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2 years ago

(i) Factorise the expression x^3 + 3x - x^2 - 3 completely.

Mathematics

1 answer:

krok68 [10]2 years ago

4 0

Step-by-step explanation:

Answer 1 put all like terms then solve

hope it helps....

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Billy received a raise after his first year on the job to $45,000 from his initial salary of $42,400. What was his real raise st

solong [7]

Billy get 5.9% raise after completing first year.

<h3>What is PERCENTAGE?</h3>

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100.

Here, Billy's initial salary = $ 42,500

After raise, salary become $ 45,000

Change in salary = Raised salary - Initial salary

= 45000 - 42500

= $ 2500

% Change = change / initial salary X 100

= 2500 / 42500 X 100

= 0.0589 X 100

≈ 5.9 %

Thus, Billy get 5.9% raise after completing first year.

Learn more about Percentage from:

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1 year ago

a bus is traveling at a constant speed.if the bus is 15 1/2 miles in 1/3 of an hour. how many miles will the bus travel in one h

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Answer:

Step-by-step explanation:

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2 years ago

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4. True or false: Lines, colors, and textures are often used to create shapes.

ioda

Answer:

true!

Step-by-step explanation:

because if we havent got lines, colors , and textures

how could shapes be created?

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1 year ago

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Round 9594.20475485 to the nearest thousand

MrRissso [65]

Answer:

it is 10,000

Step-by-step explanation:

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3 years ago

Implicit differentiation Please help

Anvisha [2.4K]

Answer:

$y''(-1) =8$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Algebra I

Factoring

Calculus

Implicit Differentiation

The derivative of a constant is equal to 0

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Product Rule: $\frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)$

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

Quotient Rule: $\frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}$

Step-by-step explanation:

Step 1: Define

-xy - 2y = -4

Rate of change of the tangent line at point (-1, 4)

Step 2: Differentiate Pt. 1

Find 1st Derivative

Implicit Differentiation [Product Rule/Basic Power Rule]: $-y - xy' - 2y' = 0$
[Algebra] Isolate y' terms: $-xy' - 2y' = y$
[Algebra] Factor y': $y'(-x - 2) = y$
[Algebra] Isolate y': $y' = \frac{y}{-x-2}$
[Algebra] Rewrite: $y' = \frac{-y}{x+2}$

Step 3: Find y

Define equation: $-xy - 2y = -4$
Factor y: $y(-x - 2) = -4$
Isolate y: $y = \frac{-4}{-x-2}$
Simplify: $y = \frac{4}{x+2}$

Step 4: Rewrite 1st Derivative

[Algebra] Substitute in y: $y' = \frac{-\frac{4}{x+2} }{x+2}$
[Algebra] Simplify: $y' = \frac{-4}{(x+2)^2}$

Step 5: Differentiate Pt. 2

Find 2nd Derivative

Differentiate [Quotient Rule/Basic Power Rule]: $y'' = \frac{0(x+2)^2 - 8 \cdot 2(x + 2) \cdot 1}{[(x + 2)^2]^2}$
[Derivative] Simplify: $y'' = \frac{8}{(x+2)^3}$

Step 6: Find Slope at Given Point

[Algebra] Substitute in x: $y''(-1) = \frac{8}{(-1+2)^3}$
[Algebra] Evaluate: $y''(-1) =8$

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2 years ago

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