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
Find (r-s) (t-s) + (s-r) (s-t) for all numbers r, s, and t. (a) 0 (b) 2 (c) 2rt (d) 2(s-r) (t-s) (e) 2(r-s) (t-s)
lyudmila [28]
Notice that the 2 expressions have 2 common terms.

(r-s) is just (s-r) times (-1)

similarly

(t-s) is just (s-t) times (-1)

this means that :

(r-s) (t-s) + (s-r) (s-t)=-(s-r)[-(s-t)]+(s-r) (s-t)

the 2 minuses in the first multiplication cancel each other so we have:

-(s-r)[-(s-t)]+(s-r) (s-t)=(s-r) (s-t)+(s-r) (s-t)=2(s-r) (s-t)

Answer:

d)<span>2(s-r) (t-s) </span>
3 0
3 years ago
Read 2 more answers
When the sugar bowl is full, it weighs 740 grams. How many tablespoons of sugar can the bowl hold?
Cerrena [4.2K]
You might need to divide the grams from table spoons
7 0
3 years ago
I need help please !!!!!!
garri49 [273]

Answer:

And the probability that the first die shows an odd number is 1/2, as is the probability that the second does. Since the dice fall independently, P(both are odd) = P(first is odd)*P(second is odd) = (1/2)*(1/2) = 1/4. Therefore P(at least one is even) = 1 - 1/4 = 3/4.

7 0
3 years ago
Read 2 more answers
Exit
Alla [95]
Each result is equally likely to occur!!
7 0
3 years ago
Read 2 more answers
4. A statistician working for the National Basketball Association supplies the television announcers with interesting statistics
Sonbull [250]

Answer: 0.038

Step-by-step explanation:

Given: Total games : n= 375

Number of games won by  the team that was winning the game at the end of the third quarter. = 300

The proportion (p) of the team that was winning the game at the end of the third quarter: p=\dfrac{300}{375}=0.8

Critical z-value for 90% confidence: z* = 1.645

Margin of error =z^*\sqrt{\dfrac{(1-p)p}{n}}

The margin of error in a 90% confidence interval estimate of p =1.645\sqrt{\dfrac{0.2\times0.8}{300}}\\= 1.645\times\sqrt{0.00053333}\\\\=1.645\times0.0231\\\\=0.0379995\approx$$0.038

Hence, the required margin of error = 0.038

7 0
3 years ago
Other questions:
  • How many decimeters are there if there are 3 centimeters.
    8·2 answers
  • Would this event be labeled as independent probability or conditional probability?
    9·1 answer
  • HELP ME PLEASE ASAP
    13·2 answers
  • The answer with the work please
    5·1 answer
  • 2. Describe the means-extremes property.
    11·1 answer
  • Can somebody help me out please
    12·1 answer
  • A train travels 25 miles in 20 minutes. What is the train speed in miles per hour?
    5·2 answers
  • Write as a single power of 6<br> (6^5)^4
    9·1 answer
  • Plss help asap!<br><br>what fraction represents numbers between 21 - 27?
    11·1 answer
  • A juice company decides to test three different brands of juice. The different brands have been labeled A¸ B¸ and C. The company
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!