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2 years ago

The average low temperature by month in Nashville is represented by the function

Mathematics

1 answer:

malfutka [58]2 years ago

4 0

Answer:

Step-by-step explanation:

Given the average low temperature by month in Nashville is represented by the function f(x)=-1.4x² + 19x +1.7, where x is the month, the average rate of change is expressed as d[f(x)]/dx = 2(1.4x) + 19

d[f(x)]/dx = 2.8x + 19

Since the number of months between March and August is 5 months and x is in months, hence we will substitute x = 5 into the resulting function to get the average rate of change from March to August as shown;

d[f(x)]/dx at x = 5

= 2.8(5)+ 19

= 14 + 19

= 33

<em>Hence the average rate of change from March to August is 33</em>

You might be interested in

a) The curve with equation y2 = x3 + 3x2 is called the Tschirnhausen cubic. Find an equation of the tangent line to this curve a

Neporo4naja [7]

Answer:

Tangent at (1,2) has value $\frac{15}{4}$ . And (-2, 4) is the point of intersection of horizontal tangent.

Step-by-step explanation:

Given curve equation,

$y^2=x^3+3x^2\hfill (1)$

To find tangent at (x,y)=(1,2) and point of intersection of horizontal tangent, differentiate (1) withrespect to x we get,

$2y\frac{dy}{dx}=x^3+3x^2$

$\implies \frac{dy}{dx}=\frac{3(x^2+2x)}{2y}$

At (1, 2), tangent line is,

$\frac{dy}{dx}|_{(1,2)}}=\frac{15}{4}$

To find point of intersection of horizontal tangent we have to do,

$\frac{dy}{dx}=0$

$\implies x(x+2)=0\implies x=0 or -2$

Thus,

At x=0, y=0

but snce,

$\lim_{y\to 0}\frac{dy}{dx}\to \infty$

at (0,0) there exist a vertical tangent. And,

At x=-2, y=4.

Thus (-2, 4) is the point of intersection of horizontal tangent.

6 0

2 years ago

Children under 10 years and older people over 65 years receive a discount on movie tickets. Let x represent the age of a person

mr_godi [17]

0<x<10

x>65

0<x<10 or x>65

4 0

2 years ago

In a large population, 61 % of the people have been vaccinated. if 4 people are randomly selected, what is the probability that

muminat

In a large population, 61% of the people are vaccinated, meaning there are 39% who are not. The problem asks for the probability that out of the 4 randomly selected people, at least one of them has been vaccinated. Therefore, we need to add all the possibilities that there could be one, two, three or four randomly selected persons who were vaccinated.

For only one person, we use P(1), same reasoning should hold for other subscripts.

P(1) = (61/100)(39/100)(39/100)(39/100) = 0.03618459
P(2) = (61/100)(61/100)(39/100)(39/100) = 0.05659641
P(3) = (61/100)(61/100)(61/100)(39/100) = 0.08852259
P(4) = (61/100)(61/100)(61/100)(61/100) = 0.13845841

Adding these probabilities, we have 0.319761. Therefore the probability of at least one person has been vaccinated out of 4 persons randomly selected is 0.32 or 32%, rounded off to the nearest hundredths.

8 0

1 year ago

Suppose that a person with a push mower can mow a large lawn in 5 hours, whereas the lawn can be mowed with a riding lawn mower

Reil [10]

------------------------------------------------------------------
Push Mower
------------------------------------------------------------------
It takes 5 hours to complete the job
1 hour = 1/5 of the job

------------------------------------------------------------------
Riding Lawn Mower
------------------------------------------------------------------
It takes 3 hours to complete the job
1 hour = 1/3 of the job

------------------------------------------------------------------
Push Mower + Riding Lawn Mower
------------------------------------------------------------------
1 hour = 1/5 + 1/3
1 hour = 3/15 + 5/15
1 hour = 8/15 of the job.

------------------------------------------------------------------
Calculate time needed to complete
------------------------------------------------------------------
8/15 of the job takes 1 hour
8/15 of the job = 1 hour

------------------------------------------------------------------
Divide by 8/15 on both side
------------------------------------------------------------------
8/15 ÷ 8/15 of the job = 1 ÷ 8/15 hour
Whole of the job = 1 x 15/8 hours
Whole of the job = 15/8 hours
Whole of the job = 1 7/8 hours

------------------------------------------------------------------
Answer: 1 7/8 hours
------------------------------------------------------------------

6 0

1 year ago

Mary was told that a line goes through the points (1, 3) and (6, -2) and has a slope of 3.

ki77a [65]

Answer:

a. The slope is incorrect

b. y = 3x, ( 0 , 0 )

c) y = 4 - x

Step-by-step explanation:

Given:-

The slope between two points (1, 3) and (6, -2) is 3.

a. Explain why the information Mary was given cannot be correct.

- The slope between two arbitrary points, ( x1 , y1 ) and (x2 , y2) is given by the following relationship:

slope = ( y2 - y1 ) / ( x2 - x1)

- Use the given points (1, 3) and (6, -2) and determine the slope:

slope = ( -2 - 3 ) / ( 6 - 1 )

slope = ( -5 ) / ( 5 )

slope = -1

- Yes, the given slope is incorrect it should be = -1

b.If the given point (1, 3) and the given slope are correct, what is the equation for the line? Give the coordinates of another point on the line

- We will assume the point (1,3) lies on line with a slope = 3.

- We will use the slope-intercept equation of line:

y = slope*x + c

Where, m : Slope

c : y-intercept

y = 3x + c

Using the given correct point to evaluate the y-intercept (c):

3 = 3*1 + c

c = 0

- The equation of line is,

y = 3x

- The origin (0,0) lies on the line y = 3x.

c. If the given points are correct for the line, what is the slope? Write an equation for the line

- We will assume the points (1, 3) and (6, -2) lies on line with a slope calculated in part (a) to be = -1.

- We will use the slope-intercept equation of line:

y = slope*x + c

Where, m : Slope

c : y-intercept

y = -x + c

Using the given points to evaluate the y-intercept (c):

3 = -1 + c

c = 4

- The equation of line is,

y = -x + 4

4 0

2 years ago