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den301095 [7]
4 years ago
5

How can linear functions be used to model situations and solve problems?

Mathematics
1 answer:
PIT_PIT [208]4 years ago
4 0
One day, you go to a store and buy a pencil. It costs $0.25.
You notice the unit price $0.25/pencil.

The next day you buy 3 pencils, they cost $0.75.
You notice the unit price is $0.75/(3 pencils) = $0.25/pencil.

For each extra pencil you buy, the increase in price is always $0.25.
This suggests a linear relation between the number of pencils, p, and the cost of the pencils, c.

You use a linear equation to give you the cost of pencils based on the number of pencils.

c = 0.25p

One day, you happen to have $4.50 in your pocket.
You'd like to buy 15 pencils, but you are not sure you have enough money.
You use your handy linear equation, and you replace p, the number of pencils, with 15 to find their cost, c.

c = 0.25p

c = 0.25 * 15

c = 3.75

After using your equation, you see that 15 pencils cost $3.75, and since you have $4.50 you have enough money to buy them. You're very happy about this, and, as soon as you get home, you write this experience in your journal, using one of the new pencils you just bought, and you make it a point to include the linear equation that helped you.
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It costs miksel $4 to make a bike bag, if he sells each gor $5. He has made a profit of $16 dollars so far
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16

Step-by-step explanation:

5-4 = 1 so total profit would be $1 for each bag.

Because he makes 1 dollar per bag this is a fairly simple to see how many he has but we will pretend its not so you have an idea of how to do this later.

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A ball slides up a frictionless ramp. It is then rolled without slipping and with the same initial velocity up another frictionl
KATRIN_1 [288]

Answer:

Rolling case achieves greater height than sliding case

Step-by-step explanation:

For sliding ball:

- When balls slides up the ramp the kinetic energy is converted to gravitational potential energy.

- We have frictionless ramp, hence no loss due to friction.So the entire kinetic energy is converted into potential energy.

- The ball slides it only has translational kinetic energy as follows:

                                   ΔK.E = ΔP.E

                                   0.5*m*v^2 = m*g*h

                                    h = 0.5v^2 / g

For rolling ball:

- Its the same as the previous case but only difference is that there are two forms of kinetic energy translational and rotational. Thus the energy balance is:

                                  ΔK.E = ΔP.E

                                  0.5*m*v^2 + 0.5*I*w^2 = m*g*h

- Where I: moment of inertia of spherical ball = 2/5 *m*r^2

             w: Angular speed = v / r

                               0.5*m*v^2 + 0.2*m*v^2 = m*g*h

                               0.7v^2 = g*h

                               h = 0.7v^2 / g

- From both results we see that 0.7v^2/g for rolling case is greater than 0.5v^2/g sliding case.

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