Mathematics College

Consider the function f(x) = 6 - 7x ^ 2 on the interval [- 6, 7] Find the average or mean slope of the function on this interval , (7)-f(-6) 7-(-6) = boxed |

Answers

Answer 1

Answer:

• Mean Slope = -7

• c=0.5

Explanation:

Given the function:

[tex]f\mleft(x\mright)=6-7x^2[/tex]

Part A

We want to find the mean slope on the interval [-6, 7].

First, evaluate f(7) and f(-6):

[tex]\begin{gathered} f(7)=6-7(7^2)=6-7(49)=6-343=-337 \\ f(-6)=6-7(-6)^2=6-7(36)=6-252=-246 \end{gathered}[/tex]

Next, substitute these values into the formula for the mean slope.

[tex]\begin{gathered} \text{ Mean Slope}=\frac{f(7)-f(-6)}{7-(-6)}=\frac{-337-(-246)}{7+6}=\frac{-337+246}{13} \\ =-\frac{91}{13} \\ =-7 \end{gathered}[/tex]

The mean slope of the function over the interval [-6,7] is -7.

Part B

Given the function, f(x):

[tex]f\mleft(x\mright)=6-7x^2[/tex]

Its derivative, f'(x) will be:

[tex]f^{\prime}(x)=-14x[/tex]

Replace c for x:

[tex]f^{\prime}(c)=-14c[/tex]

Equate f'(c) to the mean slope obtained in part a.

[tex]-14c=-7[/tex]

Solve for c:

[tex]\begin{gathered} \frac{-14c}{-14}=\frac{-7}{-14} \\ c=0.5 \end{gathered}[/tex]

The value of c that satisfies the mean value theorem is 0.5.

Related Questions

The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is less than 8". Find P(A). Outcome Probability 1 0.12 2 0.11 3 0.4 4 0.02 5 0.04 6 0.17 7 0.02 00 0.09 9 0.03

Answers

We want to calculate the probability of this event A: "the outcome is less than 8". To calculate this probability, we should first note that we have a total of 9 outcomes. So, we will first identify out of this outcomes cause the event A to happen.

Since the event A is saying that the outcome is less than 8, then the outcomes that would make the event A to happen would be the numbers from 1 to 7. However, to calculate this probabilty, we will use this property of probability.

Given an event A, we have the

Find the product of -0.6 and -2/5
Express your answer as a fraction or
mixed number in simplest form.

Answers

Answer:

6/25

Step-by-step explanation:

1) -0.6 = -6/10

= -3/5

2) -0.6*-2/5 = (-3/5)*(-2/5)

=(-3*-2)/(5*5)

=6/25

identify the constant of proportionality in the following questions. 1) y= 2x + 32) y= -3x - 4

Answers

Answer:

0. k=2

1. k=-3

Explanation:

The constant of proportionality is the number that is beside the variable x in both equations.

(1)For the equation:

[tex]y=2x+3[/tex]

The constant of proportionality is 2.

(2)For the equation:

[tex]y=-3x-4[/tex]

The constant of proportionality is -3.

Find a given that the line through M(-2, a) and N(0, -2) has gradient -4

Answers

a=6

1) Given that we have M (-2, a), N(0, -2), and the gradient -4. Let's start by applying the formula for the gradient.

G = (y_2 - y_1 ) / (x_2- x_1)

2) So "a", the second coordinate of point M is equal to 6, and as the gradient is a negative number indicates a "downhill" a decreasing direction of that line.

Gary has read 30 pages of his book. Each day he wants to read 15 pages until he finishes the book which has a total of 180 pages. Write an equation to represent the situation

Answers

ANSWER

30 + 15x = 180

EXPLANATION

We have that Gary has read 30 pages of his book.

He wants to read 15 pages every day till he finishes the 180 pages.

Let the number of days it will take him be x.

This means that after reading 15 pages for x days, he will have read:

15 * x = 15x

Therefore, the total number of pages he will have read (180) will be:

30 + 15x = 180

That is the equation that represents the situation.

