SOLViNg Equations
You are an electrician for the city where you live. You get a
call about a parking lot at baseball field where the lamp posts
keep shutting off, due to the circuit breaker. A circuit
breaker is a switch that automatically stops the flow of
electricity due to a current being too strong or some other
dangerous situation. You've been called in to figure out why
the circuit is breaking
8
One of the most common formulas dealing with electricity is
called Watt's Law. This algebraic equation states that "pi
(power measured in watts) is equal to "V" (the voltage
measured in volts ) times "T" (the current measured in amps).
P= VI
Here is what you know about the baseball field parking lot situation.
There are 9 lamp posts connected to this circuit.
Each lamp post has a 400 watt lamp installed.
The circuit is 120-volt and 20-amp.
Here is what you don't know, but can figure out:
How much power can
the circuit handle?
(Use Wate's Law)
How many watts does 9
lampposts require?
How many lampposts
could this circuit actually
handle?

(4,7) - F. (2√3, 2)

(-4, 7) - A. (-2√3, 2)

(-4,¹) - E. (4,-0) 4.(-4,-3) - B. (-2√2, -2√2)

(-4,-5) - C. (-2√2, 2√2)

(-4, 6) - D. (2,2√3)

To convert from polar coordinates to Cartesian coordinates, we use the following formulas:

x = r cos(θ)

y = r sin(θ)

where r is the distance from the origin and θ is the angle in radians.

For example, to convert (4,7) to Cartesian coordinates, we would use the following formulas:

x = 4 cos(7) = 2√3

y = 4 sin(7) = 2

Therefore, the Cartesian coordinates of (4,7) are (2√3, 2).

Learn more about polar coordinates here:

brainly.com/question/31904915

#SPJ11

It is important to note that continuous random variables typically represent measured data, such as the weight or height of an individual, while discrete random variables typically represent counted data, such as the number of heads in a series of coin flips.

The mean of a probability distribution, also known as the expected value, is a measure of central tendency that represents the average value of a random variable in the long run. It is calculated by taking the weighted average of all possible values that the random variable can take, with the weights being the probabilities of each value occurring.

In the case of a discrete random variable, the mean is calculated by multiplying each possible value by its probability and then summing the results. For a continuous random variable, the mean is calculated by integrating the product of the value and its probability density function over the entire range of possible values.

The mean is significant because it provides a measure of the central tendency of a probability distribution, which can be used to make predictions about future outcomes. It is also used in various applications, such as calculating the expected value of a financial investment or the expected number of occurrences of an event in a given time period.

It is important to note that continuous random variables typically represent measured data, such as the weight or height of an individual, while discrete random variables typically represent counted data, such as the number of heads in a series of coin flips.

To learn more about  that continuous random variables typically represent measured data, click here: https://brainly.com/question/12424636

#SPJ11

Answer: C

Step-by-step explanation:

The appropriate matching of the expression will be:

5.2 × 10 = 52

5.2 × 10² = 520

5.2 × 10³ = 5200

5.2 × 10^-1 = 0.52

It should be noted that the information illustrated is simply about the power on the numbers. This was illustrated on the information.

In this case, it should be noted that the thing to f is to multiply the numbers or count the number of zeros and illustrate on the numbers.

Therefore, the appropriate matching of the expression will be:

5.2 × 10 = 52

5.2 × 10² = 520

5.2 × 10³ = 5200

5.2 × 10^-¹ = 0.52

Learn more about expressions on:

brainly.com/question/25968875

#SPJ1

as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.

\(\stackrel{f(x)}{y}\hspace{5em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~\sqrt{4y+5}}\implies x^2=4y+5\implies x^2-5=4y \\\\\\ \cfrac{x^2-5}{4}=y\implies \cfrac{1}{4}(x^2-5)=\stackrel{f^{-1}(x)}{y}\qquad x\geqslant 0\)

now, I don't see any good reason why x ⩾ 0 or x ⩽ 0 , since any negative or positive values are perfectly valid.

