Answers
Split up the interval [0, 2] into n equally spaced subintervals:
[tex]\left[0,\dfrac2n\right],\left[\dfrac2n,\dfrac4n\right],\left[\dfrac4n,\dfrac6n\right],\ldots,\left[\dfrac{2(n-1)}n,2\right][/tex]
Let's use the right endpoints as our sampling points; they are given by the arithmetic sequence,
[tex]r_i=\dfrac{2i}n[/tex]
where [tex]1\le i\le n[/tex]. Each interval has length [tex]\Delta x_i=\frac{2-0}n=\frac2n[/tex].
At these sampling points, the function takes on values of
[tex]f(r_i)=7{r_i}^3=7\left(\dfrac{2i}n\right)^3=\dfrac{56i^3}{n^3}[/tex]
We approximate the integral with the Riemann sum:
[tex]\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{112}n\sum_{i=1}^ni^3[/tex]
Recall that
[tex]\displaystyle\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}4[/tex]
so that the sum reduces to
[tex]\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{28n^2(n+1)^2}{n^4}[/tex]
Take the limit as n approaches infinity, and the Riemann sum converges to the value of the integral:
[tex]\displaystyle\int_0^27x^3\,\mathrm dx=\lim_{n\to\infty}\frac{28n^2(n+1)^2}{n^4}=\boxed{28}[/tex]
Just to check:
[tex]\displaystyle\int_0^27x^3\,\mathrm dx=\frac{7x^4}4\bigg|_0^2=\frac{7\cdot2^4}4=28[/tex]
Related Questions
1. How much ribbon is required to wrap once around a basketball present? Basketballs are 78 cm in
diameter
2 Two cars leave the park at the same time. One travels north at a speed of 50 km/h for 2 hours. The
second car travels west at a speed of 80 km/h for 2 hours. After the 2 hours, how far apart are the two
cars? Be sure to draw a diagram illustrating this situation
3 Asmall tree is beginning to lean The owner decides to set up a tension wire to straighten the tree's
growth The owner chooses a wire which is 5 m in length to straighten the tree. The tree is 4 m high
How far must the owner secure the bottom of the wire from the base of the tree (assuming he attaches
the tension wire to the top of the tree)?
Answers
Answer:
1) 244.92cm 2) 188.68 km 3) 3m
Step-by-step explanation:
1) We are finding the circumference of the basketball in this situation. C=pi(d), d=diameter, C=circumference. So, C= 3.14(78), and finally C= 244.92 cm.
2) We can begin to approach this problem by finding how far each car has traveled over 2 hours. The car heading north is going 50 km/h, so for two hours it has covered 100 kilometers. The car going west is at 80 km/h, so for two hours it has covered 160 kilometers. Now, we could draw this as a right triangle, with one leg being the north-headed car 100 km away from the start, and the other leg being the west moving car 160 km away from the start. The hypotenuse represents the distance between them. Now we use the pythagorean theorem! north car is a, west car is b. a^2+b^2=c^2. 100^2+160^2=c^2. 35600=c^2. take the square root of both sides for c=188.68. The distance between the two cars is approx 188.68 km.
3) `This situation can be represented as a right triangle. The height of the tree, 4m, is the height of the triangle, and the wire, 5m, is the hypotenuse. We are trying to find one of the legs, which represents the ground to the base of the tree. In the pythagorean theorem, we have a^2 and c^2, and just need to find b^2. Let's plug it into the equation:
4^2+b^2=5^2
16+b^2= 25
b^2=9
b=3
hope this helped it took a long time to explain it all! :)
Each block on the grid is 1 unit by 1 unit. We wish to walk from A to B via 7 unit path but we have to stay on the grid. How many different paths can we take?
