All categories

2 years ago

Square root of -4 complex number

1 answer:

7 0

$~~~~\sqrt{-4}\\\\=\sqrt{-1 \cdot 4}\\\\=\sqrt{-1} \cdot \sqrt{4}\\\\=2i~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;\left[\text{The imaginary unit,} i=\sqrt{-1} \right]$

You might be interested in

PLEASE HELP ME GUYS OR I WONT PASS this calculus!!!!

KonstantinChe [14]

Answer:

b. $\displaystyle \frac{1}{2}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Functions
Function Notation
Exponential Rule [Rewrite]: $\displaystyle b^{-m} = \frac{1}{b^m}$
Exponential Rule [Root Rewrite]: $\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}$

Calculus

Derivatives

Derivative Notation

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]: $\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle H(x) = \sqrt[3]{F(x)}$

Step 2: Differentiate

Rewrite function [Exponential Rule - Root Rewrite]: $\displaystyle H(x) = [F(x)]^\bigg{\frac{1}{3}}$
Chain Rule: $\displaystyle H'(x) = \frac{d}{dx} \bigg[ [F(x)]^\bigg{\frac{1}{3}} \bigg] \cdot \frac{d}{dx}[F(x)]$
Basic Power Rule: $\displaystyle H'(x) = \frac{1}{3}[F(x)]^\bigg{\frac{1}{3} - 1} \cdot F'(x)$
Simplify: $\displaystyle H'(x) = \frac{F'(x)}{3}[F(x)]^\bigg{\frac{-2}{3}}$
Rewrite [Exponential Rule - Rewrite]: $\displaystyle H'(x) = \frac{F'(x)}{3[F(x)]^\bigg{\frac{2}{3}}}$

Step 3: Evaluate

Substitute in x [Derivative]: $\displaystyle H'(5) = \frac{F'(5)}{3[F(5)]^\bigg{\frac{2}{3}}}$
Substitute in function values: $\displaystyle H'(5) = \frac{6}{3(8)^\bigg{\frac{2}{3}}}$
Exponents: $\displaystyle H'(5) = \frac{6}{3(4)}$
Multiply: $\displaystyle H'(5) = \frac{6}{12}$
Simplify: $\displaystyle H'(5) = \frac{1}{2}$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Derivatives

Book: College Calculus 10e

5 0

3 years ago

Please helppppppp ❤️

liberstina [14]

Answer:

Inverse of f exists.

Step-by-step explanation:

From the graph attached,

If we do the horizontal line test for the function graphed,

We find the function as one to one function.

In other words for every input value (x-value) there is a different output value.

Since, for one-to-one functions, inverse of the functions exist.

Therefore, the answer will be,

The inverse of 'f' exists.

7 0

3 years ago

The sum of a rational number and irrational number is irrational.

tia_tia [17]

Answer:

A) Always True

6 0

4 years ago

If you shift the linear parent function, (X) = x down 6 units, what is the

jeka94

Answer:

Step-by-step explanation:

For a parent function y = f(x) and n > 0:

f(x) + n : move the graph n units up

f(x) - n : move the graph n units down

f(x + n) : move the graph n units to the left

f(x - n) : move the graph n units to the right

===================================================

We have

f(x) = x

Transformation: 6 units down

f(x) - 6 = x - 6

3 0

3 years ago

A phone call costs $0.65 for the first 3 minutes and $0.15 for each additional minute. If the total charge for the call

ira [324]

Answer:

31 Minutes

Step-by-step explanation:

4.78 = 0.15 + 0.58

0.15m = 4.78 - 0.58

m = 4.78 - 0.58 divided by 0.15 = 28 minutes

So in total we have 28 + 3 = 31 minutes

7 0

3 years ago