Answer:
[tex]\mathbf{4 \lim \limits _{n \to \infty} \sum \limits ^n_{i=1} \Big ( \dfrac{n(n+4i)}{2n^3 +(n+4i)^3} \Big )}[/tex]
Step-by-step explanation:
Given integral:
[tex]\int ^5_1 \dfrac{x}{2+x^3} \ dx[/tex]
[tex]\mathbf{Using \ Riemann \ sums; \ we \ have: }[/tex]
[tex]\int ^b_a \ f(x) \ dx = \lim_{n \to \infty} \sum \limits ^n_{i =1} \ f( a + i \Delta x) \Delta x[/tex]
[tex]here; \ \Delta x = \dfrac{b-a}{n}[/tex]
∴
[tex]\int ^5_1 \dfrac{x}{2+x^3} \ dx = f(x) = \dfrac{x}{2+x^3}[/tex]
[tex]\implies \Delta x = \dfrac{5-1}{n} =\dfrac{4}{n}[/tex]
[tex]f(a + i \Delta x ) = f ( 1 + \dfrac{4i}{n})[/tex]
[tex]f( 1 + \dfrac{4i}{n}) = \dfrac{n^2 ( n+4i)}{2n^3 + (n + 4i)^3}[/tex]
[tex]\lim_{n \to \infty} \sum \limits ^n_{i=1} \ f(a + i \Delta x) \Delta x = \lim_{n \to \infty} \sum \limits ^n_{i=1} \Big ( \dfrac{n^2(n+4i)}{2n^3 +(n+4i)^3} \Big )\dfrac{4}{n}[/tex]
[tex]\mathbf{= 4 \lim \limits _{n \to \infty} \sum \limits ^n_{i=1} \Big ( \dfrac{n(n+4i)}{2n^3 +(n+4i)^3} \Big )}[/tex]
-8,-8,-6,-2,4,12,22 quadratic sequence
9514 1404 393
Answer:
a[n] = n^2 -3n -6
Step-by-step explanation:
First differences are ...
-8 -(-8) = 0
-6 -(-8) = 2
-2 -(-6) = 4
Second differences are ...
2 -0 = 2
4 -2 = 2
Constant second differences indicate a degree 2 (quadratic) sequence.
The general formulation can be written as ...
an = a1 +(n -1)(d1 +(n -2)/2(d2)) . . . . where a1 is the first term; d1 is the first first difference; d2 is the second difference
= -8 +(n -1)(0 +(n -2)/2(2)) = -8 +(n -1)(n -2)
an = n^2 -3n -6 . . . . . formula for the n-th term
three pounds of flour cost $1.65. how much flour do you get per dollar? round your answer to the nearest hundredth.
Answer:
1.8181818181818181 etc., which rounds to 1.82
Step-by-step explanation:
1.65/3 = 1/x
3/1.65
We get 1.80 pounds of flour for 1 dollar.
What is unitary method ?Unitary method is a mathematical technique for first deriving the value of a single unit then deriving any given unit from it.
Suppose we know one mango costs 4 dollars so 20 mangoes will cost (4×20) dollars = 80 dollars.
According to the given question three pounds of flour cost 1.65 dollars.
So, One pound of flour will cost (1.65/3) dollars which is
= 0.55 dollars.
In 1 dollar we will get (1/0.55) pounds of flour which is
= 1.81 pounds.
Rounding 1.81 to nearest hundredth will be 1.80 as the rightmost digits is than 5.
learn more about unitary method here :
https://brainly.com/question/14793162
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Brian ordered a 12-inch pizza for him and some friends. They ate half of the pizza before they started
playing video games. Approximately how much of the pizza is left in the box?
A 38in2
B 57in2
C 113in2
D 144in2
Answer:
B
Step-by-step explanation:
The line y= -0.5x+b passes through the points (1,5,5), (3,p), (4,4),and (7,n) Find b,n,and p
Answer:
b = 6 n = 2.5 and p = 4.5
Step-by-step explanation:
had the same question
The value of the variables b, p, and n will be 6, 3.5, and 2.5, respectively.