Answers
Answer:
The number of path we can take to walk from A to B via a 7 unit path while staying on the grid is 35 paths
Step-by-step explanation:
Given that we are to walk via a 7 unit path, we have;
Path to walk = Right or Left from start point A
Total number of rights and left to get to point B from A must be= 7
Left direction=3 turns
Right direction=4 turns
Number of ways for the first turn = 7, the next turn has 6 ways after that 5, then 4 next, 3 next, 2 next and 1
7 × 6 × 5 × 4 × 3 × 2 × 1 out of which
four are in the right direction in 4 × 3 × 2 × 1 ways and
3 are in the left direction in 3 × 2 × 1 ways,
Number of ways=7! / 4!3!
=7*6*5*4*3*2*1 / 4*3*2*1*3*2*1
=5040/144
=35
What is the slope of the line represented by the equation y=-1/2x + 1/4?
Answers
Answer:
The slope is -1/2 and the y intercept is 1/4
Step-by-step explanation:
y=-1/2x + 1/4
This is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
The slope is -1/2 and the y intercept is 1/4
What is the units digit of (13)^4(17)^2(29)^3 ?
Answers
Rewrite the product as
[tex]13^4\cdot 17^2\cdot29^3 = (10+3)^4 (10+7)^2 (20+9)^3[/tex]
Powers of 10 and multiples of 10 don't contribute to the units digits, so we only need to consider the product
[tex]3^4\cdot7^2\cdot9^3=81\cdot49\cdot729[/tex]
and we can treat this the same way:
[tex]81\cdot49\cdot729=(80+1)(40+9)(720+9)[/tex]
Again, ignore the multiples of 10 to reduce this to the product 1*9*9 = 81, whose units digit is 1.
Answer:
I think it is 7
Step-by-step explanation:
What is an upside-down mortgage?
A. A mortgage that ends up costing more than the house that it's
financing is really worth
B. A mortgage that takes too long to pay off
C. A mortgage that you pay too much for
D. The only mortgage you can get when you can't afford a real one
Answers
Answer:
A
Step-by-step explanation:
The owner owes more than the house is worth
Answer:
A
Step-by-step explanation:
1000 ml solution of acetic acid contains 21 mL of pure acetic acid find the percent concentration of the solution simplify your answer completely
Answers
Answer:
Step-by-step explanation:
download math photo it will give you free answers
There were 100 chocolates in a box. The box was passed from person to person in one row. The first person took one chocolate. Each person down the row took one more chocolate than the person before. The box was passed until it was empty. What is the largest number of people that could have removed chocolates from the box? How do you know?
Answers
Answer: 13 people (I think)
Step-by-step explanation:
I didn't use a set equation to solve the problem, but I added 1+2+3+4... (and so on) until I got a number that was over 100. When I got to 14, the number reached 105, meaning that 13 people were able to get the number of chocolates that they desired. The fourteenth person was short 5 chocolates.
Please feel free to ask me any further questions you have! Have a wonderful day!
4x - 20 = 2x + 4 please expand
Answers
Answer:
The value of x in this equation is 12.
Step-by-step explanation:
4x - 20 = 2x + 4
Subtract 2x from 4x because they are like terms. Both terms have a variable of x attached to them.
2x - 20 = 4
Add 20 to 4 because they are also like terms.
2x = 24
Divide 2 on both sides of the equation so we can get x by itself and see what x is equals to.
x = 12
So, the value of x in this equation is 12.
Answer:
x = 12
Step-by-step explanation:
4x - 20 = 2x + 4
4x - 2x = 4 + 20
2x = 24
x = 24/2
x = 12
Find the y-intercept of the rational function. (0, −2) (−2, 0) (0, 6) (6, 0)
Answers
Answer:
(0, - 2)
Step-by-step explanation:
The y-intercept of the rational function is (0, −2).
Ella makes a smoothie for breakfast every morning. Today, she wants to use melon, apple, orange, and peach. In how many different ways (orders) can she add these fruits to her blender?
Answers
Answer: The number of different ways (orders) she can add these fruits to her blender = 24
Step-by-step explanation:
Given, Ella makes a smoothie for breakfast every morning. Today, she wants to use melon, apple, orange, and peach.
i.e. Total fruits = 4
The number of ways to order n things = n!
