Someone please please help help me please please help help please please help me please please ASAP ASAP!!!!

Draw a graph of Lin's distance of a function of time for this situation:

Pavlova-9 [17]

Step-by-step explanation:

Given

Lin walks half a mile at a constant rate i.e. Lin velocity is constant. So, in the graph, it will be a straight line through the origin.

Lin is still for five minutes and after she began sprinting for the slip up to halfway i.e. Lin is accelerating or velocity is increasing for the halfway and later she started walking for the rest of the way.

3 0

2 years ago

a spinner has 36 equal sections numbered from 1 to 36. what is the probability of the spinner landing on a number greater than 2

SCORPION-xisa [38]

Answer:

56% - 44%

Step-by-step explanation:

3 0

3 years ago

Differentiate the function. y = (3x - 1)^5(4-x^4)^5

TiliK225 [7]

Answer:

$\displaystyle y' = -5(3x-1)^4(4 - x^4)^4(15x^4 - 4x^3 - 12)$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Distributive Property

Algebra I

Terms/Coefficients
Factoring

Calculus

Derivatives

Derivative Notation

Derivative of a constant is 0

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Product Rule]: $\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)$

Derivative Rule [Chain Rule]: $\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Step-by-step explanation:

Step 1: Define

Identify

y = (3x - 1)⁵(4 - x⁴)⁵

Step 2: Differentiate

Product Rule: $\displaystyle y' = \frac{d}{dx}[(3x - 1)^5](4 - x^4)^5 + (3x - 1)^5\frac{d}{dx}[(4 - x^4)^5]$
Chain Rule [Basic Power Rule]: $\displaystyle y' =[5(3x - 1)^{5-1} \cdot \frac{d}{dx}[3x - 1]](4 - x^4)^5 + (3x - 1)^5[5(4 - x^4)^{5-1} \cdot \frac{d}{dx}[(4 - x^4)]]$
Simplify: $\displaystyle y' =[5(3x - 1)^4 \cdot \frac{d}{dx}[3x - 1]](4 - x^4)^5 + (3x - 1)^5[5(4 - x^4)^4 \cdot \frac{d}{dx}[(4 - x^4)]]$
Basic Power Rule: $\displaystyle y' =[5(3x - 1)^4 \cdot 3x^{1 - 1}](4 - x^4)^5 + (3x - 1)^5[5(4 - x^4)^4 \cdot -4x^{4-1}]$
Simplify: $\displaystyle y' =[5(3x - 1)^4 \cdot 3](4 - x^4)^5 + (3x - 1)^5[5(4 - x^4)^4 \cdot -4x^3]$
Multiply: $\displaystyle y' = 15(3x - 1)^4(4 - x^4)^5 - 20x^3(3x - 1)^5(4 - x^4)^4$
Factor: $\displaystyle y' = 5(3x-1)^4(4 - x^4)^4\bigg[ 3(4 - x^4) - 4x^3(3x - 1) \bigg]$
[Distributive Property] Distribute 3: $\displaystyle y' = 5(3x-1)^4(4 - x^4)^4\bigg[ 12 - 3x^4 - 4x^3(3x - 1) \bigg]$
[Distributive Property] Distribute -4x³: $\displaystyle y' = 5(3x-1)^4(4 - x^4)^4\bigg[ 12 - 3x^4 - 12x^4 + 4x^3 \bigg]$
[Brackets] Combine like terms: $\displaystyle y' = 5(3x-1)^4(4 - x^4)^4(-15x^4 + 4x^3 + 12)$
Factor: $\displaystyle y' = -5(3x-1)^4(4 - x^4)^4(15x^4 - 4x^3 - 12)$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Derivatives

Book: College Calculus 10e

6 0

3 years ago

A) Graph the function and label all zeros. Be sure to label the axis and what you are incrementing by.

Liono4ka [1.6K]

9514 1404 393

Answer:

graph is shown below
absolute max and min do not exist
local max: 0 at x=0
local min: -500/27 ≈ -18.519 at x=10/3

Step-by-step explanation:

The function is odd degree so has no absolute maximum or minimum. It factors as ...

g(x) = x^2(x -5)

so has zeros at x=0 (multiplicity 2, meaning this is a local maximum*) and x=5.

Differentiating, we find the derivative of g(x) is zero at x = 0 and x = 10/3.

g'(x) = 3x^2 -10x = x(3x -10) ⇒ x=0 and x=10/3 are critical points

The value of g(10/3) is a local minimum. That value is ...

g(10/3) = (10/3)^2((10-15)/3) = -500/27 ≈ -18.519

__

The local maximum is (0, 0); the local minimum is (10/3, -500/27). The graph is shown below.

_____

* When a root has even multiplicity, the graph does not cross the x-axis. That means the root corresponds to a local extremum. Since this is the left-most root of an odd-degree function with a positive leading coefficient, it is a local maximum. (The function is increasing left of the left-most turning point.)

7 0

2 years ago

In a random sample of 11 residents of the state of New York, the mean waste recycled per person per day was 2.9 pounds with a st

LUCKY_DIMON [66]

Answer:

The 80% confidence interval for the mean waste recycled per person per day for the population of New York is between 1.6 pounds and 4.2 pounds

Step-by-step explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 11 - 1 = 10

80% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 10 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.8}{2} = 0.9$ . So we have T = 1.372

The margin of error is:

M = T*s = 1.372*0.98 = 1.3

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 2.9 - 1.3 = 1.6 pounds

The upper end of the interval is the sample mean added to M. So it is 2.9 + 1.3 = 4.2 pounds

The 80% confidence interval for the mean waste recycled per person per day for the population of New York is between 1.6 pounds and 4.2 pounds

6 0

3 years ago