Mathematics College

Question 5
5 pts
Let f(x)
40e^.06t. What is the average rate of change of f over the
interval [0,3]? Give your answer as a decimal with one place of
accuracy to the right of the decimal point.

Answers

Answer 1

Answer:

[tex]R= 2.6[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 40e^{.06t[/tex]

[tex][a,b] = [0,3][/tex]

Required

Determine the average rate of change (R)

This is calculated as follows:

[tex]R = \frac{f(b) - f(a)}{b - a}[/tex]

Where

[tex]a = 0[/tex] and [tex]b = 3[/tex]

Substitute 0 for a and 3 for b

[tex]R = \frac{f(3) - f(0)}{3 - 0}[/tex]

[tex]R = \frac{f(3) - f(0)}{3}[/tex]

[tex]R = \frac{1}{3}[f(3) - f(0)][/tex]

Calculate f(3)

[tex]f(x) = 40e^{.06t[/tex]

[tex]f(3) = 40e^{.06*3}[/tex]

[tex]f(3) = 40e^{0.18}[/tex]

[tex]f(3) = 40 * 1.197[/tex]

[tex]f(3) = 47.88[/tex]

Calculate f(0)

[tex]f(x) = 40e^{.06t[/tex]

[tex]f(0) = 40e^{.06*0}[/tex]

[tex]f(0) = 40e^{0}[/tex]

[tex]f(0) = 40*1[/tex]

[tex]f(0) = 40[/tex]

So, the expression:

[tex]R = \frac{1}{3}[f(3) - f(0)][/tex]

[tex]R= \frac{1}{3}[47.88 - 40][/tex]

[tex]R= \frac{1}{3}[7.88][/tex]

[tex]R= 2.62666666667[/tex]

[tex]R= 2.6[/tex]

Hence, the average rate of change is approximately 2.6

Related Questions

Point-slope form
Complete the point-slope equation of the line through (8, —8) and (9.8).
Use exact numbers.
y-8=

Answers

Answer:

The equation in point-slope form is:

[tex]y-\left(-8\right)=16\left(x-8\right)[/tex]

The equation of the line in slope-intercept form is:

[tex]y=16x-136[/tex]

Step-by-step explanation:

Given the points

(8, -8)

(9, 8)

Finding the slope between (8, -8) and (9, 8)

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\left(x_1,\:y_1\right)=\left(8,\:-8\right),\:\left(x_2,\:y_2\right)=\left(9,\:8\right)[/tex]

[tex]m=\frac{8-\left(-8\right)}{9-8}[/tex]

[tex]m=16[/tex]

Point slope form:

[tex]y-y_1=m\left(x-x_1\right)[/tex]

Here:

m is the slope  and (x₁, y₁) is the point

substituting the values m = 16 and the point (8, -8)  in the point-slope form

[tex]y-y_1=m\left(x-x_1\right)[/tex]

[tex]y-\left(-8\right)=16\left(x-8\right)[/tex]

Thus, the equation in point-slope form is:

[tex]y-\left(-8\right)=16\left(x-8\right)[/tex]

now completing the point-slope form equation of the line

[tex]y+8=16\left(x-8\right)[/tex]

subtract 8 from both sides

[tex]y+8-8=16\left(x-8\right)-8[/tex]

[tex]y=16x-136[/tex]

Thus, the equation of the line in slope-intercept form is:

[tex]y=16x-136[/tex]

Does anyone know this?

Answers

Answer:

b

Step-by-step explanation:

the answer is b because you got 1.08c

Answer:

2nd and 3rd don't match so with process of elimination I would go with A

Step-by-step explanation:

Y=-1/4x +9 what is the slope and y - intercept

Answers

Answer:

Step-by-step explanation:

The equation is y = Mx + b

so the slope is -1/4 and the y intercept is (0,9)

Answer all these questions, please I will give brainlist:)

Answers

Answer:

hERE BRUDDA

Step-by-step explanation:

idk what he answer is pls help​

Answers

Answer:

To Protect the egg

Step-by-step explanation:

D) To protect and prevent the egg from drying out.


