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lidiya [134]
3 years ago
7

The power generated by an electrical circuit (in watts) as function of its current x (in amperes) is modeled by: P(x)=-12x^2 +12

0x.
What current will produce the maximum power?
Mathematics
1 answer:
Minchanka [31]3 years ago
6 0

Given:

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

P(x)=-12x^2+120x

To find:

The current that will produce the maximum power.

Solution:

We have,

P(x)=-12x^2+120x

Here, leading coefficient is negative. So, it is a downward parabola.

Vertex of a downward parabola is the point of maxima.

If a parabola is f(x)=ax^2+bx+c, then

Vertex=\left(\dfrac{-b}{2a},f(\dfrac{-b}{2a})\right)

In the given function, a=-12 and b=120. So,

-\dfrac{b}{2a}=-\dfrac{120}{2(-12)}

-\dfrac{b}{2a}=-\dfrac{120}{-24}

-\dfrac{b}{2a}=5

Putting x=5 in the given function, we get

P(5)=-12(5)^2+120(5)

P(5)=-12(25)+600

P(5)=-300+600

P(5)=300

Therefore, 5 watt current will produce the maximum power of 300 amperes.

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Which represents the number 16,807 in exponential form
Naya [18.7K]
7^5. Found by trial and error.
3 0
3 years ago
How do you find the base and height?
dusya [7]
A triangle is 180 degrees. Depending on their angles: Right Angle - 90 degrees
Acute Angle - less than 90 degrees and Obtuse Angle greater than 90 degrees and under 180 degrees. Hope that helps. 
8 0
3 years ago
A catering service offers 5 appetizers,4 main courses, and 8 desserts. A customer is to select 4 appetizers,2 main courses,and 3
Alisiya [41]

Answer:

468 ways

Step-by-step explanation:

Given: A catering service offers 5 appetizers, 4 main courses, and 8 desserts

To find: number of ways a customer is to select 4 appetizers, 2 main courses,and 3 desserts.

Solution:

A permutation is an arrangement of elements such that order of elements matters and repetition is not allowed.

Number of appetizers = 5

Number of main courses = 4

Number of desserts = 8

Number of ways of choosing k terms from n terms = nPk=\frac{n!}{(n-k)!}

Number of ways a customer is to select 4 appetizers, 2 main courses,and 3 desserts =  5P4+4P2+8P3

=\frac{5!}{(5-4)!}+\frac{4!}{(4-2)!}+\frac{81}{(8-3)!}\\=5!+\frac{4!}{2!}+\frac{8!}{5!}\\=5!+(4\times 3)+(8\times 7\times 6)\\=120+12+336\\=468

So, this can be done in 468 ways.

7 0
3 years ago
Jose has 1000$ in his savings account. it pays out 5% interest what is his balance after 1 year
NARA [144]

The most appropriate choice for simple interest will be given by- Balance of Jose after 1 year is $1050

What is simple interest?

Simple interest is the interest applied on the principal value after charging some certain percentage of rate for some certain amount of time.

If the principal value is p, rate is r % per annum and time is t years

Simple interest is calculated as

SI = p ₓ r ₓ t / 100

Here,

Principal for Jose = $1000

Rate = 5%

Time = 1 year

Simple interest = 1000x5x1/100

                         = $50

Amount = $(1000+50)

             = $1050

Balance of Jose after 1 year is $1050

To learn more about simple interest, refer to the link:
brainly.com/question/25793394
#SPJ10

5 0
1 year ago
josie cast a shadow of 6ft and she is 5 ft 6 in tall. A building cast a shadow of 18 ft at the same time that josie measured her
Debora [2.8K]
Josie's height = 5 ft 6 in. = 5 1/2 ft = 11/2 ft.
Josie's shadow = 6 ft.

Ratio of shadow to height = 6 / 11/2 = 12/11
So, It would be equal to ratio of building's shadow to building's height.

18/x = 12/11
x = 18*11 /12
x = 3*11 / 2
x = 16.5

In short, Your Answer would be 16.5 Feet

Hope this helps!

6 0
3 years ago
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