Therefore, the number of different ways (orders) she can add these fruits to her blender = 4!
= 4 x 3 x 2 x 1
= 24
Hence, the number of different ways (orders) she can add these fruits to her blender = 24
Answer:
the correct answere is actully 120 ways.
Step-by-step explanation:
Solving absolute value inequalities requires solving compound inequalities.
O True
O False
Answers
The statement "Solving absolute value inequalities requires solving compound inequalities" is False.
Absolute value inequalities and compound inequalities are two different types of inequalities, and solving them involves different methods. Here's a brief explanation:
Absolute value inequalities: An absolute value inequality involves an expression enclosed within absolute value symbols [tex](| |)[/tex].
To solve such an inequality, follow these steps:
Set up two separate inequalities: one with the expression inside the absolute value symbols greater than or equal to zero, and the other with the expression negated and greater than or equal to zero.Solve each inequality separately to find the possible solutions.Combine the solutions from both inequalities to determine the final solution set.Compound inequalities: A compound inequality consists of two or more inequalities joined by the logical operators "and" or "or."
To solve a compound inequality, follow these steps:
Solve each individual inequality separately.Combine the solutions based on the logical operators:If the compound inequality is joined by "and," the solution is the intersection of the individual solutions.If the compound inequality is joined by "or," the solution is the union of the individual solutions.Therefore, solving absolute value inequalities does not require solving compound inequalities. These are distinct concepts in mathematics.
Learn more about compound inequalities here:
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Help me ASAP for this question
Answers
Answer:
18 : 3
Step-by-step explanation:
Basic proportionality question. All we need to here is to expression the given fractions ( [tex]11 \frac{2}{3}[/tex], and [tex]1 \frac{17}{18}[/tex] ) as a fraction itself, and hence expressing the ratio we need to get, in fraction form.
[tex]11 \frac{2}{3} / 1 \frac{17}{18}\\\\[/tex] - So, we have expressed this in a fraction, which we want to reduce
[tex]= \frac{35}{3} / \frac{35}{18}[/tex] - The fractions have been taken as improper fractions
[tex]\\\\= \frac{35}{3}( \frac{18}{35} )\\ \\[/tex] - Now we took the inverse fraction, through multiplication
[tex]= 18 / 3[/tex] - 35 and 35 cancel out, leaving us with the simplified fraction 18 / 3
_____
So now we have 18 / 3, the ratio in fraction form. The scale is thus 18 to 3, or in other words 18 : 3.
Hope that helps!
Hey guys please help find the area
Answers
Answer: Area = 498.8 ft^2
Step-by-step explanation:
One of the segments of the kite forms a triangle.
Using a trigonometry ratio to find the base, tan 30 = opposite/ adjacent
Where opposite = 12 feet
Substitute opposite to find adjacent base.
Tan 30 = 12/base
Base = 12/tan 30
Base = 20.78 feet.
Area of a triangle = 1/2bh
Where the b = opposite = 12 feet
h = base = 20.78 feet
Substitute b and h into the formula
Area = 1/2 × 12 × 20.78
Area = 124.71 square feet.
There are 4 triangular shapes in the figure. Multiply the area by 4. That is,
124.71 × 4 = 498.9 square feet.
Therefore, the area of the shape is 498.9 ft^2
which of the following is the correct graph of the solution to the inequality. -8>-5x+2>-38
( those are the answers^)
Answers
Answer:
2<x<8
Step-by-step explanation:
-8>-5x+2>-38
first part : -5x>-38-2
-5x>-40 when divide by negative number flip the sign
x<-40/-5
x<8
second part : -8>-5x+2
-8-2>-5x
x>-10/-5
x>2
2<x<8
2<x<8
Which best summarizes the Pythagorean Theorem?
A- The sum of the squares of the lengths of the legs of a right triangle equals the square of the length of the hypotenuse.
B- The length of the hypotenuse of a right triangle is greater than the sum of the lengths of the legs.
C- The sum of the lengths of the legs of a right triangle equals the length of the hypotenuse.
