Mathematics, 01.11.2019 15:31 xwilliams83

Reimann i got it wrongand provide step by step clear explaination. i'd appreciate it.

Answers: 1

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Answers

Formula for Riemann Sum is:
$\frac{b-a}{n} \sum_{i=1}^n f(a + i \frac{b-a}{n})$
interval is [1,3] so a = 1, b = 3
f(x) = 3x , sub into Riemann sum

$\frac{2}{n} \sum_{i=1}^n 3(1 + \frac{2i}{n})$

Continue by simplifying using properties of summations.
$= \frac{2}{n}\sum_{i=1}^n 3 + \frac{2}{n}\sum_{i=1}^n \frac{6i}{n} \\ \\ = \frac{6}{n}\sum_{i=1}^n 1 + \frac{12}{n^2}\sum_{i=1}^n i \\ \\ =\frac{6}{n} (n) + \frac{12}{n^2}(\frac{n(n+1)}{2}) \\ \\ =6+\frac{6}{n}(n+1) \\ \\ =12 + \frac{6}{n}$

Now you have an expression for the summation in terms of 'n'.

Next, take the limit as n-> infinity.
The limit of $\frac{6}{n}$ goes to 0, therefore the limit of the summation is 12.

The area under the curve from [1,3] is equal to limit of summation which is 12.

Answer from: Quest

it will cost dollar $540

the living room is 3 which means if we divide 325/3 then we get $108

therefore if 1part of the living room cost $108 and 3 costed $325

then total 5part of the room will cost 5*108 which gives $540

Answer from: Quest

a. we have two

lines: y = 4-x and

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b. 4-x = 8-x^-1

x 4-x 8-x^-1

-3 7

8.33

-2 6 8.5

-1 5 9

0 4

1 3

2 2

7.5

3 1 7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:

x=-4.236

y = 4-x = 4 – (-4.236)

= 8.236

y = 8-x^-1 = .236)^-1

= 8.236

x=0.236

y = 4-x = 4 – (0.236) = 3.764

y = 8-x^-1 = 8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c. to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x and y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines. the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!

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Reimann i got it wrongand provide step by step clear explaination. i'd appreciate it.
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