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3 years ago

Explain why the expression (c+di)^2 is always a complex number for nonzero, real values of c and d

1 answer:

7 0

(c + di)^2 = c^2 + 2cdi + (di)^2
= c^2 + 2cdi - d^2
= c^2 - d^2 + 2cdi

The real part is c^2 - d^2. The imaginary part is cdi.
Since c and d are nonzero real numbers, the product cd is also nonzero and real. Even if c and d are equal, and the real part c^2 - d^2 becomes zero, the imaginary part, cdi will always have a nonzero coefficient (cd). Therefore, the imaginary part is always there.

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At a hockey game, a vender sold a combined total of 235 sodas and hot dogs. The number of hot dogs sold was 59 less than the num

Neko [114]

Answer:

147 sodas
88 hot dogs

Step-by-step explanation:

This problem is similar to many others in which the sum of two quantities and their difference are given. The solution can be found easily when the equations for the relations are written in standard form.

<h3>Setup</h3>

Let s and h represent numbers of sodas and hot dogs sold, respectively. The given relations are ...

s +h = 235 . . . . . combined total
s -h = 59 . . . . . . difference in the quantities

<h3>Solution</h3>

Adding the two equations eliminates one variable.

(s +h) +(s -h) = (235) +(59)

2s = 294 . . . . simplify

s = 147 . . . . . .divide by 2

h = 147 -59 = 88 . . . . h is 59 less

147 sodas and 88 hot dogs were sold.

<em>Additional comment</em>

The solution to a "sum and difference" problem is always the same. One of the numbers is half the sum of those given, and the other is half their difference. ((235-59)/2 = 88)

5 0

2 years ago

An executive for the movie production company wants to create a function that models this data. . Create a function that can be

stich3 [128]

Functions can be modeled by equations, tables and graphs

The equation that models the function is $y = \frac 14x +1$
The domain of the function is the set of whole numbers
The company should expect 4 box office gross in week 10

<h3>How to determine the function</h3>

From the question, we have the following ordered pairs

(x,y) = (0,1) and (4,2)

The function is a linear function.

So, we start by calculating the slope (m) using:

$m = \frac{y_2 - y_1}{x_2 -x_1}$

Substitute known values

$m = \frac{2 - 1}{4 - 0}$

$m = \frac{1}{4}$

The equation is then calculated as:

$y = m(x -x_1) +y_1$

This gives

$y = \frac 14(x -0) +1$

$y = \frac 14x +1$

The domain of the above function is the set of whole numbers

Substitute 10 for x, to calculate the number of box office gross for week 10

$y = \frac 14 * 10 +1$

$y = 3.5$

Approximate

$y = 4$

Hence, the company should expect 4 box office gross in week 10

Read more about linear functions at:

brainly.com/question/15602982

5 0

2 years ago

The answer is not D it would be B: You received a bonus at work

MissTica

What are you even talking about... What is the ???

3 0

3 years ago

a cook has 2 2/3 cup of flour. a recipe calls for 2 3/4 cups of flour. does the cook have enough flour? if not, how much more fl

NeTakaya

The cook do not have enough flour. He only has 2.67 cups of flour while the recipe needs 2.75 cups of flour. Therefore, he needs 0.08 more cups of flour in order to have enough for the recipe. Hope this answers the question. Have a nice day.

6 0

4 years ago

What is the equation of the line that passes through (-2,2) and (1,-4)?

adelina 88 [10]

Answer:

y=-2x-2

Step-by-step explanation:

Slope: -4-2/1-(-2)=-6/3=-2

Equation: y=-2x+b

Substitute: 2=-2(-2)+b

2=4+b

b=-2

Therefore, y=-2x-2

I hope this helped and have a good rest of your day!

6 0

3 years ago