Find the area of the region that lies under the parabola y=5x - x^2, where 1≤x≤4. I would definitely like to see some work :)

Answers

Answer 1

Answer:

  16.5 square units

Step-by-step explanation:

You are expected to integrate the function between x=1 and x=4:

  [tex]\displaystyle\text{area}=\int_1^4{(5x-x^2)}\,dx=\left.\left(\dfrac{5}{2}x^2-\dfrac{1}{3}x^3\right)\right|_{x=1}^{x=4}\\\\=\dfrac{5(4^2-1^2)}{2}-\dfrac{4^3-1^3}{3}=37.5-21=\boxed{16.5}[/tex]

__

Additional comment

If you're aware that the area inside a (symmetrical) parabola is 2/3 of the area of the enclosing rectangle, you can compute the desired area as follows.

The parabolic curve is 4-1 = 3 units wide between x=1 and x=4. It extends upward 2.25 units from y=4 to y=6.25, so the enclosing rectangle is 3×2.25 = 6.75 square units. 2/3 of that area is (2/3)(6.75) = 4.5 square units.

This region sits on top of a rectangle 3 units wide and 4 units high, so the total area under the parabolic curve is ...

  area = 4.5 +3×4 = 16.5 . . . square units

Find The Area Of The Region That Lies Under The Parabola Y=5x - X^2, Where 1x4. I Would Definitely Like

Related Questions

What is the range for this set of data? 7, 15, 12 3 5 8 12.

Answers

The range of the data set is 12.

Answer:

its D

Step-by-step explanation:

A town has a population of 2000 and grows at 4. 5% every year. What will be the population after 13 years, to the nearest whole number?.

Answers

Answer:

3544 people

Step-by-step explanation:

We can start by representing this as an exponential function, in the form [tex]y=a(b)^x[/tex]

2000 will be our a, or our initial value. We must convert our multiplier, 4.5% to a decimal, which is 1.045. 13 is our input since it's our number of years where we want to find the population. Now that we have our variables, lets make an equation.

[tex]y=2000(1.045)^13[/tex]

PEMDAS states that we first do exponents, so lets raise 1.045 to the 13th power.

[tex]y=2000(1.77219609724)[/tex]

Now we multiply by 2000!

[tex]y= 3544.39219448[/tex]

Rounded to the nearest whole number is 3544. Therefore, there will be 3,544 people living in the town in 13 years.

Dylan is recording the types of birds he sees while bird Dylan is recording the types of bird he sees wild bird watching in the park. On Day 1, he records seeing 16
different types of birds. On Day 2, his number drops by 25%. On Day 3, he records seeing 3 more types of birds
than on Day 2.
What was the percent increase from Day 2 to Day 3?
Enter your answer in the box.

Answers

Answer:

15%

Step-by-step explanation:

Ok so if you have to get rid of 25% of 16 than thats 12 because 4 quarters is 100 than you have to think how much does he have know which is 75% so three more types of birds adds 15% and 75 + 15= 90 and the increase was 15% so The answer is 15%

How much is the check written for in words?

Answers

Answer:

one hundred fourty dollars and eleven cents

What is the correct justification for the first step in solving this
equation? 3(x - 4) + 1 = 12x *
-
O Addition Property
O Division Property
O Commutative Property
O Distributitive Property

Answers

Answer:

x=11/9

Step-by-step explanation:

Find the 66th term of the following arithmetic sequence. 15,24,33,42

Answers

ANSWER:⇒ a₆₆ = 600

Write the general term through the pattern:

an = 9n + 6

Substitute and calculate:

a₆₆ = 600

2x(3+4)to the 2nd power​

Answers

Answer:

196

Step-by-step explanation:

When adding 3 and -9, how do you know that the sum is negative?



Answers

Answer:

You know it is negative because you are adding a small number and a bigger negative number. At first number lines are helpful to visualize it.

Step-by-step explanation:

Maybe this will help:

Let's say you are borrowing money from a friend and need to pay them back. You own your friends $9, but you only have 3. So, you give them your $3. This leaves you owning $6.

