The average value of the function y = x² – 1 on [0, 12] is

Answers

Answer 1

Answer:

47.

Step-by-step explanation:

1) the rule:

[tex]f_{avr}=\frac{1}{b-a} \int\limits^b_a {f(x)} \, dx ,[/tex]

where a;b are 0 and 12, f(x)=x²-1.

2) according to the rule above:

[tex]f_{avr}=\frac{1}{12-0} \int\limits^{12}_0 {(x^2-1)} \, dx=\frac{1}{12}(\frac{x^3}{3}-x)|^{12}_0=48-1=47.[/tex]


Related Questions

How many​ flowers, spaced every 6​ inches, are needed to surround a circular garden with a 20​-foot ​radius?

Answers

First convert the 20 ft into inches by doing 20x12 (12 inches/ft), giving you 240 inches. Then you would solve for 240/6 since you’re trying to space them by every 6 inches, leaving you with needing 40 flowers total.

20. You may already use algebra in your daily life. How do you imagine that you will use basic algebraic equations in your healthcare career? Explain.

Answers

Depending on the path that we decide to take, the algebra can help us in many forms.

As an example in the pharmaceutical/medical area, the nurses and doctors use basic algebra formulas to calculate dosages on different drugs depending on variables such as the weigh of each patient (commonly expressed as X or Y).

They used to have some paper sheets with formulas for different drug preparations (liquid ones particularly) within hospitals to avoid errors in medication.

As a healthcare provider, it is important to be able to read vital signs. Many of these are expressed as algebraic equations. Such equations can also be important when it comes to administering the right doses of medicine or converting different units of measurement.

Kathryn’s new ball has a diameter of 4 inches (in.). What is the surface area of Kathryn’s ball? Use 3.14 for π .

Answers

Answer:

50.24 in^2

Explanation:

The formula for the area of a sphere is
4πr^2, where r is the radius.

Please mark brainliest

I need the answer to this as well

Answers

C. 10x^2y + 6y^3
Due to you have two sides of 5x^2y and two sides of 3y^3

Answer:

Option C.

Step-by-step explanation:

Perimeter = 2L + 2h

[tex]P=2(5x^{2}y) +2(3y^{3} )=10x^{2} y+6y^{3}[/tex]

Hope this helps

Expand binomial (x+1)1

Answers

Answer:

x + 1

Step-by-step explanation:

Given binomial

(x + 1)¹

Use the property

a¹ = a

The binomial remains same without brackets

(x + 1)¹ = x + 1

Drag each expression to show whether it is equivalent to 54x + 18 or
(6 · 9x) + (6 · 1).

Answers

Answer:

The first one should belong in the 54x+18 due to multiplication

The second answer choice has distributive property which has to belong in the 54x+18 category

The third answer choice fits into the 6 times 9x + 6 times one category due to multiplication like the first answer choice.

The last one should be in the 54x+18 category because of the distributive property

Step-by-step explanation:

The Objectives: 54x+18 and (6(9x) + 6

The first one should belong in the 54x+18 due to multiplication

The second answer choice has distributive property which has to belong in the 54x+18 category

The third answer choice fits into the 6 times 9x + 6 times one category due to multiplication like the first answer choice.

The last one should be in the 54x+18 category because of the distributive property


pls help ill give brainliest

Answers

Answer:

y = -3x + 2

Step-by-step explanation:

use the slope formula to find the slope

replace x and y into slope intercept form with the slope you just found

A mechanic charges his customers $45 for every hour he works. He also charges the cost of parts.
For one job, he works 4.5 hours, and the parts cost $118. What is the total amount of money he
charges for the job?

Answers

W = $118 + $45h, where h=number of hours worked.

In the diagram below of ABC, AB ≅ AC, m∠A = 3x, and m∠B = x + 20.


What is the value of x?


A. 10

B. 28

C. 32

D. 40

Answers

Answer: B)28

Step-by-step explanation:

3x + x + 20 + x + 20 = 180  5x + 40 = 1805x = 140 x = 28°  






Question 5
Select the option that best describes the relationship
between the variables on the scatter plot.

