1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Alexxandr [17]
3 years ago
13

Find the values of x and y that satisfy the equation –21 + 5yi = 7x – 10i.

Mathematics
1 answer:
kap26 [50]3 years ago
8 0

Answer:

The values of x and y are x = -3 and y = -2

Step-by-step explanation:

In the complex numbers if a + bi = c + di, then the real parts are equal and the imaginary parts are equal

  • a = c
  • b = d

Let us use this rule to solve the question

∵ -21 + 5yi = 7x - 10i

∴ The real parts are -21 and 7x

∴ The imaginary parts are 5y and -10

∵ The real parts are equal

∴ 7x = -21

→ Divide both sides by 7

∴ \frac{7x}{7} = \frac{-21}{7}

∴ x = -3

∵ The imaginary parts are equal

∴ 5y = -10

→ Divide both sides by 5

∴ \frac{5y}{5} = \frac{-10}{5}

∴ y = -2

∴ The values of x and y are x = -3 and y = -2

You might be interested in
. Use Lagrange multipliers to find the maximum and minimum values of the function, f, subject to the given constraint, g. (Place
zzz [600]

Answer:

Minimum value of f(x, y, z) = (1/3)

Step-by-step explanation:

f(x, y, z) = x⁴ + y⁴ + z⁴

We're to maximize and minimize this function subject to the constraint that

g(x, y, z) = x² + y² + z² = 1

The constraint can be rewritten as

x² + y² + z² - 1 = 0

Using Lagrange multiplier, we then write the equation in Lagrange form

Lagrange function = Function - λ(constraint)

where λ = Lagrange factor, which can be a function of x, y and z

L(x,y,z) = x⁴ + y⁴ + z⁴ - λ(x² + y² + z² - 1)

We then take the partial derivatives of the Lagrange function with respect to x, y, z and λ. Because these are turning points, each of the partial derivatives is equal to 0.

(∂L/∂x) = 4x³ - λx = 0

λ = 4x² (eqn 1)

(∂L/∂y) = 4y³ - λy = 0

λ = 4y² (eqn 2)

(∂L/∂z) = 4z³ - λz = 0

λ = 4z² (eqn 3)

(∂L/∂λ) = x² + y² + z² - 1 = 0 (eqn 4)

We can then equate the values of λ from the first 3 partial derivatives and solve for the values of x, y and z

4x² = 4y²

4x² - 4y² = 0

(2x - 2y)(2x + 2y) = 0

x = y or x = -y

Also,

4x² = 4z²

4x² - 4z² = 0

(2x - 2z) (2x + 2z) = 0

x = z or x = -z

when x = y, x = z

when x = -y, x = -z

Hence, at the point where the box has maximum and minimal area,

x = y = z

And

x = -y = -z

Putting these into the constraint equation or the solution of the fourth partial derivative,

x² + y² + z² = 1

x = y = z

x² + x² + x² = 1

3x² = 1

x = √(1/3)

x = y = z = √(1/3)

when x = -y = -z

x² + y² + z² = 1

x² + x² + x² = 1

3x² = 1

x = √(1/3)

y = z = -√(1/3)

Inserting these into the function f(x,y,z)

f(x, y, z) = x⁴ + y⁴ + z⁴

We know that the two types of answers for x, y and z both resulting the same quantity

√(1/3)

f(x, y, z) = x⁴ + y⁴ + z⁴

f(x, y, z) = (√(1/3)⁴ + (√(1/3)⁴ + (√(1/3)⁴

f(x, y, z) = 3 × (1/9) = (1/3).

We know this point is a minimum point because when the values of x, y and z at turning points are inserted into the second derivatives, all the answers are positive! Indicating that this points obtained are

S = (1/3)

Hope this Helps!!!

6 0
3 years ago
Given the function {f(x)=32-x}^{2}f(x)=32−x 2 , what is f(-5)f(−5)?
erastova [34]

Step-by-step explanation:

the description is very difficult to understand with special characters and potential typing errors.

I suspect the definition is

function(x) = 32 - x²

function(-5)function(-5) is then very easily calculated.

we need to calculate function(-5) and then square the result, as function(-5)function(-5) is just a simple multiplication of the function results.

function(-5) = 32 - (-5)² = 32 - 25 = 7

so,

function(-5)function(-5) = 7 × 7 = 49

4 0
3 years ago
Suppose you have a data set that includes the values 20, 30, and 50. If you add a fourth value to this data set, and after doing
olya-2409 [2.1K]

Answer:

D. 100

Step-by-step explanation:

Mean = Sum of all numbers divided by the count of all numbers

Mean = 50

Let say that the sum of all numbers = X

50 = X / 4

200 = X

X = (20+30+50) + The 4th Value

200 = 100 + 4th Value

The 4th Value = 100

8 0
2 years ago
2ln(4x –7) –1=11 Solve for x to the nearest 100th
ArbitrLikvidat [17]
2(4x - 7) -1 = 11
8x - 14 -1 = 11
8x - 15 = 11
     + 15     + 15
8x = 26
/8      /8
x = 3. 25 ------> Rounded: 3.30
3 0
3 years ago
Write Algebraically: Thirty less than negative fifteen times a number is greater than 54 more than negative three times a number
Yuri [45]

Answer

-15x - 30 > -3x + 54

Explanation

Let's break this sentence down.

Thirty less than means [whatever goes before] minus 30.

Negative fifteen is -15.

Times a number means multiplying by a number. The number will be a variable. And in this case, the variable will be x.

Is greater than means more than.

Negative three is -3.

Times a number means multiplying by a number (in case you forgot or get confused, I wrote it again). That number will be a variable; x. This is the same number.

Now let's write down the equation.

Let's break both sides of the inequality, meaning the left side of 'greater than' and the right side.

The left side says this; "thirty less than negative fifteen times a number."

So let's write this.

So thirty less is minus 30. You are subtracting from "negative fifteen times a number."

Negative fifteen is -15... times a number is -15x.

So the left side of the inequality is -15x - 30.

The right side says this; "54 more than negative three times a number."

54 more than means adding 54 meaning + 54.

And you are adding 54 to "negative three times a number."

Negative three is -3, times a number is -3x.

So the right side of the inequality is -3x + 54.

So the full inequality is -15x - 30 > -3x + 54.

6 0
3 years ago
Other questions:
  • A penguin walks 10 feet in 6 seconds, so how long does it take for a penguin to walk 45 feet ?? Plz help me its due in a couple
    7·1 answer
  • Write the formula for a triangle with a height of 2 1/2 and a 13 in base
    7·1 answer
  • Write the equation in slope-intercept form.<br><br> y=12+(x-1)(-4)
    10·1 answer
  • Lauren is shopping and finds 6 bracelets, 2 pairs of earrings, and 3 necklaces that she likes. How many ways can Lauren select 4
    15·2 answers
  • PLEASE HELP IM TIMED
    5·2 answers
  • • Close the window with the Nearpod lesson to return to the rest of the lesson and cli
    14·1 answer
  • A cone-shaped tent has a diameter of 12 ft and a height of 6 ft. What is the approximate volume of the tent? Question 2 options:
    13·1 answer
  • Someone pls help I need assistance
    14·1 answer
  • Write a unit rate for the situation.
    7·2 answers
  • Use the distributive property to simplify the expression.<br> 4 (1/4a + b - 6)
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!