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3 years ago

Write an equation that can be used to find the degree measure of angle b Don’t put links !

Mathematics

2 answers:

dedylja [7]3 years ago

7 0

Answer:

Because they are supplementary angles, their sum is 180°.

∠b = 180° - 81°

∠b = 99°

Leona [35]3 years ago

5 0

Answer:

$180-81=b$

Step-by-step explanation:

Supplementary angles are angles that add up to 180. Normally, they are supplementary because they lie adjacent to one another on a line.

In this base, b is supplementary to 81! Meaning, to find b we can simply subtract 81 from 180.

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$4000 for 2years at 5% compounded quarterley

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3 years ago

Jane needs open-topped boxes to store her excess inventory at year's end. She purchases large

Debora [2.8K]

Answer:

x = 1,6 in ( the side of the corner squares )

V(max) = 67,58 in³

Step-by-step explanation:

The cardboard is:

L = 12 in w = 8 in

Let´s call "x" the side of the square from the corner:

Then the sides of the base of the open box are:

( L - 2*x ) and ( w - 2*x ) and x is the height

( 12 - 2*x ) and ( w - 2*x )

V(ob) = (L - 2*x ) * ( - 2*x ) * x

Wich is a function of x

V(x) = [( 12 - 2*x ) * ( 8 - 2*x ) ]*x

V(x) = ( 96 - 24*x - 16*x + 4*x²) * x

V(x) = 96*x - 40*x² + 4*x³

Tacking derivatives on both sides of the equation

V´(x) = 12*x² - 80*x + 96

V´(x) = 0 12*x² - 80*x + 96 = 0

Solving for x

x₁,₂ = 80 ± √ 6400 - 4608 / 24

x₁,₂ = 80 ± 42,33 / 24

x₁ = 5,10 We dismiss this solution since 2*x becomes 2*5,10 = 10,20

ant this value is bigger than 8 inches

x₂ = 1,60 in

Therefore dimensions of the box

a = 12 - 2*x ; a = 12 - 3,20 ; a = 8,8 in

b = 8 - 2*x ; b = 8 - 3,20 ; b = 4,80 in

And the volume of the open box is:

V(max) = 8,8*4,8*1,6

V(max) = 67,58 in³

How do we Know that is the maximun value for V?

We find V´´(x) = 24*x - 80 for x = 1,6 is negative ( V´´(x) = - 41,6 therefore V (x) has a local maximun for a value of x = 1,6

3 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

from this year to ten years later, the number of people employed as physician assistants in the country is expected to increase

wariber [46]

Answer:

101430

Step-by-step explanation:

69000=100 what about 147%. 69000×147/100=101430

8 0

2 years ago

I’m not sure on how to do this so could you show me step by step?

likoan [24]

Answer:

yes

Step-by-step explanation:

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3 years ago