Some one teach me how to do this I’m in a break out room and I don’t know how to do this

Answers

Answer:

start by putting in the y intercept, -4 on the y axis

then go up 5 and 1 right one to give your a slope of positive 5

Step-by-step explanation:

porque yo so muy inteligente,la reina...

please help meeee with this question
​

Answers

Answer:

Its possible 1 it looks like an equilateral triangle and 4 times whatever x is has to be the same as x+3 which can only be D i hope this help

Step-by-step explanation:

It is d because the one side is 4 which is the same size as the missing size so 3+1 =4 easy Peary

What property is shown in the following equation?

17 + 8 + 3 = 17 + 3 + 8

Answers

Answer:

The Commutative Law of Addition.

Step-by-step explanation:

Basically, this law says we can swap numbers over and still get the same number when we add. This has demonstrated exactly that.

Hope this helped!

Answer:

Associative property


can you guys plz help ASAP

Answers

it’s y = 1/8x - 3, so the first answer
Y = - 1/8 -3
In the question you need to subtract x from both sides then divide -8 from -x and 24

A square shaped pasture has an area of 144 square feet. What is the perimeter of the pasture?

Answers

Answer:

48 ft.

Step-by-step explanation:

sqr root 144= 12

12x4=48

the perimeter of the square should be 48 square feet.

we know that in a square, all the sides are the same length. the square root of 144 is 12, and we know the square root of a number (12) is what gives the square root (144) when multiplied by itself. the formula of area (in a square) is A = bh, where the b stands for base and the h stands for height. if the base and height multiplied equals 144, we know both the base and height are 12 square feet. so now that we know all of the sides are 12 square feet, we can finally solve perimeter. you find perimeter by adding up all the sides. 12 + 12 + 12 + 12 = 48. (you can also do 12 x 4). this is how we know the perimeter is 48 square feet.

^^ only included this in case you needed to give an explanation.

What is the solution to the system of equations graphed below?
y=-4x + 33

y=5/3x-1

Answers

Answer:

x = 6

y = 9

This is the correct answer. Not satisfied? Check out this answer expert verified answer of the same question but with a step-by-step explanation. This answer is just a simple version of rocioo's correct answer.

Expert Verified Answer (of this same question but with a step-by-step explanation):

This is the link to rocioo's answer. https://brainly.com/question/13675950

2) Which of the following is an equivalent ratio to 12:48? Choose all that apply.
a. 3:12
b. 6:24
C. 24.48
d. 24.96

Answers

3:12, because 12/4 is 3 and 48/4 is 12
its because 12:48=6:24

A square has been divided into a equal-sized pieces. Four of the peices are shaded.

Answers

Answer:

it is now 1 whole

Step-by-step explanation:

Car dealership pays a wholesale price of $10,000 to purchase a vehicle if they mark up the price 20% what is the retail price of the car

Answers

Answer:

8000

Step-by-step explanation:

10000 x 20% = 2000

10000-2000= 8000

d=.5*a*t^2 - solving for a[tex]d=.5*a*t^2[/tex]

Answers

Answer:

[tex]\displaystyle a=\frac{d}{.5*t^2}[/tex]

Step-by-step explanation:

Equation Solving

We are given the equation:

[tex]d=.5*a*t^2[/tex]

It's required to solve it for a.

Swap sides to have the letter on the left side:

[tex].5*a*t^2=d[/tex]

Divide by [tex].5*t^2[/tex]:

[tex]\mathbf{\displaystyle a=\frac{d}{.5*t^2}}[/tex]

Which two recipes have equivalent ratios of cups of flour needed to the number of cookies?

recipes cups of flour needed number of cookies
sugar 3 33
oatmeal raisin 4 40
chocolate chip 3 32
Macadamia Nut 2 22
Question 7 options:

Macadamia Nut & Oatmeal Raisin


Sugar & Oatmeal Raisin


Chocolate Chip & Sugar


Sugar & Macadamia Nut


Oatmeal Raisin & Chocolate Chip

Answers

Answer:

poop

Step-by-step explanation:

Please help me with this one

Answers

Answer:b because it has three sides.

Step-by-step explanation:

Line segment length from A to B using pythagorean theorem

Answers

Answer:

13

Step-by-step explanation:

Which number represents 50% of 1.5?
A
0.50
0.75
c
1.00
2.25

Answers

Answer:

0.75

Step-by-step explanation:

50% * 1.5

0.75

Hope this Helps!!!