Answers

Answer:

positive, leaner association

Step-by-step explanation:

Please help with this thanks! God bless you

Answers

Answer:

n=23

Step-by-step explanation:

a right angle measures 90

67+n=90

subtract 67 on both sides

n=23

Use angle addition postulate:

m∠ABD + m∠DBC = m∠ABC

Substitute values to get the required equation and solve it for n:

m∠ABD = 67°, m∠DBC = n°,  m∠ABC = 90°67 + n = 90n = 90 - 67n = 23

The function f(t) = 3 cos(pi over 6t) + 5 represents the tide in Blastic Sea. It has a maximum of 8 feet when time (t) is 0 and a minimum of 2 feet. The sea repeats this cycle every 12 hours. After nine hours, how high is the tide? 12 feet 5 feet 4.5 feet 2.5 feet

Answers

Answer:

5 feet

Step-by-step explanation:

[tex]f(t) = 3 cos \bigg( \frac{\pi}{6} t\bigg) + 5 \\ \\ plug \: t = 9 \\ \\ \implies \: f(9) = 3 cos \bigg( \frac{\pi}{6} \times 9 \bigg) + 5 \\ \\\implies \: f(9) = 3 cos \bigg( \frac{3\pi}{2}\bigg) + 5 \\ \\\implies \: f(9) = 3 cos \bigg( \pi + \frac{\pi}{2}\bigg) + 5 \\ \\\implies \: f(9) = - 3 cos \bigg( \frac{\pi}{2}\bigg) + 5 \\ [ \because \: cos ({\pi}+\theta) = -\cos \theta]\\\\\implies \: f(9) = - 3 (0) + 5 \\ ( \because \: cos \frac{\pi}{2} = 0) \\ \\ \implies \: f(9) = 0 + 5 \\ \\ \implies \: \huge{ \orange{f(9) = 5 }}[/tex]

find out 6c+4dc when c=4.5 and d=6.6
show how to do it step by step​

Answers

Answer:

145.8

Step-by-step explanation:

6c+4dc, where c=4.5 d=6.6

6(4.5) + 4(6.6) (4.5)

27 + 118.8

=145.8

PLEASE HELP ME WITH THIS!!!
Complete the sentence.
a figure but does not change its
A rotation is a transformation that
shape or size
A. flips
O B..dilates
O C. slides
O D. turns
SUBMI

Answers

Answer:

is TURNS

Step-by-step explanation:

A figure but does not change its shape and size is Turns.

What is Transformation?

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items.

A flip is a geometric movement that involves turning an object over in a straight line to create a mirror image. The distance between each point on an object and its corresponding point on the picture is equal. A reflection is another name for a flip.

Thus, thus required transformation is Turns.

Learn more about Transformation here:

https://brainly.com/question/13801312

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3(1) to the power of 2

Answers

Answer:

9

Step-by-step explanation:

Raising a number to the second means multiplying that number.  3 * 3 = 9

(x+35)(2x + 1). How do I do this

Answers

Answer:

Split brackets method see below

Step-by-step explanation:

(x+35)(2x + 1)x(2x + 1)+35(2x + 1)2[tex]x^{2}[/tex] + x + 70x + 352[tex]x^{2}[/tex] + 71x +35

what would be the best response to the question in the picture above please respond soon. (will give brainliest)

Now consider the product of a nonzero rational number and an irrational number. Again, assume x = where a and b are integers and b#0. This time lety be an irrational number. If we assume the product x.y is rational, we can set the product equal to where mand n are integers and n = 0. The steps for solving this equation for y are shown. Statement Reason cy= 02 72 D.y= substitution 8 y = multiplication property of equality a mb na Simplify Based on what we established about the classification of y and using the closure of integers, what does the equation tell you about the type of number y must be for the product to be rational? What conclusion can you now make about the result of multiplying a rational and an irrational number? ​

Answers

Answer:

The product of a rational number with an irrational number is an irrational number. To see this assume that x is a rational number and y an irrational number. Then let us assume that the product xy is rational, which means that there are integers a,b such that xy=a/b. But then we obtain y=(1/x)(a/b) which is also rational since the set of rational numbers is closed under multiplication. But this is a contradiction since y was assumed to be an irrational number.

