1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Wittaler [7]
2 years ago
15

HELPP!!! 100 POINTS AND BRAINLIEST!! Sketch the graph of the function y = 20x − x2, and approximate the area under the curve in

the interval [0, 20] by dividing the area into the given numbers of rectangles.
Part A
Use five rectangles to approximate the area under the curve.
Part B
Use 10 rectangles to approximate the area under the curve.
Part C
Calculate the area under the curve using rectangles as their number becomes arbitrarily large (tends to infinity). You do not need to sketch the rectangles.
Mathematics
1 answer:
Arte-miy333 [17]2 years ago
5 0

Answer:

Hello,

Step-by-step explanation:

Part A: see picture

Part B: see picture

Part C:

You must remenber :

\displaystyle \sum_{i=1}^{n} i= \dfrac{n*(n+1)}{2} \\\\\displaystyle \sum_{i=1}^{n} i^2= \dfrac{n*(n+1)(2n+1)}{6} \\\\\\\int\limits^{20}_0 {(20\ x-x^2)} \, dx =[\dfrac{20\ x^2}{2} -\dfrac{x^3}{3} ]^{20}_0=\dfrac{20^3}{3} =1333.\overline{3}\\\\\\

We divide the intervalle in n equal parts:

f(x)=20\ x- x^2\\\Delta x=\dfrac{20-0}{n} =\dfrac{20}{n} \\Area\ of\ a\ rectangle\ R_i=\Delta x*f(x_i)\\x_i=0+\Delta x*i=\Delta x*i\\\\\\\displaystyle \int\limits^{20}_0 {(20 \ x-x^2)} \, dx = \lim_{n \to \infty}  \sum_{i=1}^n(\Delta x* f(x_i) )\\\\=\lim_{n \to \infty}  \sum_{i=1}^n(\Delta x* (20*\Delta x*i-(\Delta x*i)^2)\\\\=\lim_{n \to \infty} (20*(\dfrac{20}{n})^2\sum_{i=1}^n(i)-(\dfrac{20}{n})^3\sum_{i=1}^n(i^2)\\\\

\displaystyle =\lim_{n \to \infty}(20*(\dfrac{20}{n})^2*\dfrac{n*(n+1)}{2} -(\dfrac{20}{n})^3*\dfrac{n*(n+1)(2n+1)}{6} \\\\=10*20^2-\dfrac{20^3}{6} *2\\\\\\=4000-\frac{8000}{3} \\\\=\dfrac{4000}{3} \\\\=1333,\overline{3}\\\\

You might be interested in
The points (4,1 ) and (x,-6 lie on the same line. If the slope of the line is 1,what is the value of x?
konstantin123 [22]

Answer:

wnsbsbwbqbqbqbqbqjqj

Step-by-step explanation:

snnaakaknananananabababababababababababa

nansskqlnzelsksuqqhnqqko

6 0
3 years ago
WRITE A EQUATION ''THE QUOTIENT OF A NUMBER AND 20.7 is 9
zhannawk [14.2K]

Answer:

186.3

To find the answer you have to do inverse operations

9×20.7=186.3

186.3÷20.7=9

3 0
2 years ago
Read 2 more answers
Simplify 8 over the quantity of 2 plus 2i
Sergeu [11.5K]

Answer should be: 2 + 2i

8 0
3 years ago
Read 2 more answers
3 kom 2.7 Eve carves a shape out of wood. What is the volume of the shap 3 cm 1 cm 2 cm 3 cm 4 cm ​
Mariana [72]

Answer:

50cm

Step-by-step explanation:

oh apdiya I just wanted to let you

8 0
2 years ago
You guessed the height of the building to be 23 feet, but it was actually 35 feet. What was your percent error? Round to the nea
marin [14]
The percent error is 34.28 %.
Hope this helps! Be safe out there.
8 0
3 years ago
Read 2 more answers
Other questions:
  • Five times a number plus 5 has the same value as twice the number plus 10
    9·1 answer
  • What type of triangle is this? Side lengths of 7.36 m, 3.16 m, and 5.45m and angles that measure 43degrees, 23 degrees, and 114d
    5·2 answers
  • F(x) = −16(x − 4)<br> + 255 <br><br> What is the value of f(x) when x = 5?
    7·1 answer
  • Bob's age is 4 times greater than Susan's. Dakota is 3 years younger than Susan. Some of Bob's, Susan's, and Dakota's age is 93.
    10·1 answer
  • This is the power to which A number is raised or the number of times it is multiplied by itself
    13·1 answer
  • I’m about to spam questions if you can answer them please do .
    6·2 answers
  • Select the line segment<br> A.<br> B.<br> C.<br> D.
    6·2 answers
  • I need a bit of help...
    14·2 answers
  • What is 5 1/2 is its simple form?
    6·1 answer
  • Maggie just worked a week for Jan's Jewels. Her pay before deductions was $98.28 and she worked 18 hours.
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!