Answer:

\(\textsf{C)} \quad f^{-1}(x)=\dfrac{1}{4}(x^2-5), \;\; x \geq 0\)

Step-by-step explanation:

Given function:

\(f(x)=\sqrt{4x+5}\)

The domain of the given function is restricted to x ≥ -⁵/₄.

Therefore, the range of the given function is restricted to f(x) ≥ 0.

The inverse of a function is its reflection in the line y = x.

To find the inverse of a function, swap x and y:

\(\implies x=\sqrt{4y+5}\)

Rearrange the equation to make y the subject:

\(\implies x^2=4y+5\)

\(\implies 4y=x^2-5\)

\(\implies y=\dfrac{1}{4}(x^2-5)\)

Replace y with f⁻¹(x):

\(\implies f^{-1}(x)=\dfrac{1}{4}(x^2-5)\)

The domain of the inverse of a function is the range of the original function.  

Therefore, the domain of the inverse function is x ≥ 0.

Therefore, the inverse of the given function is:

\(f^{-1}(x)=\dfrac{1}{4}(x^2-5), \;\; x \geq 0\)

Answer:

5

Step-by-step explanation:

Answer:

graph 3

Step-by-step explanation:

Answer: 3 sports drinks

Step-by-step explanation:

6 divde by 2= 3

36 divided by 12 =3

in other words

3x2=6

12x3=36

hope this helps

The quadratic equation is solved as;

2x² + 5x - 12 = 0

2x² + 8x - 3x - 12 = 0

2x(x + 4) - 3(x + 4) = 0

x: -4 and 3/2

From the information given, we have that the quadratic equation is;

2x² + 5x = 12

Equate the quadratic equation to zero, we have;

2x² + 5x - 12 = 0

Now, find the product of the coefficient of x² and -12. Then, find the pair factors of the value that sum up to 5, we have;

-8 and 3

Substitute the values

2x² + 8x - 3x - 12 = 0

Factorize the expressions in pairs, we get;

2x(x + 4) - 3(x + 4) = 0

Then, we have;

2x - 3 = 0

x = 3/2

and

x + 4 = 0

x = -4

x: -4 and 3/2

Learn about quadratic equations at: https://brainly.com/question/776122

#SPJ1

Answer:

wheres the picture?

Step-by-step explanation:

im ready but i dont know the problem

Adjust the parameters as needed, such as the step size (h) and the final x-value (xn), and run the code to obtain the solution for y(x).

The resulting plot will show the solution curve.

To solve the given set of differential equations using the Runge-Kutta method in MATLAB, we need to convert the second-order differential equations into a system of first-order differential equations.

Let's define new variables:

y = y(x)

z = dz/dx

Now, we have the following system of first-order differential equations:

dy/dx = z (1)

dz/dx = -k/(2y) (2)

To apply the Runge-Kutta method, we need to discretize the domain of x. Let's assume a step size h for the discretization. We'll start at x = 0 and proceed until x = infinite.

The general formula for the fourth-order Runge-Kutta method is as follows:

k₁ = h f(xn, yn, zn)

k₂ = h f(xn + h/2, yn + k₁/2, zn + l₁/2)

k₃ = h f(xn + h/2, yn + k₂/2, zn + l₂/2)

k₄ = h f(xn + h, yn + k₃, zn + l₃)

yn+1 = yn + (k₁ + 2k₂ + 2k₃ + k₄)/6

zn+1 = zn + (l₁ + 2l₂ + 2l₃ + l₄)/6

where f(x, y, z) represents the right-hand side of equations (1) and (2).

