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Firdavs [7]
3 years ago
11

The power generated by an electrical circuit (in watts) as a function of its current x xx (in amperes) is modeled by P ( x ) = −

15 x ( x − 8 ) P(x)=−15x(x−8)P, left parenthesis, x, right parenthesis, equals, minus, 15, x, left parenthesis, x, minus, 8, right parenthesis What current will produce the maximum power?
Mathematics
1 answer:
marysya [2.9K]3 years ago
7 0

Given:

The power generated by an electrical circuit (in watts) as a function of its current x (in amperes) is modeled by

P(x)=-15x(x-8)

To find:

The current which will produce the maximum power.

Solution:

We have,

P(x)=-15x(x-8)

P(x)=-15x^2+120x

Differentiate with respect to x.

P'(x)=-15(2x)+120(1)

P'(x)=-30x+120      ...(i)

To find the extreme point equate P'(x)=0.

-30x+120=0

-30x=-120

Divide both sides by -30.

x=4

Differentiate (i) with respect to x.

P'(x)=-30(1)+(0)

P'(x)=-30 (Maximum)

It means, the given function is maximum at x=4.

Therefore, the current of 4 amperes will produce the maximum power.

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<h3>What is the general equation of a Straight line? How it represents a proportional relationship?</h3>

The general equation of a straight line is -

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[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

y = mx also represents direct proportionality. We can write [m] as -

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We have a cafeteria serves lemonade that is made from a powdered drink mix. There is a proportional relationship between the number of scoops of powdered drink mix and the amount of water needed to make it. For every 2 scoops of mix, one-half gallon of water is needed, and for every 6 scoops of mix, one and one-half gallons of water are needed.

We can write the proportional relationship as -

y = kx

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2 scoops need 0.5 gallon of water

6 scoops need 1.5 gallon of water

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Equations that represents the relationship can be written as -

y = 4x + c

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2 = 4 x 1/2 + c

2 = 2 + c

c = 0

So, the equation will be y = 4x.

Graph of y = 4x is attached at the end.

For 10 scoops of water -

10 = 4x

x = 2.5 gallons of water is needed.

Therefore, all the answers to the given parts are mentioned above.

To solve more questions on proportional relationship, visit the link below-

brainly.com/question/12917806

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