Step-by-step explanation:

Question:Now consider the product of a nonzero rational number and an irrational number. Again, assume x =a/b , where a and b are integers and b ≠ 0. This time let y be an irrational number. If we assume the product x · y is rational, we can set the product equal to m/n, where m and n are integers and n ≠ 0. The steps for solving this equation for y are shown. Based on what we established about the classification of y and using the closure of integers, what does the equation tell you about the type of number y must be for the product to be rational? What conclusion can you now make about the result of multiplying a rational and an irrational number?

Answer:2

For circle B, BG = BE, BG is perpendicular to DC, and BE is perpendicular to FA. What conclusion can be made? a circle with center B and chords DC and FA, a segment from B to chord DC intersect chord DC at G, and a segment from B to chord FA intersects chord FA at E segment DC is parallel to segment FA segment CD is congruent to segment EB segment GB is parallel to segment EB segment DC is congruent to segment FA

Answers

Base on the equidistant chords theorem, chords FB and DA are congruent because they are equidistant from C.

What is the Equidistant Chords Theorem?

The equidistant chords theorem states that two chords in the same circle are congruent to each other, if they are equidistant from the center of the circle.

Thus, based on the information given we can conclude that chords FB and DA are congruent because they are equidistant from C based on the equidistant chords theorem.

Learn more about the equidistant chords theorem on:

https://brainly.com/question/7511582

Answer:

Its D The one at the top is incorrect.

Step-by-step explanation:

I got A 100% which means i got it right...

A nonstop train travels between Pearl River and Hoboken. On its trip south, traveling at a constant speed, it makes it from Pearl River to Hoboken in 1 hour and 6 minutes. On its return trip north, the train increases its speed by 10 miles per hour, and takes 42 minutes to reach Pearl River from Hoboken.

What was the train's original speed (on its trip south) in miles per hour?

Answers

Based on the information provided about the return trip, the train's speed on its trip south was 6.36 miles per hour.

What is the distance between Pearl River and Hoboken?Distance = speed x timeDistance = 10 miles per hour x  0.7 hours (42 minutes)Distance = 7 miles

What is the speed on the trip south?Speed = distance / timeSpeed= 7 miles / 1.1 (66 minutes)Speed= 6.36 miles per hour

Learn more about speed in: https://brainly.com/question/6280317

Find the slope of the line 11x - 4y = 21.

Answers

Answer: 11/4

Step-by-step explanation: no need :”)

What causes a heart attack?
A. When the arteries increase
B. When LDL metabolizes cholesterol
C. When the heart is starved of oxygen
D. When HDL returns cholesterol to the heart

Answers

Answer:

C.When the heart is starved of oxygen

Rewrite the parametric equations in Cartesian form: X(t) = -3sin t, y(t) = 3 cos t​

Answers

Hi the answer is 9sin ur welcome Hope this helps have a great day

Answer:

[tex]( \frac{x}{3} ) {}^{2} + ( \frac{y}{3}) {}^{2} = 1[/tex]

or x² +y²= 9

Step-by-step explanation:

In Cartesian form, the equation is expressed only in terms of y and x.

x= -3sin(t) -----(1)

y= 3cos(t) -----(2)

I've written x instead of x(t) as in the later part of the working, we will be having an equation of only x and y, thus x will no longer be a function of t. This applies to equation 2, where I have replaced y(t) with y.

Relating sine to cosine:

sin²(t) +cos²(t)= 1

[sin(t)]² +[cos(t)]²= 1 -----(3)

From (1):

[tex] \frac{x}{ - 3} = \sin(t) [/tex]

[tex] \sin(t) = - \frac{x}{3} [/tex] -----(3)

From (2):

[tex] \frac{y}{3} = \cos(t) [/tex]

[tex] \cos(t) = \frac{y}{3} [/tex] -----(4)

Substitute (4) &(5) into (3):

[tex]( - \frac{x}{3} )^{2} + ( \frac{y}{3}) {}^{2} = 1[/tex]

[tex]( \frac{x}{3} ) {}^{2} + ( \frac{y}{3} ) {}^{2} = 1[/tex]

The steps below are optional as the above is already considered to be the Cartesian form.