What is a linear equation?A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The equation of the line is given below.
y = -0.5x + b
The line is passing through (4, 4), then the value of b will be
4 = -0.5 × 4 + b
4 = - 2 + b
b = 4 + 2
b = 6
Then the equation will be
y = - 0.5x + 6
The equation is passing through (3, p), then the value of p will be
p = -0.5 × 3 + 6
p = - 1.5 + 6
p = 3.5
The equation is passing through (7, n), then the value of n will be
n = -0.5 × 7 + 6
n = - 3.5 + 6
n = 2.5
Then the value of the variables b, p, and n will be 6, 3.5, and 2.5, respectively.
More about the linear equation link is given below.
https://brainly.com/question/11897796
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Katrina used 2 5/6 packs of mechanical pencils in the first 2/3 of the year.
At what rate is Kelly using mechanical pencils?
A. 1 8/9 packs per year
B. 2 1/6 packs per year
C. 3 1/2 packs per year
D. 4 1/4 packs per year
Katrina is using 21//6 (B) packs per year
NAME
7. Factor each quadratic expression,
Step-by-step explanation:
x² - 2x - 35 = (x - 7)(x + 5).
x² + 3x - 54 = (x + 9)(x - 6).
x² - 4x + 4 = (x - 2)².
x² - 121 = (x + 11)(x - 11).
2x² + x - 15 = (2x - 5)(x + 3).
6x² - 7x - 24 = (3x - 8)(2x + 3).
3x² - 10x + 8 = (3x - 4)(x - 2).
10x² + 9x - 9 = (5x - 3)(2x + 3).
12x² + 25x + 12 = (4x + 3)(3x + 4).
15x² - x - 6 = (5x + 3)(3x - 2).
Help due in 30 min!!!!!!!!!!!!!!!
Answer:
b. - 1/4
Step-by-step explanation:
Start at the point highest on the line(3,4). Subtract the x value of the second point, from the x value of the first point.(3-7) Then do the same with the y values.(4-3) This gives you x=-4and y= 1. Slope= y/x, so you get -1/4
Plzz help for once!! The cost y (in dollars) to rent a kayak. it costs $27 to rent the kayak for 3 hours.
a. Write an equation that represents the situation.
An equation that represents the situation is y=___?
Answer:
y= 81$
Step-by-step explanation:
$27 X 3= 81
Answer:
y = 9h
i don't know if this is what you were looking for or not
Step-by-step explanation:
riley bought a piano for $4000 and made a down payment of $400. if the balance is financed at a simple interest rate pf 8% with 24 equal monthly payments, what are the installments
Answer:
Total cost with interest and down payment: $4288
Monthly payment with interest: $162
(if this doesnt answer your question, plz let me know what you mean by installments and ill try again)
Step-by-step explanation
If the price of potatoes used to make French fries increases, what will happen to ketchup?
a. Increase in supply c. Decrease in supply
b. Increase in demand d. Decrease in demand e. None of the above
Answer:
D
Step-by-step explanation:
Help plz:)))I’ll mark u Brainliest
Answer:
if the other person answers give it to them :)
What is the last digit of 777^777?
Answer:
7 I. guessing oh wait nah its fish
Dan says that all quadrilaterals are parallelograms. Tom says that it is not true. Explain who is correct??
Answer:
Tom is correct
Step-by-step explanation:
Quadrilaterals are polygons that have four sides.
Square, rectangle, parallelogram, kite, rhombus are all examples of quadrilateral
Parallelogram is a type of quadrilateral with opposite sides equal and parallel
help meeeeeeeeeeeeeee pleaseeee
The second option (5n)
["Product" is for multiplication]
Hi I’m doing a test and I need help please tell me the answer |
V
Answer: It’s 8
Step-by-step explanation: I just went to desmos
Question 17
O Mark this
Find the sum of the first 10 terms of the following geometric sequences:
{3, 6, 12, 24, 48...}
3069
3066
O
3072
O 3075
Answer:
[tex]S_{10} = 3069[/tex]
Step-by-step explanation:
Given
[tex]Sequence = \{3, 6, 12, 24, 48...\}[/tex]
Required
Determine the sum of the first terms
First, we calculate the common ratio (r)
[tex]r = \frac{T_2}{T_1}[/tex]
[tex]r = \frac{6}{3}[/tex]
[tex]r = 2[/tex]
The required sum is:
[tex]S_n = \frac{a(r^n-1)}{r-1}[/tex]
Substitute 3 for a, 2 for r and 10 for n
[tex]S_{10} = \frac{3(2^{10}-1)}{2-1}[/tex]
[tex]S_{10} = \frac{3(1024-1)}{2-1}[/tex]
[tex]S_{10} = \frac{3(1023)}{2-1}[/tex]
[tex]S_{10} = \frac{3(1023)}{1}[/tex]
[tex]S_{10} = \frac{3069}{1}[/tex]
[tex]S_{10} = 3069[/tex]
4.
