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sammy [17]
2 years ago
10

The power generated by an electrical circuit (in watts) as a function of its current ccc (in amperes) is modeled by: P(c)=-20(c-

3)^2+180P(c)=−20(c−3) 2 +180
Mathematics
1 answer:
alekssr [168]2 years ago
5 0

Answer:

The current that produces maximum power is 3A

Step-by-step explanation:

Given

P(c) = 20(c - 3)^2

Required [Missing from the question]

The current that produces maximum power

First, we represent the function in standard form

P(c) = 20(c - 3)^2

P(c) = 20(c - 3)(c - 3)

Open bracket

P(c) = 20(c^2 -6c+ 9)

P(c) = 20c^2 -120c+ 180

The maximum value of c is:

Max(c) = \frac{-b}{2a}

Where:

f(x) = ax^2 + b^2 + c

By comparison: P(c) = 20c^2 -120c+ 180

a = 20

b = -120

c = 180

So, we have:

Max(c) = \frac{-b}{2a}

Max(c) = \frac{-(-120)}{2 * 20}

Max(c) = \frac{120}{40}

Max(c) = 3

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Connor have five times as much money as jayden. Cannor gave some money to jayden. Now they have £8.50 what amount of money jayde
valkas [14]

Answer:

Cornor has $14.17 initially

Step-by-step explanation:

The complete question is as follows

Connor has five times as much money as Jayden. Connor gives some money to Jayden. They now have £8.520each. How much did Connor have at the start?

solution

In this question, we are concerned with knowing how much that both had initially.

Let the amount of money Jayden has be £x . Since Cornor has Five times this, he has £5x

Let the amount of money Cornor gave Jayden be £y.

This means ;

5x - y = 8.50 .....(

(i)and also x + y = 8.50 ......(ii)

It is this equations we solve simultaneously

From i, we can say let y= 5x - 8.50, and we insert this into equation ii

x + 5x - 8.50 = 8.50

6x = 17

x = 17/6

x = $2.83

y = 5x - 8.50

y = 5(2.83) - 8.50

y = $5.67

The amount of money Cornor has at first is 5x = 5(17/6)

5x = $14.17

5 0
3 years ago
Graph each of the equations and then determine which one represents the rank catcher that is elevated
Tanya [424]
We have two functions that are Parabolas. A parabola is a type of quadratic function which is a special type of “U”-shaped curve called. So let's solve this problem for the first parabola and then for the second one.

1. Graph of the first equation

We have that:

y=x^2-2x+3

So if we graph this equation, the parabola that matches it is shown in Figure 1.

1.1 Direction of Parabola

In general, a parabola or quadratic function is given by the following way:

y=ax^2+bx+c \\ \\ where \ "a" \ is \ called \ the \ leading \ coefficient

Given that our leading coefficient is positive, then the direction of the parabola is upward, that is, it opens upward.

1.2 Location of vertex with respect to the x-axis

The vertex a parabola can be found as follows:

(-\frac{b}{2a},f(-\frac{b}{2a}))

But: \\ \\ a=1 \\ b=-2 \\ c=3 \\ \\ Accordingly: \\ \\ -\frac{b}{2a}=-\frac{(-2)}{2(1)}=1 \\ \\ f(1)=1^2-2(1)+3=2 \\ \\ So \ the \ vertex \ is: \\ \\ V(1,2)

So the vertex is located two units above the x-axis.

<span>1.3 Determine if the graph depicts the rain gauge
</span>
A rain gauge is an instrument used by meteorologists and hydrologists to gather and measure the amount of liquid precipitation<span> over a set period of time.
</span>
From Figure 4 we can affirm that this is the parabola that resembles a rain gauge elevated from the ground. 

1.4 Why or why not?

It basically the question asks for the parabola that has a vertex well above the x-axis. From Figure 4, you can see that the elevated parabola is in fact:

y=x^2-2x+3

2. Graph of the second equation

We have that:

y=x^2+4x+4

So if we graph this equation, the parabola that matches it is shown in Figure 2.

2.1 Direction of Parabola

As in the previous problem, given that our leading coefficient is positive, then the direction of the parabola is also upward, that is, it opens upward.

2.2 Location of vertex with respect to the x-axis

The vertex of a parabola can be found as follows:

(-\frac{b}{2a},f(-\frac{b}{2a}))

In \ this \ case: \\ \\ a=1 \\ b=4 \\ c=3 \\ \\ Accordingly: \\ \\ -\frac{b}{2a}=-\frac{4}{2(1)}=-2 \\ \\ f(-2)=(-2)^2+4(-2)+4=0 \\ \\ So \ the \ vertex \ is: \\ \\ V(-2,0)

So the vertex lies on the x-axis.

2.3 Determine if the graph depicts the rain gauge

This parabola does not resembles a rain gauge elevated from the ground.

2.4 Why or why not?

As you can see the parabola touches the x-axis. If the x-axis represents the ground, then the rain gauge is touching it, that is, it is not elevated.

3. Graph of the third equation

We have that:

y=3x^2+21x+30

So if we graph this equation, the parabola that matches it is shown in Figure 5.

3.1 Direction of Parabola

As in the previous parabolas, given that our leading coefficient is positive, then the direction of the parabola is also upward, that is, it opens upward.

3.2 Location of vertex with respect to the x-axis

In \ this \ case: \\ \\ a=3 \\ b=21 \\ c=30 \\ \\ Accordingly: \\ \\ -\frac{b}{2a}=-\frac{21}{2(3)}=-\frac{7}{2} \\ \\ f(-\frac{7}{2})=3(-\frac{7}{2})^2+21(-\frac{7}{2})+30=-\frac{27}{4} \\ \\ So \ the \ vertex \ is: \\ \\ V(-\frac{7}{2},-\frac{27}{4})

So the vertex is shifted \frac{27}{4} units downward the x-axis.

3.3 Determine if the graph depicts the rain gauge

This parabola does not resembles a rain gauge elevated from the ground.

3.4 Why or why not?

The vertex of this parabola lies on the negative y-axis. So it is not elevated from the ground.

5 0
2 years ago
Danielle earns a 8.25% commission on everything she sells at the electronics store where she works. She also earns a base salary
jeka94

Danielle earned $979.75 last week.

Step-by-step explanation:

Base salary = $625 per week

Commission = 8.25%

Cost of items sold = $4300

Amount of commission = 8.25\% \of \cost\ of\ sold\ items

Amount\ of\ commission=\frac{8.25}{100}*4300\\Amount\ of\ commission=\frac{35475}{100}\\Amount\ of\ commission=\$354.75

Total earning last week = Base salary per week + amount of commission

Total\ earning = 625+354.75\\Total\ earning=\$979.75

Danielle earned $979.75 last week.

Keywords: Commission, Percentage

Learn more about percentages at:

  • brainly.com/question/5922969
  • brainly.com/question/6013189

#LearnwithBrainly

4 0
2 years ago
ASAPpppppppppppppppppppppp
Bogdan [553]

Answer:

-4/5

Step-by-step explanation:

2/5 ÷ -1/2

Copy dot flip

2/5 * -2/1

-4/5

8 0
3 years ago
Which of the following statements is true?
Inessa05 [86]

Answer: the number -5 is a real number

Real numbers are both negative and positive numbers. -5 is a negative number. Since real numbers include negative numbers, -5 is the answer.

Hope this helps!

7 0
3 years ago
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