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dsp73
3 years ago
5

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

+ 120c What is the maximum power generated by the circuit? _____ watts
Mathematics
1 answer:
Ksenya-84 [330]3 years ago
7 0

Answer:

The maximum power generated by the circuit is 300 watts.

Step-by-step explanation:

A quadratic function is one that can be written as an equation of the form:

f (x) = ax² + bx + c

where a, b and c (called terms) are any real numbers and a is nonzero.

In this case, f(x) is P(c) [the power generated], x is the current c (in amperes), a = -12, b = 120 and c = 0.

The vertex is a point that is part of the parabola, which has the value as ordered  minimum or maximum function. If the scalar a> 0, the parabola opens or faces up and the vertex is the minimum of the function. In contrast, if a <0, the parabola opens downward and the vertex is the maximum of the function.

The calculation of the vertex, which in this case will be the maximum of the function, is carried out as follows:

  • The value of x, in this case the value of current c in amperes, can be calculated with the formula c=\frac{-b}{2*a} . In this case: c=\frac{-120}{2*(-12)} So c= 5 amperes. The current is 5 amperes.
  • The value of y, in this case the value of the electric current in watts, is obtained by substituting the value of c previously obtained in the function. In this case: P(5)= -12*5²+120*5. So P(5)= 300 watts

<u><em>The maximum power generated by the circuit is 300 watts.</em></u>

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Khan Academy Question
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Answer:

84

Step-by-step explanation:

Since we are given line OP perpendicular to line DR, then angles PDR and ODR are right angles.

Angles PDA and ADR are complementary.

Angles ODU and UDR are complementary.

Angles ADR and UDR are given as congruent.

We can conclude that angles PDA and ODU are congruent.

By AA Similarity, triangles APD and UMD are similar.

DP/DM = PA/MU

3.75/10 = 4.5/MU

3.75MU = 10 × 4.5

MU = 12 (altitude of triangle DUO)

OD = OM + MD =  4 + 10 = 14 (base of triangle DUO)

area = base × height / 2

area = 14 × 12 / 2

area = 84

4 0
1 year ago
he sum of the first two terms of a G.P is 27 whereas the sum of the second and third term is 54. Find the first term and the com
viktelen [127]

Answer:

{ \tt{sum =  \frac{a(r {}^{n - 1} )}{n - 1} }} \\ 27 =  \frac{a(r {}^{2 - 1} )}{2 - 1}  \\ { \bf{27 = ar -  -  - (i)}} \\  \\ 54 =  \frac{a( {r}^{3 - 1} )}{3 - 1}  \\ { \bf{108 = a {r}^{2} -  -  - (ii) }} \\ { \tt{(ii) \div (i) : }} \\ r =  \frac{108}{27}  \\ { \bf{common \: ratio = 4}} \\ { \bf{first \: term =  \frac{27}{4}  }}

7 0
3 years ago
Can somebody please help me
olasank [31]

Answer:

70

Step-by-step explanation:

Complementary angles equal 90 degrees

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I hope this helps!

5 0
2 years ago
Graph a line whose x-intercept is 9 and y-intercept is 7​
sweet-ann [11.9K]
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3 years ago
Find the value of the discriminant for <img src="https://tex.z-dn.net/?f=7x%5E%7B2%7D%20%2B5x%2B1%3D0" id="TexFormula1" title="7
kondor19780726 [428]

Answer:

No real roots

Step-by-step explanation:

Given

7x² + 5x + 1 = 0 ← in standard form

with a = 7, b = 5, c = 1

To determine the nature of the roots use the discriminant

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3 years ago
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