The limit of the given Riemann sum is 256.
The given expression represents a Riemann sum for the function f(x) = 3x^3 - 9x over the interval [2, 6], where xi* is any point in the ith subinterval, and δx = (b-a)/n is the width of each subinterval.
Using the formula for the Riemann sum with right endpoints, we have xi* = 2 + iδx for i = 1, 2, ..., n. Substituting these values, we get:
n i=1 [3(xi*)^3 − 9xi*]δx = δx [3(2 + δx)^3 - 9(2 + δx) + 3(2 + 2δx)^3 - 9(2 + 2δx) + ... + 3(2 + nδx)^3 - 9(2 + nδx)]
= δx [3(2^3 + 3(2^2)δx + 3(2)(δx^2) + (δx)^3) - 9(2 + δx) + 3(2^3 + 3(2^2)(2δx) + 3(2)(4δx^2) + (8δx)^3) - 9(2 + 2δx) + ... + 3( (2 + nδx)^3) - 9(2 + nδx)]
= δx [3(8 + 12δx + 6δx^2 + δx^3) - 9(2 + δx) + 3(8 + 24δx + 24δx^2 + 8δx^3) - 9(2 + 2δx) + ... + 3((2 + nδx)^3) - 9(2 + nδx)]
= δx [3(8 + 12δx + 6δx^2 + δx^3) + 3(8 + 24δx + 24δx^2 + 8δx^3) + ... + 3((2 + nδx)^3) - 9(nδx)]
= δx [3(8n + 12δx(n(n+1)/2) + 6δx^2(n(n+1)(2n+1)/6) + δx^3(n^2(n+1)^2/4)) - 9(nδx)]
Taking the limit as n tends to infinity, we have δx = (6-2)/n = 4/n and nδx = 4. Therefore, the expression simplifies to:
lim n→[infinity] n i=1 [3(xi*)^3 − 9xi*]δx = lim n→[infinity] 4 [3(8n + 12(4/n)(n(n+1)/2) + 6(4/n)^2(n(n+1)(2n+1)/6) + (4/n)^3(n^2(n+1)^2/4)) - 9(4)]
= lim n→[infinity] 4 (96n + 64 + 64 + 64) - 144 = 256
Therefore, the limit of the given Riemann sum is 256.
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What is the slope of the line that passes through the points (3, -20) and (11, 16)?
please I'm being timed
Answer:
9/2
Step-by-step explanation:
(3, -20) & (11, 16)
To find the slope of the line that passes through these points, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)
Plug in these values:
(16 - (-20)) / (11 - 3)
Simplify the parentheses.
= (36) / (8)
Simplify the fraction.
36/8
= 9/2
9/2 is the most simplified fraction. This is your slope.
Hope this helps!
Chad has a rope that is 24 yards long. How many pieces of rope measuring 4/7 of a yard can he divide his rope into?
Answer:
42
Step-by-step explanation:
Chad has a rope that is 24 meters long
He wants to divide the rope so each piece will be 4/7 yards
= 24÷ 4/7
= 24× 7/4
= 168/4
= 42
Hence he can divide the rope into 42 pieces
Solve the system of equations 2x - 2y = - 14 and 2x + 6y = - 6 by combining the equations.
sorrryy I don't know how to delete this so...
Step-by-step explanation:
step 1. first combine by subtraction.
step 2. 0x -8x = -8
step 3. y = 1
step 4. x = -6.
step 5. the answer is (-6, 1).
help pls ;;-;; ye thxs
Answer:
You still need help? :P
Step-by-step explanation:
Evaluate the expression when a=5 and b= -5.
-a +8b
At the market you can buy six bags of apples for $25 at the archer you can get eight bags of Apple for $35 which is the better deal
Answer:
$25
Step-by-step explanation:
g(n) = 4n h(n) = n2 + 3n Find g(h(n))
Answer:
g(h(n)) = 4n² + 12n
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
Terms/CoefficientsFunction NotationAlgebra II
Composite FunctionsStep-by-step explanation:
Step 1: Define
g(n) = 4n
h(n) = n² + 3n
g(h(n)) is n = h(n)
Step 2: Find
Substitute in function h(n) as n: g(h(n)) = 4(n²+ 3n)[Distributive Property] Distribute 4: g(h(n)) = 4n² + 12nThe square of an add number is
Create an expression that is equivalent to 9(3x + 5 + x) without using
parentheses.
Answer:
27x + 45 + 9x
37x + 45
it's here
A salesperson at a jewelry store earns 8% commission each week. Last week, Ali sold $450 worth of jewelry. How much did Ali make in commission? How much did the jewelry store make from her sales?
Answer:
she earned 36$ and the store earned 409.5
Step-by-step explana
8% of 450
91% of 450
cupcakes and points for those who answer this question for me
(the screenshot)
Answer:
2.06
Step-by-step explanation:
The original decimal is 2.0625.
Since the thousandths place is 2, we can't round up. So we can keep the 6 which is in the hundredths place giving us 2.06
A jewelry box has a volume of 14 cubic inches. The area is 7 square inches. What is the height of the jewelry box.
Answer:
2 inches
Step-by-step explanation:
a=Lw
v=lwh
lw= 7
14/7=2
A carpenter has 6 feet of wood. How many inches of wood does the carpenter have?
Answer:
72 inches!