3-9=-6

negative = owes money

what are the length and width of a rectangular traffic sign if the length exceeds the width by 22 inches and the perimeter is 136 inches?

Answers

Answer: L=46in

Step-by-step explanation:

Using the formulaP=2(l+w)Solving forll=P2﹣w=1362﹣22=46in

Marcelo has 6 red marbles in his marble collection. The red marbles make up 12% of all the marbles. How many marbles are in Marcelo’s collection? Show your work.

Answers

If 6/? makes of 12/100, we need to divid 100 by two to figure out the denominator of six. This is because to go from 12 to six (the numerators), you divide by two, so you do it for the denominator as well. This would give 6/50, which means there are 6 red marbles out of 50 marbles in the collection.

The total number of marbles in Marcel's collection is 50.

What is the percentage?

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that Marcelo has 6 red marbles in his marble collection. Red marbles make up 12% of all the marbles.

The number of marbles in Marcel's collection is calculated as,

12% of marbles = 6

1% of marbles = 6 / 12

100% of the marbles= ( 6 / 12) x 100

100% of the marbles = 50

To know more about percentages follow

https://brainly.com/question/24304697

#SPJ2

help plss i need help

Answers

it’s b. you divide by 5 on both sides and at the end you’ll get x= 6

Write the slope-intercept form of the equation for the line.

Answers

Answer:

The slope-intercept form is written as y = mx+b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis). It's usually easy to graph a line using y=mx+b.

Step-by-step explanation:

help me out please i need help

Answers

Answer:

Triangle 1: isosceles

Triangle 2: equilateral

Triangle 3: Scalene

help ;_;
find the cube root


³√64. ³√-216
[tex] - \times \frac{343}{100} } [/tex]

Answers

Step-by-step explanation:

³√64 = 4

therefore 4³ = 64.

³√-216 = -6

therefore -6³ = -216

What is the answer of 150⅗ – 10 – 129⅘​

Answers

Answer:

10.8 or 5 4/5

Step-by-step explanation:

Im guess its right answer

Help !!!!!!!!!! How can I Select the expressions that are factored correctly.

Answers

Answer:

[tex]3x^2 + 14x + 8 = (3x+2)(x+4)[/tex]

[tex]x^2-10x+25=(x-5)^2[/tex]

Step-by-step explanation:

[tex]x^2 - 26 = (x-6)^2[/tex]

[tex](x-6)(x-6)[/tex]

[tex]x^2-6x-6x+36[/tex]

[tex]x^2-12x+36[/tex] (wrong)

[tex]3x^2 + 14x + 8 = (3x+2)(x+4)[/tex]

[tex](3x+2)(x+4)[/tex]

[tex]3x^2+12x+2x+8[/tex]

[tex]3x^2+14x+8[/tex] (true)

[tex]x^2-7x+10=(x+5)(x+2)[/tex]

[tex](x+5)(x+2)[/tex]

[tex]x^2+2x+5x+10[/tex]

[tex]x^2+7x+10[/tex] (wrong)

[tex]x^2-10x+25=(x-5)^2[/tex]

[tex](x-5)^2[/tex]

[tex](x-5)(x-5)[/tex]

[tex]x^2-5x-5x+25[/tex]

[tex]x^2-10x+25[/tex] (true)

Hope this helps!

I need the answer step by step pls asap

Answers

Answer:

27

Step-by-step explanation:

[tex] \frac{2 {}^{3} \times 3 {}^{4} \times 4}{3 \times 32 } [/tex]

Make everything in the form of exponet.

[tex] \frac{ {2}^{3} \times {3}^{4} \times {2}^{2} }{3 {}^{1} \times 2 {}^{5} } [/tex]

Use the rule.

[tex]a {}^{m} \times {a}^{n} = a {}^{m + n} [/tex]

[tex] \frac{2 {}^{3 + 2} \times {3}^{4} }{3 \times {2}^{5} } [/tex]

[tex] \frac{2 {}^{5} \times {3}^{4} }{3 \times {2}^{5} } [/tex]

Cancel out like Terms.

