the sum of hours driven on the first day and hours driven on the Second day. It becomes

20/3 + 23/4 = (80 + 69)/12

= 149/12 hours

7 0

3 years ago

Least to greatest<br><br>35%, 32/100, 1/3, .305, 3/10

Goryan [66]

Answer: 3/10 , 32/100 , 1/3 , 35% , 305

Step-by-step explanation:

1. Change 3/10 to a decimal

= 0.3

2. change 32/100 to a decimal

=0.32

3. Change 1/3 to a decimal

=0.3

4. Order and Done !

6 0

3 years ago

Read 2 more answers

In one city, 3,546 people attended a concert but in another city, 9,238 people attended the same band's concert. Estimate how ma

Angelina_Jolie [31]

The answer is 5,7000

7 0

3 years ago

I dont know how to do geometry like that and i need help on my assignment ​

I dont know how to do geometry like that and i need help on my assignment