Divide polynomial and monomial 49c^2 d^2 - 70c^3 d^3 - 35c^2d^4 /7cd^2

Answers

[tex]\frac{49c^2d^2-70c^3d^3-35c^2d^4}{7cd^2}[/tex]

start separating the fraction into smaller fractions

[tex]\frac{49c^2d^2}{7cd^2}-\frac{70c^3d^3}{7cd^2}-\frac{35c^2d^4}{7cd^2}[/tex]

then, divide each of the fractions

[tex]7c-10c^2d-5cd^2[/tex]

HighByte Entertainment sells four types of products: video games, DVDs, CDs, and radios. The numbers sold for 2020 and 2021 are shown in the double bargraph below. Use this graph to answer the questions.

Answers

Solution

Use this graph to answer the questions below:

The numbers sold for 2020 and 2021 are shown in the double bar above

1. The number of radio sold in 2021 = 440

2. Which products sold more in 2021 than in 2020 :

The only products that sold more in 2021 than in 2020 is video games

3. Which products sold the least over the two years

The products that sold the least = DVDS

Alani want to buy a 3366 buycie She reconsidering e payment options. The image shows Option A, which consists of making an initial down payment then smallet. equesized weekly payments. Option consists of making 6 equal payments over a week WE Weekly Bike Payments A-What factors should Alanl take into consideration before deciding between Option A and Option B? B- Communicate Precisely Suppose Alani could modify Option A and still pay off the bike in 5 weeks. Describe the relationship between the down payment and the weekly payments.

Answers

[tex]\begin{gathered} partA)In\text{ option A, she must have a save money in order to give the down payment}.\text{ } \\ \text{This large initial payment }will\text{ lighten the other payments.} \\ In\text{ option B, its not necessary to have a save monye, however, each payment could be substantial} \end{gathered}[/tex][tex]\begin{gathered} partB)A\text{lani can modify option A in such a way that Its not neccesary the have too much saved money and st}ill \\ \text{pay w}eekly. \\ \text{The relation betw}een\text{ down and w}ekly\text{ payment is that as large is the first one, the w}eekly\text{ payment is smaller} \end{gathered}[/tex]

Taylor has $430 in her savings account. The annual simple interest at the bank is 2%. How much intreast will she earn on her savings in 9 months?

Answers

we have the following equation

[tex]m(t)=430+430\cdot0.02\cdot t[/tex]

where t is the time in years, as we have 9 months, we have to change to years

[tex]t=\frac{9}{12}=\frac{3}{4}=0.75[/tex]

so after 9 months we get

[tex]430+430\cdot0.02\cdot0.75=430+6.45[/tex]

So she will earn $6.45 in 9 month

A group of 23 students want to see the show at the planetarium. Tickets cost $11 for each student who is a member of the planetarium’s frequent visitor program and $13 for each student who is not a member. The total cost of the students’ tickets is $261.

Answers

Out of 23 students 19 students are the member of planetarium's frequent visitor program and 4 students are not the members.

Given,

The total number of students in a group = 23

Cost of ticket for member of planetarium's frequent visitor program = $11

Cost of ticket for the student who is not a member = $13

The total cost of the students ticket = $261

Lets take,

The number of students with membership = x

The number of students without membership = y

Total number of students, x + y = 23 -----------(1)

Now,

Total cost for the tickets, 11x + 13y = 261

Now, Multiply 13 with (1)

We get,

13x + 13y = 299

Solve for x

13x + 13y = 299 -

11x + 13y = 261

2x + 0 = 38

2x = 38

x = 38/2

x = 19

Now, put x in (1)

19 + y = 23

y = 23 - 19

y = 4

That is,

The number of students with membership is 19 and the number of students without membership is 4.

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There are 17 girls at a party with 30 guests. What fraction
of the party guests are girls?

Answers

Answer:

17/30

Step-by-step explanation:

There are 17 girls at a party with 30 guests. What fraction of the party guests are girls?