We can now write the MATLAB code to solve the differential equations using the Runge-Kutta method:

function [x, y, z] = rungeKuttaMethod()

   % Parameters

   k = 1;              % Constant k

   h = 0.01;           % Step size

   x0 = 0;             % Initial x

   xn = 10;            % Final x (adjust as needed)

   n = (xn - x0) / h;  % Number of steps

   % Initialize arrays

   x = zeros(1, n+1);

   y = zeros(1, n+1);

   z = zeros(1, n+1);

   % Initial conditions

   x(1) = x0;

   y(1) = 0;

   z(1) = 0;

   % Runge-Kutta method

   for i = 1:n

       k1 = h * f(x(i), y(i), z(i));

       l1 = h * g(x(i), y(i));

       k2 = h * f(x(i) + h/2, y(i) + k1/2, z(i) + l1/2);

       l2 = h * g(x(i) + h/2, y(i) + k1/2);

       k3 = h * f(x(i) + h/2, y(i) + k2/2, z(i) + l2/2);

       l3 = h * g(x(i) + h/2, y(i) + k2/2);

       k4 = h * f(x(i) + h, y(i) + k3, z(i) + l3);

       l4 = h * g(x(i) + h, y(i) + k3);

       y(i+1) = y(i) + (k1 + 2*k2 + 2*k3 + k4) / 6;

       z(i+1) = z(i) + (l1 + 2*l2 + 2*l3 + l4) / 6;

       x(i+1) = x(i) + h;

   end

   % Plotting

   plot(x, y);

   xlabel('x');

   ylabel('y');

   title('Solution y(x)');

end

function dydx = f(x, y, z)

   dydx = z;

end

function dzdx = g(x, y)

   dzdx = -k / (2*y);

end

% Call the function to solve the differential equations

[x, y, z] = rungeKuttaMethod();

Learn more about differential equations click;

https://brainly.com/question/32645495

#SPJ4

Expression which represents the amount of money spend by each woman is equal to [ 9 + 1.35 + (one- half)(3.50 + 1.74)].

As given in the question,

Condition for the expression:

Sally and Anne both went for a movie.

Each one purchased a drink.

Shared one popcorn and one veggie bought by them.

Consider movie ticket price = 9

drink price = 1.35

Popcorn price = 3.50

Veggie price = 1.74

Explanation for different expressions are:

1. one-half (9 + 1. 35 + 3. 50 + 1. 74)

Here sum of all the amount is divided equally, which is not correct as movie ticket and drink they have purchased individually.

2.  9 + 1. 35 + one-half (3. 50 + 1. 74)

This is correct option as it represents :

Movie ticket price = 9

Drink = 1.35

one-half (3. 50 + 1. 74) = one popcorn and one veggie divided equally.

3. 18 + 2. 70 + one-half (3. 50 + 1. 74)

As per consideration of price this is not correct option.

Movie ticket price =18

Drink = 2.70

one-half (3. 50 + 1. 74) = one popcorn and one veggie divided equally.

4. 9+1. 35+2(3. 50+1. 7)

This is not correct option as popcorn and veggie price is doubled.

Therefore, expression which represents the amount of money spend by each woman is equal to [ 9 + 1.35 + (one- half)(3.50 + 1.74)].

Learn more about expression here

brainly.com/question/14083225

#SPJ4

Answer:

24:14

Step-by-step explanation:

Answer:

The answer is -135

Step-by-step explanation:

We can do 160 times 3 which is 480 for the 3 times he withdrew $160 from his total. (Withdraw means taking, so subtraction).

Then, we do 480 minus 354 which is -135.

Answer:

no

Step-by-step explanation:

the bet displays 3 hexagonal bases when in the figure there is only 2 bases.

Answer:

No.

Step-by-step explanation:

Examples of three-dimensional figures are: Cuboid, Cube, Cylinder, Sphere, Pyramid, and a Cone.

Answer:

eight years.

Step-by-step explanation:

Given:

a.) A plot of land for sale has a width of x ft. and a length that is 8 ft. less than its width.

b.) A farmer will only purchase the land if it measures 240 ft.