[tex] \frac{3 {}^{4} }{3} [/tex]

Use the property

[tex] \frac{a {}^{m} }{a {}^{n} } = {a}^{m - n} [/tex]

So we have

[tex]3 {}^{4 - 1} = 3 {}^{3} [/tex]

[tex]3 {}^{3} = 27[/tex]

Answer: 3^3

(2^3 x 3^4 x 4)/(3 x 32)
= (2^3 x 3^4 x 2^2)/(2^5 x 3)
= 3^4/3
= 3^3

Expand the following expression: 15(2+5x)

Answers

Answer:

30+75x

Step-by-step explanation:

15(2+5x)

15 multiple by 2 = 30
15 multiple by 5x = 75x
Answer is 30+75x

A Man's dream was to talk to his loved ones for a decade non stop. His network provider has a call rate of 11kobo/secs How much airtime does he need to accomplish his unrealistic dreams​

Answers

Answer:

315,532,800 or 315,619,200 if you are going by seconds, but if it is asking for kobo then just multiply 11 by this, I am probably wrong, if I am I am so sorry

Step-by-step explanation:

Solve and reduce to lowest terms: 6 x 3/8

PLEASE HELP FIVE MINUTES!! WILL GIVE BRANLEST

Answers

Answer:

18/8 or as a mixed number 2 ¹/4

Step-by-step explanation:

just times 6/1 by 3/8 which is 18 over 8 and simplify it into 2 ¹/4

Hii! Goodafternoon/morning!

Your question is asking how much is 3/8 + 3/8 + 3/8 is.

Normally, we would find a common denominator. But since they are all the same fraction, we don't need to.

First we need to figure out what 6×3 equals. That is 18.

We can't multiply 6×8.

So

We have to write the fraction has

18/8

But thats not simplified. So we need to turn this into a mixed number.

18/8 simplified is 2 2/8

We need to simplify that again.

2 2/8 simplified is 2 1/4.

So the answer is

2 and 1/4.

Brainliest??

-Nat

In circle C, r=32 units. What is the area of circle c

Answers

Answer:

≈3216.99088 OR 32π

Step-by-step explanation:

A=πr2=π·32≈3216.99088 OR 32π

(This purple side is what will be graded for the 605 project when you submit it!)

Complete your project on this side!

For this activity, you will need two coins.
First, you will determine the theoretical probability of events.
Then, you will flip the coins 100 times and determine the experimental probability of the events.

Flip two coins 100 times, and record the results of each coin toss in a table like the one below:

Result
Frequency
Two Heads
28
Two Tails
30
1 Head, 1 Tail
42



complete below


Answer the following questions based on the data you gathered. You must show your work to receive credit.

1. What is the theoretical probability that a coin toss results in two heads showing?

2. What is the experimental probability that a coin toss results in two heads showing?


3. What is the theoretical probability that a coin toss results in two tails showing?

4. What is the experimental probability that a coin toss results in two tails showing?


5. What is the theoretical probability that a coin toss results in one head and one tail showing?


6. What is the experimental probability that a coin toss results in one head and one tail showing?


7. Compare the theoretical probabilities to your experimental probabilities. Why might there be a difference?

Answers

1. The theoretical probability that a coin toss results in two heads showing is 25% :

The probability of a head showing the first time is 50%
The probability of getting a head twice is 50% x 50% = 25%

2. The experimental probability that a coin toss results in two heads showing is 28/100 (28%)

3. The theoretical probablity that a coin toss results in two tails showing is 25% ( 50% x 50% )

4. The experimental probability that a coin toss results in two tails showing is 30/100 (30%)

5. The theoretical probability that a coin toss results in one head and one tail showing is 25% (also 50% x 50%)

6. The experimental probability that a coin toss results in one head and one tail showing is 42/100 (42%)

7. The theoretical probabilities have a difference from experimental probabilities because theoretical probabilities are equal odds of happening, while experimental probabilities might be biased because we might get tails for example, 10 times in a row, which messed up the odds.

Hope this helps. somehow.