17/30

RATIOS/UNIT RATESRead and answer the question.Jessica sold 4 out of 32 boxes of the cookies her Girl Scout troop sold onSaturday. Select ALL the choices that display an equivalent ratio to thenumber of boxes Jessica sold to the total boxes sold.8 to 641:80 11O 21602:15

Answers

[tex]\begin{gathered} \text{ She sold 4 of 32, sothe initial ratio is } \\ 4\colon32,or_{} \\ \frac{4}{32} \\ \text{But we kno that} \\ \frac{4}{32}=\frac{8}{64} \\ \\ \text{and simplifyng,} \\ \frac{4}{32}=\frac{2}{16} \\ \\ \\ \text{ Or, dividying the expression 4:32 by 4, we get} \\ 1\colon8 \\ \\ \text{Thus another equivalent ratios are} \\ 1\colon8 \\ \frac{2}{16} \\ \frac{8}{64} \end{gathered}[/tex]

find the area of figure using 3.14 for pi. round your answer to nearest tenth if necessary.

Answers

Given a figure to find the area of the figure.

The given figure is the combination of two triangles and a semi-circle.

Here the radius and the base of the triangle is 10 yd and the height of the triangle is 21 yd. So, the area of the figure is;

[tex]\begin{gathered} A=2\times\frac{1}{2}\times\text{base}\times\text{height}+\frac{\pi r^2}{2} \\ =10\times21+\frac{3.14\times10^2}{2} \\ =210+\frac{314}{2} \\ =210+157 \\ =367 \end{gathered}[/tex]

Thus, the area of the figure is 367 yd^2.

write the equation of the line in slope-intercept form given the follow[tex]slope = - \frac{5}{4} \: y - intercept \: (0 \: - 8)[/tex]

Answers

Let's begin by identifying key information given to us:

[tex]\begin{gathered} slope=-\frac{5}{4}\: \\ y-intercept\: (0\: -8) \end{gathered}[/tex]

The point-slope equation is given by:

[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-intercept\: (0\: -8)\Rightarrow(x_1,y_1)=(0,-8) \\ (x_1,y_1)=(0,-8) \\ m=-\frac{5}{4} \\ y-\mleft(-8\mright)=-\frac{5}{4}(x-0) \\ y+8=-\frac{5}{4}x-0 \\ y=-\frac{5}{4}x-8 \\ \\ \therefore\text{The slope-intercept form is }y=-\frac{5}{4}x-8 \end{gathered}[/tex]

the circumference of a circle is 18pi ft. what is the area in square feet.

Answers

We have first the formula of the circumference of a circle

[tex]C=2\pi r[/tex]

In order to know the area we need to know the radius of the circle, it can be obtained using the formula above and the next information.

C=18pi

r is the radius

[tex]18\pi=2\pi r[/tex]

then we isolate the r

[tex]\begin{gathered} r=\frac{18\pi}{2\pi} \\ r=9 \end{gathered}[/tex]

the radius is 9 ft

then we can calculate the area using the next formula

[tex]A=\pi r^2[/tex]

we substitute the value of the radius

[tex]\begin{gathered} A=\pi(9)^2 \\ A=81\pi ft^2 \\ A=254.47ft^2 \end{gathered}[/tex]

Solve F(x) for the given domain. Include all of your work in your final answer. Submit your solution.

F(x) = x2 + 3x - 2

F(a) =

Answers

For a given function f(x) = x² + 3x - 2, f(a) is a² + 3a - 2 and f(x - 1) = x² + x - 4

Given,

The function f(x) = x² + 3x - 2

We have to find f(a) and domain f(x - 1)

Here,

f(x) = x² + 3x - 2

Then,

f(a) = a² + 3a - 2

Now,

f(x - 1) = (x - 1)² + 3(x - 1) - 2

f(x - 1) = x² - 2x + 1 + 3x - 3 - 2

f(x - 1) = x² + x - 4

That is,

For a given function f(x) = x² + 3x - 2, f(a) is a² + 3a - 2 and f(x - 1) = x² + x - 4

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Hello, can you please help me solve this question ASAP!!!

