Please help with algebra

Help with b please. thank you

erastovalidia [21]

Answer:

See explanation.

General Formulas and Concepts:

Algebra I

Terms/Coefficients
Factoring

Algebra II

Polynomial Long Division

Pre-Calculus

Parametrics

Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Derivative Property [Addition/Subtraction]: $\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]$

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

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

Parametric Differentiation: $\displaystyle \frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle x = 2t - \frac{1}{t}$

$\displaystyle y = t + \frac{4}{t}$

Step 2: Find Derivative

[x] Differentiate [Basic Power Rule and Quotient Rule]: $\displaystyle \frac{dx}{dt} = 2 + \frac{1}{t^2}$
[y] Differentiate [Basic Power Rule and Quotient Rule]: $\displaystyle \frac{dy}{dt} = 1 - \frac{4}{t^2}$
Substitute in variables [Parametric Derivative]: $\displaystyle \frac{dy}{dx} = \frac{1 - \frac{4}{t^2}}{2 + \frac{1}{t^2}}$
[Parametric Derivative] Simplify: $\displaystyle \frac{dy}{dx} = \frac{t^2 - 4}{2t^2 + 1}$
[Parametric Derivative] Polynomial Long Division: $\displaystyle \frac{dy}{dx} = \frac{1}{2} - \frac{7}{2(2t^2 - 1)}$
[Parametric Derivative] Factor: $\displaystyle \frac{dy}{dx} = \frac{1}{2} \bigg( 1 - \frac{9}{2t^2 + 1} \bigg)$

Here we see that if we increase our values for t, our derivative would get closer and closer to 0.5 but never actually reaching it. Another way to approach it is to take the limit of the derivative as t approaches to infinity. Hence $\displaystyle \frac{dy}{dx} < \frac{1}{2}$ .

Topic: AP Calculus BC (Calculus I + II)

Unit: Parametrics

Book: College Calculus 10e

7 0

3 years ago

The perimeter of a college basketball court is 96 meters and the length is 14 meters more than the width. What are the dimension

soldi70 [24.7K]

Answer:

length = 32m, width= 16m

Step-by-step explanation:

l=2w

2(2w+w)=96

2(3w)=96

6w=96,w= 96/6 = 16m

l=2w=2x16=32m

8 0

3 years ago

Read 2 more answers

If you purchase 27 guppies, and the increase rate of 35% per year,how many guppies will you have after 3 years

dem82 [27]

Answer:

66

Step-by-step explanation:

year 1: 35% of 27

convert 35% into a decimal :0.35

0.35 x 27= 9.45

27+ 9.45= 36.45 , thats what you have left at the end of year 1

year 2: 35% of 36.45

0.35 x 36.45= 12.7575

36.45 + 12.7575= 49.2075, thats whats left at the end of year 2

year 3: 35% of 49.2075

0.35 x 49.2075= 17.222625

49.2075+ 17.222625= 66.430125, thats whats left at the end of the 3rd year.

you cant have 66.430125 of a guppy so it rounds to a whole number- 66

let me know if this was helpful :)

7 0

3 years ago

For the given true statements, what can you conclude using the Law of Syllogism?

musickatia [10]

Answer: If a quadrilateral is a square, then it is a rectangle. (choice D.)

Step-by-step explanation:

The Law of Syllogism states that if the following two statements are true: If p , then q . If q , then r . Then we can derive a third true statement: If p , then r .

We can apply this rule in the conditional statements:

If a quadrilateral is a square, (p) then it has four right angles. (q)

If a quadrilateral has four right angles, (q) then it is a rectangle. (r)

Therefore:

If a quadrilateral is a square, (p) then it is a rectangle. (r)

I hope this helps!

5 0

3 years ago

Of the 206 bones in the human skeleton, 106 are in the hands and feet. What fraction of these bones is not in the hands and feet

Mkey [24]

53/103 and no it cant be simplified. also a high school student answered this. feel the shame

8 0

4 years ago