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3 years ago

If i^2 = −1 and x = i + 9, which is the result of squaring x?

Mathematics

1 answer:

Anestetic [448]3 years ago

8 0

Answer:

80 + 18i

Step-by-step explanation:

i² = -1

x = i + 9

x² = (i + 9)²

Applying; (a + b)² = a² + 2ab + b² concept,

x² = i² + 18i + 81

We know that i² = -1

So x² = -1 + 18i + 81

x² = 81 - 1 + 18i = 80 + 18i

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Answer:

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Step-by-step explanation:

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4 years ago

Which ordered pair is the solution to the system of equations?

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3 years ago

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olga55 [171]

Answer:

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Step-by-step explanation:

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3 years ago

Read 2 more answers

A block of ice has a square top and bottom and rectangular sides. At a certain point in

Lilit [14]

Answer:

$\frac{dV}{dt} = 360 \ cm^3/h$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Geometry

Volume of a Rectangular Prism: V = lwh

Calculus

Derivatives

Derivative Notation

Differentiating with respect to time

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

Step 1: Define

$l = 30 \ cm\\w = l\\\frac{dl}{dt} = 2 \ cm/h\\h = 20 \ cm\\\frac{dh}{dt} = 3 \ cm/h$

Step 2: Differentiate

Rewrite [VRP]: $V = l^2h$
Differentiate [Basic Power Rule]: $\frac{dV}{dt} = 2l\frac{dl}{dt} \frac{dh}{dt}$

Step 3: Solve for Rate

Substitute: $\frac{dV}{dt} = 2(30 \ cm)(2 \ cm/h)(3 \ cm/h)$
Multiply: $\frac{dV}{dt} = 360 \ cm^3/h$

Here this tells us that our volume is decreasing (ice melting) at a rate of 360 cm³ per hour.

3 0

3 years ago

How many solutions does the following equation have?

IrinaK [193]

Answer:
Exactly one solution

Explanation:
The first step we need to take to find the answer is to find the value of y.

7(y+3)=5y+8
Expand the parentheses
7y+21=5y+8
Subtract both sides by 21
7y+21-21=5y+8-21
7y=5y-13
Subtract both sides by 5y
7y-5y=5y-13-5y
2y=-13
Divide both sides by 2
2y/2=-13/2
y=-6.5

Now, we plug y back into the original equation.

7(y+3)=5y+8
7(-6.5+3)=5(-6.5)+8
Expand the parentheses
-45.5+21=-32.5+8
-24.5=-24.5

Because both sides of the equation is equal and the equation is true, we can conclude that the equation has one solution.

I hope this helps!

7 0

3 years ago