D- For any triangle, the sum of the squares of any two side
lengths is equal to the square
of the third side length.
Answers
Answer: A
Step-by-step explanation:
[tex]a^{2} + b^{2} = c^{2}[/tex]
A and B are the legs of the triangle, and c is the hypotenuse. A would make the most sense.
The sum of the squares of the lengths of the legs of a right triangle equals the square of the length of the hypotenuse.
What is Pythagoras theorem?" In a right angled triangle the square of the hypotenuse is equals to the sum of the square of the other two sides of the right angled triangle."
According to the question,
As per the Pythagoras theorem ,
(Hypotenuse)² = (Adjacent side)² + ( opposite side)²
Hence, we conclude that Option A is correct.
Learn more about Pythagoras theorem here
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Solve for x in the diagram below.
Answers
Answer:
x = 34°
Step-by-step explanation:
As you can see, in your pic there is a straight angle which is equal to 180°
Therefore, all the 3 angles combined will be equal to 180°
What is the measure of the missing angle x?
Answers
Answer:
C. 60°
Step-by-step explanation:
Add the two given angles and subtract from 180°
Answer:
C. 60
Step-by-step explanation:
The total degrees in a triangle is 180. Add up the given angles measures and subtract from 180 to find x.
52 + 68 + x = 180
120 + x = 180
x = 60
Which best describes the relationship between the lines with equations
Answers
Hey there! :)
Answer:
B, they are the same line.
Step-by-step explanation:
Begin by converting each equation to slope-intercept form to make it easier to see the relationship:
-3x - 4y = 1
-4y = 3x + 1
y = -3/4x - 1/4
-------------------
-6x - 8y = 2
-8y = 6x + 2
y = -3/4x - 1/4
The lines are the same. Therefore, B is the correct choice.
Determine whether the function is linear or quadratic. Identify the quadratic, linear, and constant terms.
Answers
Answer:
B
Step-by-step explanation:
Use FOIL method
3x(5x) + 3x(- 2) + 3(5x) + 3(- 2)
Simplify to get 15 x^{2} -6x+15x-6
Combine like terms to get 15x^2+9x-6
quadratic funcntion
quadratic term: 15x^2
linear term: 9x
constant: -6
(sorry this was late I had other work and I didn't see this until now)
please mark me brainliest!
find two rational numbers between [tex]\sqrt[3]{8}[/tex] and [tex]\sqrt{9}[/tex]
Answers
Step-by-step explanation:
[tex] \sqrt[3]{8} = 2 \\ \sqrt{9} = 3[/tex]
so between 2 and 3
you can say:
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.22
2.1875838
2.7583883
Using this table, calculate the profit at each level of bicycle production. One bike: -$ Two bikes: $ Three bikes: $ Four bikes: $ Five bikes: $ Six bikes: $ Seven bikes: $
Answers
Answer:
Step-by-step explanation
You solve with math
what is y=-1/4x+4 written in standard form? plsss help!
Answers
Answer:
The standard form of this slope-intercept form is x + 4y = 16.
Answer:
x + 4y =16
Step-by-step explanation:
[tex]y= \frac{-1}{4}x+4[/tex]
Multiply by 4
[tex]4y=4*\frac{-1}{4}x+4*4\\\\[/tex]
4y = -x + 16
x + 4y =16
What is the area of this face?
100 in2
200 in2
150 in
400 in2
Answers
Answer: 200 in
Step-by-step explanation:
Try to split up the face into pieces. You can make the first piece the square on the top. Only, you don't know the value of the bottom side, but you can see that it is 10 (if you look at the top at the back). So, if you do your multiplication, 10 x 10 = 100. So, that is the area of the first square. The next square also has a width and height of 10, (10 on the bottom, and follow the side to the other 10). Do the multiplication again (same as above) and get 100. Now that you have the area of the two pieces, you add then together: 100+100=200
Please feel free to let me know if you have any questions!
Answer: The yellow face has an area of 200 in^2
Step-by-step explanation:
The height of each of the two square areas is 10 in. The width is 10. A=w × h
10 × 10 = 100. Times 2 for the total for the yellow face.