Answers

SOLUTION:

Step 1:

In this question, we have that:

Step 2:

Part A:

We are meant to show that the equation:

[tex]5sinx=1+2cos^2x[/tex]

can be written in the form

[tex]2sin^2\text{x + 5 sin x - 3=0}[/tex]

Proof:

[tex]\begin{gathered} \text{5 sin x = 1 + 2 cos }^2x\text{ } \\ \text{But cos}^2x+sin^2x\text{ = 1} \\ \text{Then,} \\ \cos ^2x=1-sin^2x\text{ } \\ \text{Hence,} \\ 5sinx=1+2(1-sin^2x_{}) \\ 5sinx=1+2-2sin^2x \\ 5sinx=3-2sin^2x \end{gathered}[/tex]

Re-arranging, we have that:

[tex]2sin^2x\text{ + 5 sin x - 3 = 0 }[/tex]

Part B:

b) Hence, solve for x in the interval:

[tex]0\text{ }\leq\text{ x }\leq\text{ 2}\pi[/tex]

the area of a triangular wedge is 90 square inches the height is 18in what is the base

Answers

it is given that,

the height of the wedge is h = 18 in

the area of the wedge is A = 90 square in.

we know that the area of a triangle is

A = 1/2 x base x height

put values,

90 = 1/2 x base x 18

90/18 = 1/2 x base

5 = 1/2 x base

base = 5 x 2

base = 10 inches,

thus, the base of the wedge is 10 inches,

State what additional information is required in order to know that the triangles are congruent for the
reason given.
SSS
C
D
Y
X
A) WX = ED or XY = DC
C) YW = CE
B) ZW
ZE
D) XY = DC

Answers

Answer:

C. YW≅CE

Step-by-step explanation:

SSS is used when three pairs of sides are congruent. Two pairs of congruent sides are given. YW≅CE would be the third pair and therefore prove the triangles are congruent by SSS.

the output is 9 less than 5 times the input"

Answers

Let the output is y and the input is x, then

output is means y =

9 less than 5 times input means 9 less than 5x

Then

y = 5x - 9

a man pushes a car with a force of 127.5n along a straight horizontal road.he manages to increase the speed of the car from 1 m/s to 2.8 m/s in 12 seconds. find the mass of the car. figure out acceleration first.

Answers

In order to determine the mass of the car, you first calculate the acceleration of the car, by using the following formula:

[tex]a=\frac{v_2-v_1}{\Delta t}[/tex]

where:

v2: final speed of the car = 2.8 m/s

v1: initial speed of the car = 1 m/s

Δt: time interval = 12 s

You replace the previoues values into th formula for the acceleration:

[tex]a=\frac{2.8m/s-1.0m/s}{12s}=0.15\frac{m}{s^2}[/tex]

Next, you the Newton's second law to find the mass of the car. You proceed as follow;

[tex]F=ma[/tex]

where:

m: mass of the car = ?

a: acceleration of the car = 0.15m/s²

F: force exerted on the car by the man = 127.5N

You solve for m in the formula for F, and you replace the values of the other parameters to obtain m, just as follow:

[tex]m=\frac{F}{a}=\frac{127.5N}{0.15m/s^2}=850\operatorname{kg}[/tex]

Hence, the mass of the car is 850kg

1. What would you do with each problem in order to get it in its simplest properform? Use words to explain the specific details to why you used thatprocess/rule.Number 2 a and b

Answers

Given

[tex]-6y^0\text{ and \lparen-6y\rparen}^0[/tex]

The solutions can be seen below.

Explanation

[tex]\begin{gathered} a)\text{ }-6y^0=-6\times y^0=-6\times1=-6 \\ b)\text{ }(-6y)^0=1 \end{gathered}[/tex]

In "a," only the y-value is raised to the power of 1 hence, the reason why y^0 became 1 which then multiplies -6 to get -6. However, in "b", the entire expression is raised to the power of zero, which will then give 1 as the answer.