WILL GIVE BRAINLIEST

CAN SOMEONE GIVE A EXPLAINATION ABOUT CLOSURE PROPERTY WITH A SIMPLE EXAMPLE THAT IS EASY TO UNDERSTAND

Answers

Explanation:

A set is "closed" for a particular operation if performing that operation on members of the set always gives a member of the set.

closed example

For example, the set {0, 1} is closed for multiplication:

  0 × 0 = 0

  0 × 1 = 0

  1 × 1 = 1 . . . all result values are members of the set

Performing multiplication on any two members of the set gives a member of the set.

__

not closed example

The same set {0, 1} is not closed for addition:

  0 +0 = 0

  0 +1 = 1

  1 +1 = 2 . . . not a member of the set

Performing addition on any two members of the set does not always give a member of the set.

_____

Additional comment

Sometimes you are asked to demonstrate closure of a particular set using a particular example. As we see with addition, above, some examples may seem to demonstrate closure, while another example may prove the set is not closed. In short, you can demonstrate that the set is closed for a particular operation on a particular example, but that does not demonstrate closure in general.

On the first day it was posted online, a music video got 390 views. The number of
views that the video got each day increased by 30% per day. How many total views
did the video get over the course of the first 13 days, to the nearest whole number?

Answers

Answer:

The answer is 7212 views

Step-by-step explanation:

Given;A music video got 390 views.The number of views that the video got each day increased by 30% per day.To Find;Total views did the video get over the course of the first 13 days

So, For the first day the number of views is 390

Second Day

30% increased of total views

390 × 30 ÷ 100 = 11.7 = 12

390 + 12 = 402

Third Day

30% increased of total views

402 × 30 ÷ 100 = 120.6 = 121

402 + 121 = 523

Fourth Day

30% increased of total views

523 × 30 ÷ 100 = 156.9 = 157

523 + 157 = 680

Fifth Day

30% increased of total views

680 × 30 ÷ 100 = 204

680 + 204 = 884

Sixth Day

30% increased of total views

884 × 30 ÷ 100 = 265.2 = 265

884 + 265 = 1149

Seventh Day

30% increased of total views

1149 × 30 ÷ 100 = 344.7 = 345

1149 + 345 = 1494

Eight Day

30% increased of total views

1494 × 30 ÷ 100 = 448.2 = 448

1494 + 448 = 1942

Ninth Day

30% increased of total views

1942 × 30 ÷ 100 = 582.6 = 583

1942 + 583 = 2525

Tenth Day

30% increased of total views

2525 × 30 ÷ 100 = 757.5 = 758

2525 + 758 = 3283

Eleventh Day

30% increased of total views

3283 × 30 ÷ 100 = 984.9 = 985

3283 + 985 = 4268

Twelth Day

30% increased of total views

4268 × 30 ÷ 100 = 1280.4 = 1280

4268 + 1280 = 5548

Thirteenth Day

30% increased of total views

5548 × 30 ÷ 100 = 1664.4 = 1664

5548 + 1664 = 7212

Thus, Total views did the video get over the course of the first 13 days is 7212 Views.

 

-TheUnknownScientist 72

PLEASE HELP!! MATHH
SUPER DESPERATE EVEN 1 ANSWER IS FINE

Answers

Answer:

4 x 3 x 2

Step-by-step explanation:

Hope that helps, I'm like 95% sure that's the answer.

Answer:

Question 1: C. 4 × 3 × 2 ×  [tex]\frac{1}{8}[/tex]  × [tex]\frac{1}{8}[/tex]  × [tex]\frac{1}{8}[/tex]

Question 2: The volume is [tex]\frac{1}{12}[/tex] or 0.083333333

Question 3: The volume fo the solid figure is 234

Step-by-step explanation:

1. Volume of a rectangular prism = (length × width × height) cubic units

Length = 4 ×  [tex]\frac{1}{8}[/tex]

Width = 3 × [tex]\frac{1}{8}[/tex]

Height = 2 × [tex]\frac{1}{8}[/tex]

Volume = 4 ×  [tex]\frac{1}{8}[/tex] × 3 × [tex]\frac{1}{8}[/tex]  × 2 × [tex]\frac{1}{8}[/tex]

Volume = 4 × 3 × 2 ×  [tex]\frac{1}{8}[/tex]  × [tex]\frac{1}{8}[/tex]  × [tex]\frac{1}{8}[/tex]

So the correct option is:

C. 4 × 3 × 2 ×  [tex]\frac{1}{8}[/tex]  × [tex]\frac{1}{8}[/tex]  × [tex]\frac{1}{8}[/tex]

2.