Step-by-step explanation:
since there are 12 inches in a foot, and there are 6 feet, you would multiply 6 x 12, so the answer would be 72 inches !!
i hope this helps ! ! :D
Which number sentence is true? A. –38.44 6.2 = 6.2 B. –38.44 (6.2) = –6.2 C. –38.44 (–6.2) = –6.2 D. 38.44 6.2 = –6.2
Answer:
Option B:
[tex]-\frac{38.44}{6.2} = -6.2[/tex]
Step-by-step explanation:
Given
Options A to D
Required
Determine which is true
Option A:
[tex]-\frac{38.44}{6.2} = 6.2[/tex]
[tex]-6.2 = 6.2[/tex]
This is not true
Option B:
[tex]-\frac{38.44}{6.2} = -6.2[/tex]
[tex]-6.2 = -6.2[/tex]
This is true
There is no need to check further
Determine whether the second polynomial is a factor of the first.
6x2 + 5x +54; x-4
Select the correct choice below and fill in the answer box to complete your choice.
O A. No, because the polynomial 6x² + 5x + 54 evaluated at 4 is equal to
OB. Yes, because the polynomial 6x + 5x +54 evaluated at - 4 is equal to
OC. No, because the polynomial 6x + 5x +54 evaluated at - 4 is equal to
OD. Yes, because the polynomial 6x + 5x + 54 evaluated at 4 is equal to
Answer:
No, because the polynomial 6x² + 5x + 54 evaluated at 4 is equal to 170.
Step-by-step explanation:
A polynomial should have a factor (let's say a) that would make the polynomial equal to zero when we substitute that factor (a) into the polynomial.
An air conditioning repair company has a flat
service fee and charges an hourly rate. One
customer pays $180 for two hours of work.
Another pays $230 for three hours of work.
Write a linear function for this situation. Use h
For the number of hours.
C(h) =
Answer:
Step-by-step explanation:
Dn80 pipe 88millimeters is According to the plan All openings must be 40mm larger than the pipe. You know that
Answer:
128mm
Step-by-step explanation:
Given
[tex]Pipe = 88mm[/tex]
[tex]Ope\ nnings = 40mm\ larger[/tex]
Required
Determine the length of the openings of the pipe
To do this, we simply add 40mm to the length of the pipe.
This gives:
[tex]Ope\ nings = 88mm + 40mm[/tex]
[tex]Ope\ nings = 128mm[/tex]
Hence, the opening must be 128mm
y/-9=1/18 solve for y
Answer:
y=-1/2
Step-by-step explanation:
helpppp meeee plz...
Answer:
3 coefficient po
Step-by-step explanation:
sana maka tulong
HELP I NEED HELP ASAP
Answer:
C) Linear
Step-by-step explanation:
To find this, I turned the situation into an expression. The expression representing this would be: 2x + 5 (a linear function). The 2x represents how much his dad gives Joseph weekly. The 5 represents how much Joseph already has.
Hope it helps!
Linda is making a mosaic stepping stone to place in
her garden. The stone is shown below. How much
mosaic glass tile will Linda need to cover the surface
of five stepping stones? Use 3.14 for pie.
Help please lol
Answer:
D 565.2 in
Step-by-step explanation:
First you need to find the area of the stepping stone. The rule for area of circle is pi times radius squared. To find the radius you divide 12 by 2 = 6. After you do 6 times 6= 36 you multiply 36 times pi (3.14) = 113.04. After we find the are of the stepping stone we multiply it by five to get how many inches we have to cover. 113.04 times 5= 565.2 in.
iv) The number 211539 is divisible by
Answer:
The answer would be the number 3
7:5 is equivalent to...?
Answer:
6:0
Step-by-step explanation:
Thank me later :)))))))))
The bill at the restaurant was $18.79 estimate the amount to leave as a $10 tip
A. $2.00
B. $3.00
C. $9.00
D. $21.00
Perimeter? =
Area? =
Answer:
Your answer is
Area = 16.23
perimeter = 24
Mark my answer as brainlist . I need that urgently . Folow me for more answer.
Step-by-step explanation:
30 POINT !!!! NEED IT ASAP
what is the HCF ofusin prime factorization of 30 and 36
Answer:
Step-by-step explanation:
Prime factorization
30 = 2 × 3 × 5
36 = 2² × 3²
HCF = 2 × 3 = 6
A cat leaps from the ground into the air with an initial vertical velocity of 11 ft/s. After how many seconds does the cat land on the ground?
Answer:
11/16 of a second
Step-by-step explanation:
E = MV^2 ÷ 2 + mgh, If M=20, h=15, E=4900, g=9.8. Find V
Answer:
V = 14 m/s
Step-by-step explanation:
[tex]E = MV^2 ÷ 2 + mgh \\ \\ 4900 = 20V^2 ÷ 2 + 20 \times 9.8 \times 15 \\ \\ 4900 = 10V^2 + 2,940\\ \\ 4900 - 2940 = 10V^2 \\ \\ 1960 = 10V^2 \\ \\ V^2 = \frac{1960}{10} \\ \\ V^2 = 196 \\ \\ V = \sqrt{196} \\ \\ V = 14 \: m {s}^{ - 1} [/tex]
Don notices that the side opposite the right angle in a right triangle is always the longest of the three sides. Is this also true of the side opposite the obtuse angle in an obtuse triangle?
Answer:
Yes
Step-by-step explanation:
The line has to be loner to connect the other two.