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3 years ago

What is the perimeter of a rectangle with length of √18 and width of √8 in simplest form?

Mathematics

1 answer:

EastWind [94]3 years ago

4 0

Answer:

P=10√2

Step-by-step explanation:

Perimeter of rectangle= 2 length + 2 width

P=2l+2w

P=2(√18)+2(√8)

P=2(√9*2)+2(√4*2)

P=2*3*√2 +2*2√2

P=6√2+4√2

P=10√2

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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: $y''(-1) =8$

6 0

3 years ago

Read 2 more answers

A sports team donates 252 tickets to a sporting event, with tickets to be shared equally among 9 classrooms. How many tickets do

Tcecarenko [31]

Answer:

28 tickets

Step-by-step explanation:

252/9=28

8 0

3 years ago

Write the rate as a unit rate. 44 points in 4 quarters

Margaret [11]

Answer:

44 p points in 4 quarters = llets per Qtr.

3 0

3 years ago

Please help me with this page!! I was absent and had the flu, and I need help!! Thankyou!

sashaice [31]

A . 1/15 equals 0.66 b. 5/12 equals 0.4166 c. 1/3 equals 0.333 d. 5/12 equals 4.6 as a round number 8). 0.4 equals 4/10 equals 2/5 9) 7.32 equals 7 3/2 10) 0.2 equals 2/10 equals 1/5 Hope this helps:)

7 0

3 years ago

What is the value of x in the equation 5(3x + 4) = 23

abruzzese [7]

5(3x+4)=23

15x+20=23

15x=23-20

15x=3

x=3/15

x=1/5=0.2

4 0

2 years ago