We have to fold the shape into a rectangular prism, look at the picture

Volume of a right rectangular prism =  (length × width × height)

Length = [tex]\frac{1}{3}[/tex]

Width =  [tex]\frac{1}{3}[/tex]

Height = [tex]\frac{3}{4}[/tex]

Volume = [tex]\frac{1}{3}[/tex] ×  [tex]\frac{1}{3}[/tex]  ×  [tex]\frac{3}{4}[/tex]

Multiply [tex]\frac{1}{3}[/tex] times [tex]\frac{1}{3}[/tex] by multiplying numerator times numerator and denominator times denominator.

[tex]\dfrac{ 1 \times 1 }{ 3 \times 3 } \times \left( \dfrac{ 3 }{ 4 } \right)[/tex]

Do the multiplications in the fraction [tex]\dfrac{ 1 \times 1 }{ 3 \times 3 }[/tex]

[tex]\dfrac{ 1 }{ 9 } \times \left( \dfrac{ 3 }{ 4 } \right)[/tex]

Multiply [tex]\frac{1}{9}[/tex] times [tex]\frac{3}{4}[/tex] by multiplying numerator times numerator and denominator times denominator.

[tex]\dfrac{ 1 \times 3 }{ 9 \times 4 }[/tex]

Do the multiplications in the fraction [tex]\dfrac{ 1 \times 3 }{ 9 \times 4 }[/tex]

[tex]\frac{3}{36}[/tex]

Reduce the fraction [tex]\frac{3}{36}[/tex] to the lowest terms by extracting and canceling out 3

Fraction form: [tex]\frac{1}{12}[/tex]

or

Decimal form: 0.083333333

So the volume of the right rectangular prism is [tex]\frac{1}{12}[/tex]

3. Look at the picture with the solid figure labeled

We can think of this shape as two different prisms ( A and B)

Volume of A = 4.5 × 6 × 6.5 = 175.5

Volume of B = 3 × 3 × 6.5 = 58.5

Total volume of the whole figure = 175.5 + 58.5

175.5 + 58.5 = 234

So the volume of the solid figure is 234

17. What is the measure, in degrees, of angle x?

Answers

Let ,

130° + y = 180° — ( i )

x + 107° + y = 180° — ( ii )

now ( i )

130° + y = 180°

y = 180° - 130°

y = 50°

now substituting value of y in equation ( i )

[tex]x + 107 + y = 180 \\ x + 107 + 50 = 180 \\ x + 157 = 180 \\ x = 180 - 157 \\ [/tex]

x = 23°

I've been trying to solve my homework for the last one hour

Answers

Answer:

3+1+4+8+6 // 3+1+4+9+5 // 4+7+4+5+2

Step-by-step explanation:

Here is three combinations, i am not sure if you are supposed to use all of the numbers or not but this is what i found.

Nina and Jo both ran a 13 km race. Nina took 2 hour 10 minutes to run the whole race. Jo started the race 7 minutes later than Nina but caught up when they had both travelled 11 km. If Nina and Jo both ran at constant speeds, what is Jo's speed to 2 dp?

Answers

I searched it up and it said the answer is 6.0869 mph

-9r
r=7
Please help I'm tired and can't think

Answers

Answer:

-63

Step-by-step explanation:

-9 multiply by 7

Hey there!


