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vladimir2022 [97]
3 years ago
9

In the diagram, MQ = QP = PO = ON. Triangles Q M P, M P N, and P N O are connected. Sides Q M, Q P, P O, and N O are congruent.

If NP is greater than MP, which must be true? Segment OP is longer than segment MQ. Segment MN has the same length as segment MP. The measure of angle Q equals the measure of angle O. Angle O is larger than angle Q.
Mathematics
1 answer:
aliya0001 [1]3 years ago
7 0

Answer:

MQ IS GREATER I THINK I GAD THAT SAME QUESTION

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A soup can in the shape of a right circular cylinder is to be made from two materials. The material for the side of the can cost
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Answer:

Radius = 1.12 inches and Height = 4.06 inches

Step-by-step explanation:

A soup can is in the shape of a right circular cylinder.

Let the radius of the can is 'r' and height of the can is 'h'.

It has been given that the can is made up of two materials.

Material used for side of the can costs $0.015 and material used for the lids costs $0.027.

Surface area of the can is represented by

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Now the function that represents the cost to construct the can will be

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C = 0.054πr² + 0.03πrh ---------(1)

Volume of the can = Volume of a cylinder = πr²h

16 = πr²h

h=\frac{16}{\pi r^{2}} -------(2)

Now we place the value of h in the equation (1) from equation (2)

C=0.054\pi r^{2}+0.03\pi r(\frac{16}{\pi r^{2}})

C=0.054\pi r^{2}+0.03(\frac{16}{r})

C=0.054\pi r^{2}+(\frac{0.48}{r})

Now we will take the derivative of the cost C with respect to r to get the value of r to get the value to construct the can.

C'=0.108\pi r-(\frac{0.48}{r^{2} })

Now for C' = 0

0.108\pi r-(\frac{0.48}{r^{2} })=0

0.108\pi r=(\frac{0.48}{r^{2} })

r^{3}=\frac{0.48}{0.108\pi }

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and h = \frac{16}{\pi (1.12)^{2}}

h = 4.06 inches

Let's check the whether the cost is minimum or maximum.

We take the second derivative of the function.

C"=0.108+\frac{0.48}{r^{3}} which is positive which represents that for r = 1.12 inch cost to construct the can will be minimum.

Therefore, to minimize the cost of the can dimensions of the can should be

Radius = 1.12 inches and Height = 4.06 inches

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Answer:

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Step-by-step explanation:

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Answer:

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