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ICE Princess25 [194]
3 years ago
15

In 1924, the tempature in Fairfield, Montana, dropped from 63 degrees to 21 in 12 hour. What was the average hourly change in te

mpature
Mathematics
1 answer:
Drupady [299]3 years ago
8 0
Find the change
the change is 63-21=42
42 degrees in 12 hours
we want to find xdegrees/1hour
42/12=3.5 degrees per hour
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Ok so take 5 and divide that by 2 then whatever answer u get multiply that times 3.14 and are u solving for circumference
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The equation is y = 2/3x - 1
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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
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A.) 5 layers with 48 balls in each layer would equal 250 balls in the box
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B.) 15 layers with 48 balls in each layer would equal 720
(15x48=720)
7 0
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Answer:

divide the cost of the dog food by three and thats ur answer

Step-by-step explanation:

7 0
3 years ago
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