Answers
Answer:
Part (a)Given:
[tex]\displaystyle \int\limits_{1}^{3} x^2 \:dx[/tex]
Trapezium Rule
[tex]\displaystyle \int\limits_{a}^{b} y \:dx \approx \dfrac{1}{2}h\left[(y_0+y_n)+2(y_1+y_2+...+y_{n-1})\right] \quad \textsf{where }h=\dfrac{b-a}{n}[/tex]
Calculate the width of each strip (h).
Given:
a = 1b = 3n = 5[tex]\implies h=\dfrac{3-1}{5}=0.4[/tex]
Create a table with the x and y values:
[tex]\large\begin{array}{| c | c | c | c | c | c | c |}\cline{1-7} x & 1 & 1.4 & 1.8 & 2.2 & 2.6 & 3\\\cline{1-7} y & 1 & 1.96 & 3.24 & 4.84 & 6.76 & 9\\\cline{1-7}\end{array}[/tex]
Put all the values into the formula:
[tex]\begin{aligned}\displaystyle \int\limits_{1}^{3} x^2 \:dx & \approx \dfrac{1}{2}(0.4)\left[(1+9)+2(1.96+3.24+4.84+6.76)\right]\\& = 0.2\left[10+2(16.8)\right]\\\\& = 0.2\left[10+33.6\right]\\\\& = 0.2\left[43.6\right]\\\\& = 8.72 \end{aligned}[/tex]
Part (b)[tex]\begin{aligned}\displaystyle \int\limits_{1}^{3} x^2 \:dx &=\left[\dfrac{1}{3}x^3\right]^3_1\\& = \dfrac{1}{3}(3)^3-\dfrac{1}{3}(1)^3\\& = 9-\dfrac{1}{3}\\& = \dfrac{26}{3}\end{aligned}[/tex]
The exact area as a decimal is [tex]\sf 8.\dot{6}[/tex]. Therefore, the estimated answer of 8.72 is an overestimate.
Part (c)Answer to (a) = 8.72
To find the maximum possible error:
Identify the last non-zero digit to the right of the decimal point → 2The precision of the number is the place value: 0.01Divide the precision by 2Therefore, the maximum possible error for 8.72 is 0.005.
Part (d)Trapezoid Error formula
[tex]|E| \leq \dfrac{(b-a)^3}{12n^2}\left[\textsf{max}|f''(x)|\right],\quad a \leq x \leq b[/tex]
Calculate the second derivative:
[tex]f(x)=x^2[/tex]
[tex]f'(x)=2x[/tex]
[tex]f''(x)=2[/tex]
Input the values into the formula:
[tex]\implies |E| \leq \dfrac{(3-1)^3}{12n^2}(2) < 0.001[/tex]
[tex]\implies 16 \leq 0.012n^2[/tex]
[tex]\implies 36.5148...\leq n[/tex]
[tex]\implies 37\leq n[/tex]
Related Questions
In a class of 28 students, 21 have a cat and 9 have a dog. There are 7 students who
have a cat and a dog. What is the probability that a student has a dog given that they
do not have a cat?
Answers
The probability that a student has a dog given that they do not have a cat is 1/14.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
In a class of 28 students, 21 have a cat and 9 have a dog.
There are 7 students who have a cat and a dog.
The probability that a student has a dog given that they do not have a cat
= 2/ 28
= 1/14
Learn more about probability here;
https://brainly.com/question/11234923
#SPJ1
A pulley is used to pull a boat to the dock. The rope is attached to the boat 7 feet below the level of the pulley. What is the distance from the boat to the dock when the rope is 25 feet long?
Answers
Answer: 24 ft
Step-by-step explanation:
By the Pythagorean theorem,
[tex]7^{2}+x^{2}=25^{2} \\ \\ 49+x^{2}=625 \\ \\ x^{2}=576 \\ \\ x=\boxed{24 \text{ ft}}[/tex]
Which property was used to simplify the expression?
O distributive property
O commutative property
O associative property
O inverse property
4(b+2)=4b+8
Answers
The expression is
4(b+2)=4b+8See
4(b)+4(2)4b+8Its distributive property which states that
a(b+c)=ab+acOption A
Sheila counted 9 blue jays and 21 sparrows at the bird feeder. What was the ratio of blue jays to sparrows?
Answers
Answer:
9/21
= 1/7
Step-by-step explanation:
ratio means the comparison of two things
need help would be apperacited .
