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Wittaler [7]
3 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]3 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}\\\\

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alexandr402 [8]

Answer:

The shape and rate parameters are \frac{1}{12} and 3.

Step-by-step explanation:

Let <em>X</em> = service time for each individual.

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The random variable follows an Exponential distribution with parameter, \lambda=\frac{1}{\beta}=\frac{1}{12}.

The service time for the next 3 customers is,

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All the <em>X</em>_{i}'s are independent Exponential random variable.

The sum of independent Exponential random variables is known as a Gamma or Erlang random variable.

The random variable <em>Z</em> follows a Gamma distribution with parameters (<em>α</em>, <em>n</em>).

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First, multiply the top equation by 2 and bottom by -3.
60x+60y=900
-60x-75y=-1035
————————
-15y=-135
—————-
-15=-15
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So the answer should be 9.
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3 years ago
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Answer: 35

Step-by-step explanation:

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2 years ago
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Peter inherits 15.000 dollars and place money with a bank. The interest rate are 3 percent. How many money will he get after 1ye
NeTakaya
The simplest form of an interest equation is A = P(1+rt)

where A = the total amount of money at the end, P = the principal (or amount of money you started with), r = the rate in percent, and t = the time in years.

In this case, P = 15000, r = 0.03 (because 3% in decimal form is 0.03), and t = 1:

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3 years ago
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Zina [86]
I don’t know but maybe 2
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