From the given description of the measurement of the land, we generate the following equations:

Width = w

Length = w - 8

Area of the Land = 240 ft.^2

Area = Width x Length

240 = (w)(w - 8)

240 = w^2 - 8w

w^2 - 8w - 240 = 0

Question 1: Create an equation in terms of w that models this situation.​

Answer: 240 = w^2 - 8w

Factoring out 240 = w^2 - 8w, we get:

240 = w^2 - 8w

w^2 - 8w - 240 = 0

w^2 - 8w - 240 = 0 → (w - 20)(w + 12) = 0

First possible measure of the width,

w - 20 = 0

w = 20 ft.

Second possible measure of the width,

w + 12 = 0

w = -12 ft.

A dimension must never be a negative value, therefore, the width must be equal to 20 ft.

Let's determine the length,

Length = w - 8

= 20 - 8

Length = 12 ft.

Summary:

The equation that models the situation: 240 = w^2 - 8w or w^2 - 8w = 240

The measure of the length = 12 ft.

The measure of the width = 20 ft.

Answer:

$8,232.50

Step-by-step explanation:

After saving 2/7 of his salary each month, Harun had $1335 left to spend. His brother, Jamal, saves 3/8 of his salary. If both of them save the same amount of money, how much is there salary altogether?

Harun : 1,335/(2/7) = $4,672.50 total salary

Jamal: 1,335/(3/8) = $3,560 total salary

Both salaries: $4,672.50 + $3,560 = $8,232.50

Answer:

5 days

Step-by-step explanation:

Given: bacteria to increase from 2000 to  50,000

To find: Number of days that a culture of bacteria will take to increase from 2000 to  50,000

Solution:

The growth of bacteria is represented by the equation: \(P(t)=P_0e^{kt}\)

Here, t denotes time, k denotes growth rate and \(P_0\) denotes initial population of bacteria.

Take \(P_0=2000\), \(P(t)=50000\) and \(k=0.657\)

\(50000=2000e^{0.657t}\\\frac{50000}{2000}=e^{0.657t}\\25=e^{0.657t}\\0.657t=\ln 25\\t=\frac{\ln 25}{0.657}=4.9\approx 5\,\,days\)

A change in the price of chicken, the good's own price, will cause a movement along the demand curve for chicken, a normal good, resulting in an increase in the quantity demanded.

The demand curve for chicken represents the relationship between the price of chicken and the quantity of chicken demanded by consumers. The law of demand states that there is an inverse relationship between the price of a good and the quantity demanded, holding all other factors constant. In other words, as the price of chicken decreases, the quantity demanded of chicken increases, and vice versa.

A movement along the demand curve for chicken occurs when there is a change in the price of chicken. When the price of chicken decreases, ceteris paribus, consumers are willing to purchase more chicken at the lower price, resulting in an increase in the quantity demanded along the demand curve. Conversely, when the price of chicken increases, consumers are willing to purchase less chicken at the higher price, resulting in a decrease in the quantity demanded along the demand curve.

Other factors that can shift the demand curve for chicken include changes in consumer income, the prices of substitute or complementary goods, and changes in consumer preferences. However, these factors cause a shift in the entire demand curve, rather than a movement along the curve.

Learn more about Quantity:

brainly.com/question/12986460

#SPJ11

Answer:

Bottom left

Step-by-step explanation:

It does not make a straight line

Answer:

4

Step-by-step explanation:

Multiply both sides by 7.

5s+8=28

Subtract 8 from both sides.

5s=20

Divide 5 from both sides,

s=4

Answer:

Hiiiii

The answer is s=4

Answer: The vertex form of a parabola is:

y = a(x - h)^2 + k

Where (h, k) is the vertex of the parabola.

In this case, we are given that the vertex is (1, -2), so the equation of the parabola will be:

y = a(x - 1)^2 - 2

We know that the parabola passes through (0, -5), and it is given by the equation.

