Which of these demonstrates the identity property of multiplication

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

A sundae costs $2. Additional toppings cost $0.50 each. Write and graph an equation in two variables that represents the total c

vazorg [7]

Answer:

y = 0.5x + 2

My graph looks like this:

8 0

3 years ago

Answer quick for brainliest <3

Dovator [93]

Answer:

9 and 198

Step-by-step explanation:

Multiply the bottom by 18 or divide the top by 18.

18 is the proportional relationship.

4 0

3 years ago

A recent study compared the time spent together by single- and dual-earner couples. According to the records kept by the wives d

sergij07 [2.7K]

Answer:

There is evidence to show that the single-earner couples on average spend more time watching television together

Step-by-step explanation:

Given that a recent study compared the time spent together by single- and dual-earner couples. According to the records kept by the wives during the study, the mean amount of time spent together watching television among the single-earner couples was 61 minutes per day, with a standard deviation of 15.5 minutes. For the dual-earner couples, the mean number of minutes spent watching television was 48.4 minutes, with a standard deviation of 18.1 minutes.

$H_0: \bar x=\bar y\\H_a: \bar x > \bar y$

(Right tailed test where x stands for single earner and y for double)

Let us assume sample sizes are 500 each.

Difference -12.600

Standard error 1.066

95% CI -14.6913 to -10.5087

t-statistic -11.823

DF 998

Significance level P < 0.0001

Since p is less than alpha we reject null hypothesis.

There is evidence to show that the single-earner couples on average spend more time watching television together

4 0

3 years ago

A bowl contains 1 grapefruit (G), 1 plum (P), 1 orange (0) and 1 banana (B). Ravi takes two pieces of fruit from the bowl. Compl

kkurt [141]

Answer:

GP, GO, GB, PO, PB, OB

Step-by-step explanation:

7 0

3 years ago