I need help with this problem.

A rectangle has an area of 72 swaure units. The width of the rectangle is 9 units. The length of the rectangle is 2x + 4. What i

vichka [17]

Answer:

8 units

Step-by-step explanation:

Area of a rectangle = Width multiplied by Length

Substitute in all the known numbers into this formula to get

72 = (9) × $(2x+4)$

Solve the equation for x, to find out the length

$9(2x+4)=72$

$2x+4=72/9$

$2x+4=8$

$2x=8-4$

$2x=4$

$x=4/2$

$x=2$

Length of the rectangle = $(2x+4)$

$2(2)+4$

$4+4=8$

5 0

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

6 0

3 years ago

Read 2 more answers

Can anyone please help me on this?

Elena L [17]

Answer:

b

Step-by-step explanation:

ive done this beffore im a pro

3 0

3 years ago

Find the area of the composite shape. Use 3.14 as pi. TENTH! Use your formula sheet!

murzikaleks [220]

59.6 is the answer rounded to the nearest tenth

8 0

2 years ago

Identify the range of the function shown in the graph. help

amm1812

Answer:

-5 ≤ y ≤ 5

Step-by-step explanation:

maximum y value is 5

minimum y value is -5

-5 ≤ y ≤ 5

5 0

3 years ago