-5 = a(0 - 1)^2 - 2

so,

a = 1/3

The final equation of the parabola is :

y = 1/3(x-1)^2 - 2

so, the points that are on the parabola are:

A. (2,-3)

B. (-1,-14) is not true,

y = 1/3 (-1 -1)^2 - 2 = -1/3 + 2 = 1/3 ≠ -14

C. (3,2)

D. (2,-5)

E. (3,-14) is not true

y = 1/3 (3-1)^2 - 2 = -4/3 ≠ -14

F. (-2,7) is not true

y = 1/3 (-2-1)^2 - 2 = -7/3 + 2 = -1/3 ≠ 7

Therefore A, C and D are the correct answers.

Step-by-step explanation:

Question: In a sale, the price of a book is reduced by 25%. The price of the book in the sale is £12. Work out the original price of the book

Answer: £16

Step-by-step explanation:

To determine the original price of the book, we can use the fact that the sale price is 75% (100% - 25%) of the original price. Let's denote the original price as x.

75% of x = £12

To solve for x, we can set up the equation:

0.75x = £12

To isolate x, we divide both sides of the equation by 0.75:

x = £12 / 0.75

x = £16

Therefore, the original price of the book was £16.

Relative frequency distributions are generally more useful than frequency distributions when comparing data sets of different sizes.

Frequency distributions can show the actual number of observations falling in each range or the percentage of observations. In the latter sample, the distribution is called a relative frequency distribution.

Frequency distribution tables can be utilised for both categorical and numeric variables. Continuous variables should only be used with class intervals, which will be described shortly.

A relative frequency distribution displays the proportion of the total number of observations associated with each value or class of values and is related to a probability distribution, which is extensively used in statistics.

--This question is incomplete; the complete question is

"Relative frequency distributions are generally more useful than frequency distributions when _____."--

To know more about Relative frequency distributions, here

https://brainly.com/question/28341501

#SPJ4

Answer:

Booker:  $103.50 profit

Finley:  $34.50 profit

Step-by-step explanation:

b = # of candles Booker sold

f = # of candles Finley sold

1)  b = 3f

2) f = b - 12    substitute b=3f into this equation to get an expression all in terms of f, then solve for f

f = 3f - 12

-2f = -12

f = -12/2 = 6    now plug this into either equation and solve for b

b = 3(6) = 18

Booker:  18 candles x $5.75 profit/candle = $103.50 profit

Finley:  6 candles x $5.75 profit/candle = $34.50 profit

Answer:

1/50

Step-by-step explanation:

The given vectors h1, 2, 4, 3i, h1, 1, 0, 1i, and h2, 1, 1, 3i in R4 are linearly dependent, as determined by creating a matrix with the vectors as columns and row reducing it. The row-reduced matrix has a row of zeros, indicating that one of the vectors can be expressed as a linear combination of the other two.

The given vectors are h1, 2, 4, 3i, h1, 1, 0, 1i, and h2, 1, 1, 3i in R4. To determine whether these vectors are linearly independent or linearly dependent, we can create a matrix with the vectors as columns and row reduce it. If the row-reduced matrix has a row of zeros, then the vectors are linearly dependent. Otherwise, they are linearly independent.

Constructing the matrix with the given vectors as columns, we get:

\begin{bmatrix} 1 & 1 & 2 \\ 2 & 0 & 4 \\ 4 & 1 & 0 \\ 3 & 1 & 1 \end{bmatrix}

Row reducing this matrix, we get:

\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{bmatrix}

Since the row-reduced matrix has a row of zeros, the given vectors are linearly dependent. Specifically, the fourth vector can be expressed as a linear combination of the first three vectors. Therefore, we can conclude that the vectors h1, 2, 4, 3i, h1, 1, 0, 1i, and h2, 1, 1, 3i in R4 are linearly dependent.

To learn more about row-reduced matrix : brainly.com/question/31478850

#SPJ11

Answer:

Part A: 12 + X

Step-by-step explanation:

Part A - He earned $12 for walking the dogs on Saturday and Bill did the same thing on Sunday but it just says he earned extra money so X = unknown number so its 12 + X

Answer:

a^2 +b^2= c^2

Step-by-step explanation:

to prove that a triangle have right angles triangle you have to use the Pythagoras theorem