Answers
A function on a graph to figure it out you can do the line test where you draw a line through the graph and if the line touches two points its not a function. With this in mind bottom right is for sure one and the top left looks like one but i cant really tell...
Step-by-step explanation:
You play a game that requires rolling a six-sided die and then randomly choosing a colored card from a deck containing 3 red cards, 6 blue cards, and 8 yellow cards. Find the probability that you will roll a 5 on the die and then choose a red card.
Answers
The probability of getting a red card and rolling a 5 is = 3/85
How to find the probability?First, we want to find the probability of rolling a 5.
There are 6 outcomes on the six-sided die, so the probability of getting a particular value is:
P = 1/5.
Then, the probability of randomly drawing a red card is given by the quotient between the number of red cards and the total number of cards:
P' = 3/(3 + 6 + 8) = 3/17
The joint probability is given by the product between the individual probabilities:
prob = P*P' = (1/5)*(3/17) = 3/85
If you want to learn more about probability:
https://brainly.com/question/251701
#SPJ1
A patient has been prescribed 1 gram (g) of Drug A. The stock dose is available in 250 milligram (mg) tablets. How many tablets would you administer per dose?
Answers
Answer:
4
Step-by-step explanation:
1 g = 1,000 mg
1,000/250 = 4
I need help please asap?!!!
Answers
Answer:
3660
Explain
3660ml×1L/100ml
= 3.66L
x² + 10x + 3 = -21?!?!!?!?!!!?
Answers
Answer:
-6,-4
Step-by-step explanation:
if you have to evaluate its 4
and there is 2 solutions
What are the coordinates of point F?
Answers
Answer:
C. 4, -2 1/2
Step-by-step explanation:
(x,y)
its kinda easy
By using a problem-solution structure, the author is able to show readers how people are hurting the planet. The structure also shows how we can change and what we can do to help solve the problems we have caused. It inspires people to take action
Answers
Answer:
One of the problems humans have made is a large amount of pollution.
And so some of the ways we can fix this is;
1- Using electric cars.
2- Using reusable packaging.
3- For the final one you could use stuff that easily and quickly to break down naturally materials.
Step-by-step explanation:
Solve the proportion: 35=x20
Answers
Answer:
either x = 1.75 or x = 700 , question wasn't clear
Step-by-step explanation:
Because you put the x in front of 20 , you might be meaning x/20 (second answer listed)? Or, you put the variable on the wrong side of 20. (first answer listed)
If you meant to type 20x
35 = 20x
÷20 ÷20 *
1.75 = x
*divide both sides by 20 to isolate x
x = 1.75
(x = [tex]\frac{35}{20}[/tex])
--------------------------------------------------------------------------
If you meant to type x/20
35 = [tex]\frac{x}{20}[/tex]
·20 ·20 *
700 = x
*multiply both sides by 20 to isolate x
700 = x
Please help you can see how stressed I am
Answers
answer send in this photo there is answer any doubt you can ask again
_multiply(-26) = -468
please help who will give me full solution I will mark him/her brainlist please help please please
Answers
Answer:
Step-by-step explanation:
Note
I think the question means "What do you multiply -26 by to get - 468
call the number that you need x
x * -26 = - 468 Divide both sides by - 26
-26x/-26 = - 468/ - 26 There are 2 minus signs on the right. They cancel.
x = 18
Conclusion
When you multiply 18 * -26 the answer is --468
Answer: 18
50 POINTS!! What is (-4, 3) (-3, -1) in point slope form?
Y=4x+16
Y-3=-4(x+4)
Answers
Explanation:
[tex]\bf point \ slope \ form: y-y_{1}=m\left(x-x_{1}\right)[/tex]
Find the slope: given points: (-4, 3), (-3, -1)
[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
Insert values
[tex]\rightarrow \sf slope: \ \dfrac{-1-3}{-3-(-4)} =-4[/tex]
Equation in point slope form:
[tex]\sf\rightarrow y - 3 = -4(x - (-4))[/tex]
[tex]\sf\rightarrow y - 3 =-4(x + 4)[/tex]
Additional, in slope intercept form:
[tex]\sf\rightarrow y = mx + b \quad where \ 'm \ is \ slope' \ and \ 'b \ is \ y-intercept'[/tex]
[tex]\sf\rightarrow y = -4 x - 16 +3[/tex]
[tex]\sf\rightarrow y = -4x -13[/tex]
I want to learn more about mean.
What is the mean?
Numbers:
4.5, 1, 9.25, 2, 6, 9.