-9r

= -9(7)

= -9 + -9 + -9 + -9 + -9 + -9 + -9

= -9 - 9 - 9 - 9 - 9 - 9 - 9

= -18 - 18 - 18 - 9

= -36 - 18 - 9

= -54 - 9

= -63


Thus, your answer is: -63


Fun fact!
2 negatives equals positive

2 positives equals positive

1 negative & 1 positive equals negative

1 positive & 1 negative equals negative


That’s why your result was a negative because you had 1 negative (-9) and 1 positive (7)

Good luck on your assignment & enjoy your day!


~Amphitrite1040:)

The figure shows a parallelogram ABCD where BÀD=65. E lies on DC such that BÈD=125.
Find:
(I) ADB
(ii) CBE​

Answers

Answer:

ADB

Step-by-step explanation:

hlo have you forgotten me hlo hru zunair

Other Questions
please help 5 POINTS THIS TIME SORRY MIGHT BE DOING A GIVE AWAY GIVING BRAINLIEST Find the length of a rectangle given that the perimeter is 32 feet and the length is 1 foot more than four times the width. 15 points!!I need 10-18 if you know any please help me out!! In the context of the passage as a whole, the first paragraph (lines 16) primarily serves tochallenge existing ideas about the topic the authors will addressprovide context for the issue that the authors will attempt to solveemphasize the authors claim by illuminating the dangers of unhealthy eatingsuggest that the authors argument will help the audience gain better healthimply that the authors intended audience has an intrinsic bias that must be overcome Explain: what is meant by having power over your money.Explain: Why should you set up an emergency fund? How much money should be in an emergency fund? What should the fund be used for?State and explain the five principles of money?An expense you can acquire and then choose to exclude overtime would be ______.the utility billstaxescredit card debtout of pocket medical and dental costs. You and your team of expert engineers are to improve the safety of a section of highway roadway. This is a flat concrete road surface. It is used both by passenger cars (1200 kg) and trucks ( 36,000 kg). The present velocity limit is 15.64 m/s and the radius of turn is 110 m.The Normal force of each vehicle. Only number 5 please help which binomial must be added to (-2r+12) so the the sum of 2 polynomial is (6r-7)a.) 4r-19b.) 4r+5c.) 8r-19D.)8r+5 After earning your first $1000, you deposit the whole amount$1000into an account that grows at an interest rate of 12% annually. The earned interest is calculated and added to the account once a year.Which function represents the amount of money in the account after t years?(Assume that you do not make any additional deposits or withdrawals.) ______damage by free radicals is related to the development of many diseases, including: cancer, heart disease, arthritis, cataracts, macular degeneration and Parkinson's disease. how many values are in the range 17 to 118? A- 102B- 135C- 100D- 67.5 Assume interest is compounded monthly. The ______ annual rate will express this rate as though it were compounded annually. 1. Qu te gusta en el almuerzo? Order each set of numbers from least to greatest.a. 5, -5, 7, -1, 6b. -12, -12.4, 12, 12 1/2 , -2, 1/2, 12 1/4, -12.1 Write an equation in Point-Slope Form for the given information.m=4/5;(2,0) Please answer both question fully. I WILL GIVE BRAINLEST !! I WILL GIVE BRAINLEST !!!!For the complete redox reactions given, identify the oxidizing and reducing agents.2Sr + O2 --> 2SrO Prompt 1: So far, you have read Chapters 14 of Alices Adventures in Wonderland by Lewis Carroll. Share who your favorite character is in the novel. Describe what you like about that character and why you feel a personal connection to him or her.Prompt 2: In this unit, you read many different literary texts across different genres:A novel Alices Adventures in WonderlandShort stories of different genres: Mayan Adventure, Benitos Ugly Bowl, The Bread Lesson, The Mystery of the Moving Statue, A Big Move, The Impossible Flight.A play: An Adventure Around The Corner.A script adapted from teleplay: Uncharted Galaxies.Choose two selections from different genres you liked best. Provide a short description explaining what specifically interested you about both of these genres. Then, compare the selections and share what aspects they have in common. What percentage of the message is lost when you send a text? I cant believe you got A on that testA. 93B. 72C. 7D. 14 If anyone minds, can someone answer this and show your work pls.