Simplify:


3(8) 0 • (3) –2

a–27

b24/9

c–216

d 1/3

Answers

Answer:

-2a-27b.2^3/3c-2161/3

Order -3/4, 3/8, -1 1/8, -1/2 from least to greatest.Which is correct?

-1 1/8, -3/4, -1/2, 3/8

-1/2, -3/4, 1 1/8, 3/8

3/8, 1 1/8, -3/4 , -1/2​

Answers

Answer:

LEAST TO GREATEST: should be A. (-11/8, -3/4, -0.5, 3/8) hope this helped

Step-by-step explanation:

-1/2 is negative .0 = -0.5

-3/4 is negative .75 = -0.75

-11/8 is negative 1. 3 = -1.3

3/8 is a positive .375 = 0.375

Let Me Know if i was right.    :)

Answer:

-1 1/8, -3/4, -1/2, 3/8

Step-by-step explanation:

convert to improper fractions and same denominator

-1 1/8 = -9/8

-3/4 = -6/8

-1/2 = -4/8

3/8 = 3/8

Because -1 1/8 is further left on the number line, then -3/4, then -1/2, and finally 3/8.

Two workers win prize of £240, they share prize money in ratio of 3.5, how much does one get

Answers

Answer:
90
Step-by-step explanation:
Total Prize 240
Sharing at 3:5 = 3+5 = 8
240/8 = 30

Simplify the expression.


5(2) + 2(4 + 3)

21
24
84
140

Answers

Answer:

24

Step-by-step explanation:

5(2) + 2(4 + 3)

5 x 2 + 2 x 7

10 + 14 = 24

Here you go! :D

24 , i would explain but uhhh , actually ; 10+14= 24
5(2)=10
2(4+3)
4+3=7
7(2)=14
10+14=24

Help me fast pleaseeeee

Answers

Answer:

y=-2x-2

Step-by-step explanation:

Find slope and y intercept

Which two expressions are equivalent?
A 4(x + 5) and 4x + 9 C 4(x + 5) and 4x + 20
B 4(x + 5) and 4x + 5 D 4(x + 5) and 4 + x + 4 + 5

Answers

the answer is c bc when you multiple they equal

Two artillery bases are located at the points A and C represented in the figure. Each of the bases locates an enemy airplane at point B. The base at A measures the angles of elevation to the airplane to be 95∘ and the distance between the two bases is 739 meters. If the distance from the base at C to the plane is 2,517 meters, what is the measure, in degrees, of ∠CBA?

Answers

Answer:

the answer is 17 here is the step below

Step-by-step explanation:

Use the Law of Sines to find the distance. For a triangle with angles A, B, and C, and opposite sides a, b, and c, the Law of Sines states that sinAa=sinBb=sinCc.

In this case, the angle at point B, let it be α, needs to be found. The Law of Sines can be used to relate α, the two known sides, and the angle at point A.

The Law of Sines states that sinα739=sin95∘2517.

By simplifying, sinα=739sin95∘2517. Since α is acute, α=sin−1(739sin95∘2517)≈17.0∘.

The measure of the angle is 17 degrees if the A measures the angle of elevation to the airplane to be 95∘ and the distance between the two bases is 739 meters.

What is the triangle?

In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

We have a triangle shown in the picture

To find the measure of the angle ∠CBA

Applying sin law:

sin95/2517 = sin∠CBA/739

0.292 = sin∠CBA

∠CBA = sin⁻¹(0.292)

∠CBA = 17 degrees

Thus, the measure of the angle is 17 degrees if the A measures the angles of elevation to the airplane to be 95∘ and the distance between the two bases is 739 meters.

Learn more about the triangle here:

brainly.com/question/25813512

#SPJ2

Help me please please

Answers

Answer:

Step-by-step explanation:

i have no idea what to do

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

Answers

It’s 2x^3-3x^2-9x+10

Can someone please help me with this question

Answers

Answer:

Eat some mc donolds then ur good

Step-by-step explanation:

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o need help with my math its manly slope m

Answers

Answer:

nvm everybody hates me

Step-by-step explanation:

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