Answers
What are the vertical and horizontal asymptotes for the function f(x)=3^2/x^-4
O horizontal asymptote: y = -2, y = 2
vertical asymptote: x = 3
O horizontal asymptote: y = -4, y = 1
vertical asymptote: x = 3
O horizontal asymptote: y = 3
vertical asymptote: x=-4, x=1
O horizontal asymptote: y = 3
vertical asymptote: x= -2, x=2
3x²242
?
-4
Answers
The vertical asymptotes x = - 2, 2 and Horizontal asymptotes y = 3
Option A is the correct answer.
What are Function?Function are mathematical statement which links an independent variable to dependent variable.
It always comes with a defined domain and range.
The equation mentioned is incorrect in the question w.r.t. to the solutions mentioned, The right equation is
[tex]\rm f(x) = \dfrac{3 x^2}{x^{2}-4}[/tex]
This function can also be written as
[tex]\rm f(x) = \dfrac{3 x^2}{x^{2}-2^2}\\\\\rm f(x) = \dfrac{3 x^2}{(x+2)(x-2)}[/tex]
Vertical asymptotes are defined when the denominator of a rational function tends to zero.
To find the equation/s let the denominator equal zero.
Denominator tends to zero for x = -2 and x = +2
Horizontal Asymptote is when the function f(x) is tending to zero.
for x = +∞ and x = - ∞
Let the rational function [tex]f(x)= \dfrac{mx^a}{nx^b}[/tex] where and a and b are degree of numerator and denominator.
If a < b , then the y axis y = 0 is a horizontal asymptote.
If b = a then horizontal asymptote is the line y = p/q
Here the value is b = 2 and a = 2
Since b = a the horizontal asymptote is the line
y = m/n where m = 3 and n = 1
Therefore y = 3
So , vertical asymptotes x = - 2, 2
Horizontal asymptotes y = 3
Option A is the correct answer.
To know more about Function
https://brainly.com/question/12431044
#SPJ1
Answer:
A
Step-by-step explanation:
just took the test
A fighter tank targets an enemy helicopter flying at an altitude of 1250 ft. If the ground
distance between the tank & the helicopter is 875 ft, what angle of elevation must the
cannon be raised to in order to hit the target?
Answers
By using trigonometric relations, we will see that the angle of elevation must be 55°.
How to find the angle of elevation?
We can see this as a right triangle, where one cathetus measures 1250ft (altitude) and the other cathetus measures 875ft.
The angle of elevation is the angle such that the adjacent cathetus is the one measuring 875ft.
Then we can use the relation:
tan(a) = (opposite cathetus)/(adjacent cathetus)
tan(a) = 1250ft/875ft
To find the angle of elevation, we can use the inverse tangent function:
a = Atan(1250ft/875ft) = 55°
The angle of elevation must be 55 degrees.
If you want to learn more about right triangles:
https://brainly.com/question/2217700
#SPJ1
93/100
Natalie needs 3 1/2 cups of flour to make 4 dozen cookies. How many.cups will she
need to make 2 dozen cookies?
7 cups
1 cup
13/4 cups
11/2 cups
Answers
Answer:
3/4 cups
Step-by-step explanation:
3 1/2 divided by 2
pls help i will give brainliest. use the examples step to solve the problems,it's my second time posting this
Answers
Answer:
A=144cm2,B=33cm2,C=18cm2,D=21.98cm2
Step-by-step explanation:
A=12*12
B=11*3
C=1/2*4*9
D=π*7cm2. (π = 3.14
The radius of the larger circle is 5m. The radius of the smaller circle is 2.5m. What’s the approximate area of the shaded region of the larger circle?
Answers
Answer: C
Step-by-step explanation:
The line passes through point (0,6) and has a slope of 7. The equation of the line is?
Answers
Answer:
y = 7x + 6
Step-by-step explanation:
The general equation for a line in slope-intercept form is:
y = mx + b
In this form, "m" is the slope and "b" is the y-intercept. Remember, the y-intercept is the y-value when x = 0. As such, the point (0,6) gives you the y-intercept.