[tex] \frac{ {x}^{2} }{9} + \frac{y {}^{2} }{9} = 1[/tex]

Multiplying both sides by 9:

x² +y²= 9

Suppose $f(3) = 4$. Name a point that must be on the graph of $y=f(x)+4.$

Enter your answer as an ordered pair.

Answers

Answer:

  (x, y) = (3, 8)

Step-by-step explanation:

The graph for y is a translation upward 4 units of the graph of f(x).

__

A point on the graph of f(x) is given as ...

  (x, f(x)) = (3, f(3)) = (3, 4)

Then a point on the graph of y will be ...

  (x, y) = (x, f(x) +4)) = (3, f(3)+4) = (3, 4 +4)

  (x, y) = (3, 8)

-3(p-4)=-2p+1 what is p

Answers

Answer: p=11

Step-by-step explanation:

-3(p-4) = -2p+1

-3p+12=-2p+1

+2p +2p

-p+12=1

-12 -12

(-1)-p=-11 (-1)

p = 11

Check answer:

-3(11-4)=-2(11)+1

-3(7)=(-22)+1

-21 = -21

given sin0= 2/3 and angle 0 is in quadrant 2, what is the exact value of cos0 in simplest form? simplify all radicals if needed

Answers

Answer: ( -[tex]\sqrt{5}[/tex] / 3)

Step-by-step explanation:

sin(angle) = opposite/hypotenuse

opposite =2

hypotenuse = 3

solve for adjacent side with pythagorean theorum

opposite^2 + adjacent^2 = hypotenuse^2

2^2 + adjacent^2 = 3^2

4 + adjacent^2 = 9

adjacent^2 = 9 - 4

adjacent^2 = 5

adjacent = [tex]\sqrt{5}[/tex]

-[tex]\sqrt{5}[/tex] since it is in the second quadrant

cosx = (adjacent/hypotenuse)

cosx = (-[tex]\sqrt{5}[/tex]/3)

(-[tex]\sqrt{5}[/tex]/3)

What is the mode of the data represented in this line plot? Enter your answer in the box. A dot plot on a number line. The number line ranges from 5 to 11. The number 5 has 2 marks above it. The number 6 has 4 marks above it. The number 7 has 3 marks above it. The number 8 has 6 marks above it. The number 9 has 2 marks above it. The number 10 has 4 marks above it. The number 11 has 2 marks above it.

Answers

The mode of the data in the line plot is the data with the highest number of marks

The mode of the data is 8

How to determine the mode?

From the line plot, we have the following frequency table:

Number        Frequency

5                       2 marks

6                       4 marks.

7                        3 marks

8                        6 marks

9                         2 marks

10                         4 marks

11                         2 marks

The number with the highest mark is 9

Hence, the mode of the data is 8

Read more about mode at:

https://brainly.com/question/14532771

Answer: The mode is 8

Step-by-step explanation: Mode means the number that shows up must in the graph and since 8 is the highest that goes the mode is 8. Also I did the k12 quiz.

SOMEONE PLEASE HELP!!!! ILL GIVE BRAINLIEST

Answers

Answer:

Your Answer is A.

Step-by-step explanation:

Looking at the picture the LM is the original and wants to translate it to L'M'.

So Right 5 and 2 up.

Answer:

A

Step-by-step explanation:

LM is 5 units away from LM'

LM is 2 units down from LM'

BRAINLIEST please if this helped!

Which angles are supplementary to each other?
PLS HELP!

Answers

Answer: Angles 6 and 7

Step-by-step explanation:

These angles form a linear pair, and angles that form a linear pair are supplementary.

If v = X + 4t, v is the velocity and X is the displacement, how to find X in terms of t?​

Answers

[tex]x = vt\\\\\implies x= (x+4t)t\\\\\implies x=xt+4t^2\\\\\implies x -xt= 4t^2\\\\\implies x (1-t) =4t^2\\\\\implies x = \dfrac{4t^2}{1-t}[/tex]

last year a company made a profit of one and a quarter million dollars.Each year the company reinvests 1/3 of the profit How much of this profit eill they reinvest​

Answers

Answer:

$83,333

Step-by-step explanation:

1 000 000*1/4

250 000

250 000*1/3 = 83 333.33

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