3.
If the base of the triangle is 4.1 cm. and the
height is 5.7 cm., what is the approximate area
bh
of the triangle? (Area of a triangle = home :)
a. 23.3 cm b. 15.5 cm
c. 11.7 cm
Answer:
area=basexheight
area=4.1x5.7
area=23.3
Two cars depart an intersection.
One goes north.
The other goes west.
Each car travels at a constant speed of 30 miles per hour.
Assuming the roads go on forever, what will be the distance between the cars after 1 hours and 30 minutes in miles?
Answer:
The distance between them after 1 hour and 30 minutes will be of 63.64 miles.
Step-by-step explanation:
This question can be solved using the Pythagorean Theorem.
Both cars travel at a constant speed of 30 miles per hour. So, after 1 hour and 30 minutes, which is 1 and a half hour, they will have traveled 30*1.5 = 45 miles.
The distance between them is the hypotenuse of a right triangle, in which the sides are 45. So
[tex]d^2 = 45^2 + 45^2[/tex]
[tex]d = \sqrt{45^2 + 45^2}[/tex]
[tex]d = 63.64[/tex]
The distance between them after 1 hour and 30 minutes will be of 63.64 miles.
David’s bowling score is 1 less than 3 times Aaron’s score. The sum of their scores is 179. Find the score of each student, Use the variable a for Aaron’s score
Answer: List all of the solutions.
1
=
3
=
179
=
Step-by-step explanation:
Two less than the quotient of a number and 3 is 16. What is the number? Let n be the unknown number
Answer:
13
Step-by-step explanation:
16/1 -3/1 = 16-3
= 13answer is unknow no.
Mrs. Fuller is trying to organize all of her children's toys into a large toy box. Each toy
has the dimensions of 4 inches x 3 inches x 3 inches. The toy box measures 4 feet x 2
feet x 3 feet. How many toys will be stored in the large toy box?
Answer: 1,152 toys can be stored in the box.
Step-by-step explanation:
For an object with measures L (length) by W (width) by H (height) the volume is calculated as:
V = L*W*H
We know that the measures of each toy are: 4in x 3in x 3in
Then the volume of each toy is:
V = 4in*3in*3in = 36in^3
The toy box is 4ft x 2ft x 3 ft
First we should write the measures in the same units as before, we know that:
1ft = 12 in.
Then:
4ft = 4*12 in = 48 in
2ft = 2*12in = 24in
3ft = 3*12in = 36in
Then the measures of the box are:
48in x 24in x 36in
Then the volume of the box is:
V = 48in*24in*36in = 41,472 in^3
Now, the number of toys that can be stored in the box is the same as the number of times that 36in^3 is in 41,472 in^3
this is equal to the quotient between 41,472 in^3 and 36in^3
N = 41,472 in^3/36in^3 = 1,152
1,152 toys can be stored in the box.
n +8<-2 or 8+ n > 5
I’m supposed to solve and graph this compound which I did but I’m not sure if it’s correct or not it’s after school hours and I’m not allowed to contact my teacher
I got n<-10 Or n>-3
I just want to know if I did this correct please? Sorry for the messy handwriting in the picture
Answer:
the first one n + 8 < -2 is correct, the second one is correct too, but its just the graph that is wrong. n > -3, since its greater, it should increase in number, so the line would go toward the right, the opposite direction you drew down.
Step-by-step explanation:
Hope this helps
The following stemplot displays the number of forest fires (the stem is in tens of thousands) that occurred each year over the period from 1980 to 2012.
4 | 024477889
5 | 001222234477888
6 | 02378
7 | 348
How many data values are in this data set?
Answer:
32 values
Step-by-step explanation:
Given the stem. Plot :
STEM ___ Leaf
4 | 024477889
5 | 001222234477888
6 | 02378
7 | 348
The data values include the stem with each value in the leaf : Hence, the number of data points is the number of values in the leaf of the stem plot.