1. Input, X 9753 1 Output, y 1 2 2 3 4 Function - Yes or no

Answers

before we can dtermone whether it is a function, there must be a relationship between X and y i.e they must have a constannt of proportionality as shown:

From the table:

when x = 9, y = 1

when x = 7, y = 2

when x = 5, y = 2

when x = 3, y = 3

when x = 1, y = 4

let us determine the constant of proportionality from the given values as shown:

k = y2-y1/x2-x1

when x = 9, y = 1

when x = 7, y = 2

k = 2-1/7-9

k = 1/-2

k = -1/2

Also

when x = 5, y = 2

when x = 3, y = 3

k = 3-2/3-5

k = 1/-2

k = -1/2

Also;

when x = 5, y = 2

when x = 3, y = 3

k = 3-2/3-5

k = 1/-2

k = -1/2

Since all the constant of proportionality are the same;

Hence y = kx

y = -1/2 x

This shows that the tabke is a function and X is directly proportional to y. hence the answer is YES, it is function

Answer is Yes it’s a function

Reason

For every x value there is a unique y value, so the x value “input” cannot be repeated. If there are two like x values, there will be two points on your graph that will not pass the vertical line test. The vertical line test is used to determine if a set is a function or not.

See attachment for example.

What is 150% of 38.

Answers

We are asked to find 150% of 38

Step 1:

Convert the 150% to decimal by removing the % sign which means dividing by 100.

150/100 = 1.5

Step 2:

Now simply multiply the decimal percentage with the number 38

1.5×38 = 57

Therefore, 150% of 38 is found to be 57

SKIPPYTHEWALRUS U CAN'T ANSWER THIS QUESTIONI NEED CORRECT ANSWER 100 POINTS ONLY ANSWER CORRECTLY

A line passes through the points (7,9) and (10,1). What is its equation in point-slope form?

Use one of the specified points in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.

Answers

Answer:

y - 1 = -8/3(x - 10)

also valid:

y - 9 = -8/3(x - 7)

Step-by-step explanation:

Point-slope equation is a fill-in-the-blank formula that is sort of a shortcut for writing the equation of a line. Point-slope is named that bc you fill in a point and the slope.

Point-slope Eq:

y - Y = m(x - X)

fill in the slope for the m and fill in any point on the line for the X,Y.

First slope:

Slope is y-y over x-x

9-1 / 7-10

= 8/ -3

= -8/3

So slope is -8/3 fill that in for the m.

y -Y = -8/3(x-X)

Pick one of the points (either one it totally doesn't matter)

Let's use (10,1)

fill in 10 for X and 1 in place of Y.

the y in the very front stays a y and the first x in the parentheses stays an x, so there will be two variables in your completed answer.

y - 1 = -8/3(x - 10)

make sure the parentheses on the right is beside the -8/3 fraction and is NOT written on the bottom, beside the 3 only.

Solve 2/3 (6w+12) this equation

Answers

Answer:

4w+8

Step-by-step explanation:

6x + 14y what is the letter y in this problem?

Answers

The value of letter y in this problem is y = 6x / -14

How to solve the equation

The equation says that 6x + 14y

To solve the equation that we have here, we would have to equate to 0

such that we would have the equation as 6x + 14y = 0

6x + 14y = 0

then we would have

6x = - 14y

remember that when positives crosses over we would have it turn as negative.

Next we would have to divide through by - 14 in order to get the value of y

hence we would have

-14y / -14 = 6x / -14

then we would have y as

y = 6x / -14

Answers

SOLUTION

In a box and whisker plot, the firt dot on the box is Q1

The second dot on the box is Q2

The third dot on the box is Q3

Q2 is the median

From what we see,

[tex]Q2=25[/tex]

Hence the answer is 25, option D

how to calculate 1+2?

Answers

[tex]\begin{bmatrix}{g} & {4} \\ {2} & {1}\end{bmatrix}+\text{ }\ln \tan ^{-1}[/tex]

mathematics assignment

Answers

Examining the function the graph that is correct is the graph in option C

What is graph ?

A graph is a representation of data using accepted means of presentation.

The graph used in the question is in cartesian coordinate and it a parabolic graph

How to find the correct graph

The given data is h(x) = -x² - 4

Examining the given function

The term -x² is a negative term hence the graph opens downwards

The value of h(x) when x = 0 is -4. Therefore the graph will have an intercept at -4

The graph of option C is the one that meets the required criteria hence the nest option

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