Don't be confused by the 5-inch offset.
THE IMAGE DOWN BELOW MATH PLEASE HELP ME WITH THIS ALEGEBRA IM CRYING YALL
Answers
Answer:
25%
Step-by-step explanation:
The formula that we can use in this problem would be:
$decreased / Original $
So we would have
28-21 / 28
7 / 28
1/4
1/4=25
So, the percent decrease if 25%
Answer:
25
Step-by-step explanation:
Formula for percent increase or decrease:
(new number - old number)/(old number) * 100%
In this case,
old number = $28
new number = $21
Plug numbers into formula:
($21 - $28)/($28) * 100%
= -$7/$28 * 100%
= -0.25 * 100%
= -25%
A negative answer means a percent decrease.
A positive answer means a percent increase.
The percent change here is -25%, so it is a percent decrease of 25%
Calculate the circumference
Answers
Answer:
circumference= 2πr
2×22×13
7
44×13
7
572
7
81.71cm
The cost of a car is supposed to be no more than 80% of the value for the next year's
model. If a car costs $14,000, what is the cost of the next year's model?
Answers
Answer:
x ≥ $17, 500
Step-by-step explanation:
To find the cost of the next year model, we will follow the steps below;
Let x be the value of next year's model
$14000 ≤ 80% of x
80% of x ≥ $14000
80% × x ≥$14000
80x/100 ≥ $14000
multiply both-side of the equation by 100
80x ≥ $1400000
Divide both-side of the inequality by 80
80x /80 ≥ $1400000 / 80
x ≥ $17, 500
Therefore the cost of next year's model is
x≥$17, 500
Given P(X) = 0.5, P(Y) = 0.4, and P(Y|X) = 0.3, what are P(X and Y) and P(X or Y)?
Answers
Answer:
P(X and Y) =0.2, P(X or Y)=0.7
Step-by-step explanation:
P(X or Y)
P(X∪Y) = P(X)+P(Y) - P(X∩Y)
= 0.5 + 0.4 - 0.2
= 0.7
or 1-P(Y|X)=1-0.3=0.7
P(X and Y)
P(X∩Y) = P(X) × P(Y)
= 0.5 × 0.4
= 0.2
I hope it helps
Jill is 5 kilometers away from Joe. both begin to walk toward each other at the same time. Jill walks at 1 km/hr. they meet in 2 hours. how fast is Joe walking? show work plz
Answers
Answer:
1.5km/hr.
Step-by-step explanation:
jill is walking 1 km/hr. and meets in 2 hours. so jill crossed 2 km in 2 hours. so joe has to (5-2) or 3 km and he walked 3 km on 2 hours as the question. that means joe was walking 3/2 km/hr or 1.5 km/hour
I will give brainliest to the quick and correct answer.. Please Help!
Drag each value or expression to the correct location on the equations and sentences. Each value and expression can be used more than once, but not all values and expressions will be used. Gary works at a bakery, and he needs to select a rectangular cookie sheet with an area of 192 square inches. The area of the cookie sheet is represented by the expression given below.
Answers
Answer:
Length is 12 and width is (x+4) means 16
Step-by-step explanation:
Given:
Area of cookie sheet = 192 in²
Area = x² + 4x
Computation:
x² + 4x = 192
x(x + 4) = 192 , The length is x and width is (x+4)
x² + 4x -192 = 0
x² + (16 + 12)x -192 = 0
x² + 16x + 12x -192 = 0
x(x + 16) - 12(x + 16)
(x + 16)(x - 12)
Because length can not be negative (-16) so,
Length is 12 and width is (x+4) means 16
Is Figure B a scale copy of Figure A? Choose 1 answer: (Choice A) Yes (Choice B) No
Answers
Answer:
no
Step-by-step explanation:
Answer: B) No
Step-by-step explanation:
When you dive 9 by 3 you get 3.
When you divide 7.3 by 2.2 you get 3.318181818...