The values are :
40, 42, 44, 44, 47, 47, 48,48, 49
50, 50, 51, 52,52, 52, 52, 53, 54, 54, 57, 57, 58, 58, 58,
60, 62, 63, 67, 68
73, 74, 78
need help asap please
Answer:
114°
Step-by-step explanation:
First we have to calculate the value of c Then
3c - 84° + c = 180° <being co-interior angles >
4c - 84° = 180°
4c = 180° + 84
4c = 264°
c = 264° / 4
c = 66°
Now
<R = 3 * 66° - 84°
= 114°
<P = <R ( being opposite angles of rhombus )
<P = 114°
Hope it will help :)
Point D (-5, 3) and point E (6, -2) are located on a coordinate grid.
Which measurement is the best representation of the distance between point D and point E in units?
Answer:
Rounding to the nearest number, the answer would be 12 units
Step-by-step explanation:
I hope this helped! Please mark me as brainliest if you can!
Hello please help me through 11-13 .
Answer:
Step-by-step explanation:
Points to remember while solving a system of linear equations,
1). If the equations have same slope, solution of the system will have no solution.
2). If both the equations are same, system will have infinitely many solutions.
3). If both the equations have different coefficients of variables, system of equations will have exactly one solution.
Question 11,
ax + 4y = 10 ------ (1)
-9x - 6y = -15
-3x - 2y = -5
-6x - 4y = -10
6x + 4y = 10 -------(2)
For infinitely many solutions,
Coefficients of variables will be same.
a = 6 will be the answer.
Option B is the correct option.
Question 12,
[tex]y=-\frac{3}{2}x+4[/tex] ---------(1)
[tex]y=-\frac{3}{2}x-4[/tex] ----------(2)
Since, slopes of both the equations are same as [tex]-\frac{3}{2}[/tex], lines will be parallel.
System will have NO SOLUTION.
Question 13,
x + 3y = 6 ------- (1)
6x + 18y = 36
x + 3y = 6 -------- (2)
Both the equations are same.
Therefore, system of the equations will have infinitely many solutions.
2x - 3y = -3 ------(1)
4x + 6y = 18
2x + 3y = 9 -------(2)
Coefficients of the variables are different, therefore, one solution.
3x + 2y = 6 -------(1)
6x - 4y = 24
3x - 2y = 12 -------(2)
One solution.
8x - 10y = 6
4x - 5y = 3 -------(1)
-4x + 5y = 3
4x - 5y = -3 ------(2)
One solution.
4x + 10y = 16
2x + 5y = 8 --------(1)
10x + 25y = 40
2x + 5y = 8 --------(2)
Infinitely many solutions.
1 - r= - 5help me please
Answer:
r = 6
Step-by-step explanation:
1 - r = -5
Subtract 1 on both sides
-r = -5 -1
-r = -6
Divide by -1 on both sides
r = 6
HELP PLEASE HELP
What is the solution for 3 ≥ y − 2
y ≤ 5
i think this is the answer..
What’s the answer to
250 = 4(1 - 7x)
Answer:
x = -123/14
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtract Property of EqualityStep-by-step explanation:
Step 1: Define
250 = 4(1 - 7x)
Step 2: Solve for x
Divide both sides by 4: 125/2 = 1 - 7xSubtract 1 on both sides: 123/2 = -7xDivide -7 on both sides: -123/14 = xRewrite: x = -123/14Step 3: Check
Plug in x into the original equation to verify it's a solution.
Substitute in x: 250 = 4(1 - 7(-123/14))(Parenthesis) Multiply: 250 = 4(1 + 123/2)(Parenthesis) Add: 250 = 4(125/2)Multiply: 250 = 250Here we see that 250 does indeed equal 250.
∴ x = -123/14 is the solution to the equation.
Jane drove 693 miles in 11 hours.
At the same rate, how long would it take her to drive 411 miles?
Answer:
approx. 6.523809523809524 hours
Step-by-step explanation:
Let us first find how long it takes Jane to drive 1 mile.
11/693 = approx. 0.015873015873016 hours to drive one mile.
She drives 411 miles, so we can multiply that by 411:
0.015873015873016 * 411 = approx. 6.523809523809524 hours
I hope this helps! :)
Answer:
6.52 hours
Step-by-step explanation:
693 miles divided by 11 hours = 63 miles per hour.
411 miles divided by 63 miles = 6.52380952 miles
Round to 2 decimal places: 6.52 hours