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Marina CMI [18]
3 years ago
10

The kinetic energy (in joules ) of a moving object can be calculated from the expression 1/2mv to the second power, where m is t

he mass of the object in kilograms and v is it’s speed in meters per second. Find the kinetic energy of a 0.145-kg baseball that is thrown at a speed of 40 meters per second. E = ______ joules

Mathematics
1 answer:
yulyashka [42]3 years ago
7 0

E = 1/2 m v^2

E = 1/2 (0.145) (40)^2

E = 0.0725 x 1600

E = 116 kg m^2/s^2

1 joule = 1 kg m^2/s^2

so here E in joules is 116 joules

so E = 116 joules

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A community bird-watching society makes and sells simple bird feeders to raise money for its conservation activities. The materi
blondinia [14]

Answer:

The required function is: P(x)=-3x^2+78x-360

The price for each feeder to maximize profit should be $13.

The maximum weekly profit is $147

Step-by-step explanation:

Consider the provided information.

Part (A)

The materials for each feeder cost $6, and the society sells an average of 30 per week at a price of $10 each.

Let x be the price per feeder.

Profit = Revenue - cost

So the profit per feeder is x-6

If we increase then for every dollar increase, it loses 3 sales per week.

This can be written as:

30-3(x-10)

30-3x+30

-3x+60

Where x-10 represents the increase in price and 3  represents the decrease in sales per week.

Thus the profit will be:

P(x)=(x-6)(-3x+60)

P(x)=-3x^2+78x-360

Hence, the required function is: P(x)=-3x^2+78x-360

Part (B) What price should the society charge for each feeder to maximize profits? What is the maximum weekly profit?

The above function is a downward parabola so the maximum will occur at vertex.

The x coordinate of the vertex of parabola is: x=\frac{-b}{2a}

Substitute a=-3, b=78 and c=-360 in above.

x=\frac{-78}{2(-3)}=13

Hence, the price for each feeder to maximize profit should be $13.

Now substitute the value of x in P(x)=-3x^2+78x-360

P(x)=-3(13)^2+78(13)-360=$147

Hence, the maximum weekly profit is $147

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Answer:

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Step-by-step explanation:

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