You have been given the slope (7) and the y-intercept (6). Therefore, you can just substitute these values in for their variables to determine the equation of the line.
slope = m = 7
y-intercept = b = 6
y = mx + b
y = 7x + 6
2. Consider the following dot plot and answer the following questions : A. Find the measures of central tendency Construct the Box Plot
Answers
The measures of central tendency for this data set are as follows:
Mean = 3.55.Median = 3.5.Mode = 3.How to calculate measures of central tendency?In Mathematics, there are three (3) main measures of central tendency and these include the following:
MeanMedianModeFor the mean, we have:
Mathematically, the mean for this data set would be calculated by using this formula:
Mean = [F(x)]/n
For the total number of data, we have:
F(x) = 0 + 1 + 1 + 1 + 2 + 2 + 3 + 3 + 3 + 3 + 4 + 4 + 4 + 5 + 5 + 5 + 6 + 6 + 6 + 7
F(x) = 71
Substituting the parameters into the formula, we have:
Mean = [F(x)]/n
Mean = 71/20
Mean = 3.55.
For the median, we have:
First of all, we would order the data from lowest to highest and then determine the median as follows:
Data = {0, 1, 1, 1, 2, 2, 3, 3, 3,} 3, 4, {4, 4, 5, 5, 5, 6, 6, 6, 7}
Median = {3 + 4}/2
Median = 7/2
Median = 3.5.
How to calculate the mode?A mode refers to the most frequently occurring number in a data set. Thus, the mode for this data set is equal to 3.
In conclusion, a box plot of the measures of central tendency for this data set is shown in the image attached below.
Read more on mean here: https://brainly.com/question/9550536
#SPJ1
Use the functions a(x) = 7x + 10 and b(x) = 12x - 18 to complete the function operations listed below.
Part A: Find (a + b)(x). Show your work.
Part B: Find (a - b)(x). Show your work.
Part C: Find (a - b)(x). Show your work.
Part D: Find a[b(x)]. Show your work.
Answers
The value of the sum, difference and composite function a[b(x)] are 19x - 8, -5x + 28 and 84x - 136 respectively
Sum and difference of functionsGiven the following functions a(x) = 7x + 10 and b(x) = 12x - 18
Take the sum
(a+b)(x) = a(x) + b(x)
(a+b)(x) = 7x + 10 + 12x - 18
(a+b)(x) = 19x- 8
Take the difference
(a-b)(x) = a(x) - b(x)
(a-b)(x) = 7x + 10 - 12x + 18
(a-b)(x) = -5x + 28
For the composite function a[b(x)].
a(12x- 18) = 7(12x-18) - 10
a[b(x)] = 84x - 126 - 10
a[b(x)] = 84x - 136
Hence the value of the sum, difference and composite function a[b(x)] are 19x - 8, -5x + 28 and 84x - 136 respectively
Learn more on functions here: https://brainly.com/question/25638609
#SPJ1
Decagon, a=22 m, s=14.3 m
Answers
The area of the decagon is 1573.39 square meters
How to determine the area of the decagon?The given parameters are:
Side length, s = 14.3 mApothem, a = 22 mThe area of a decagon is calculated using:
[tex]A = \frac 52s^2\sqrt{5 + 2\sqrt 5[/tex]
Substitute 14.3 for s
[tex]A = \frac 52 * 14.3^2\sqrt{5 + 2\sqrt 5[/tex]
Evaluate the exponent
[tex]A = \frac 52 * 204.49\sqrt{5 + 2\sqrt 5[/tex]
Evaluate the product and the roots
A = 1573.39
Hence, the area of the decagon is 1573.39 square meters
Read more about areas at:
https://brainly.com/question/24487155
#SPJ1
Michael Jordan scores the following points over 8 games: 24, 17, 28, 19, 23, 20, 13, 19. What is the mean (average) number of points she scored over those 8 games
Answers
Answer:
19
Step-by-step explanation:
Answer:
20.375
Step-by-step explanation:
To calculate the mean, in this situation, you first add up the game scores and divide it by the amount of games.
So, first we add 24+17+28+19+23+20+13+19 = 163
Because there are 8 games, we do 163 / 8 = 20.375
or 20.4 to 1dp
Hope this helped! If anything requires clarification, don't hesitate to ask me. I can assure you this is the right answer.
- profparis
Charles would like to buy a new car that costs $32 000. The dealership offers to finance the car at 2.4%/a compounded monthly for five years with monthly payments. The dealer will reduce the selling price by$3000 if Charles pays cash. Charles can get a loan from his bank at 5.4%/a compounded monthly. Which is the best way to buy the car? Justify your answer with calculations.
Answers
Charles would like to buy a new car that costs $32 000. The dealership offers to finance the car at 2.4%/a, it's best for Charles loans from the bank to buy car.
Which is the best way to buy a car?Generally, the equation for the monthly loan payment is mathematically given as
[tex]R=\frac{\frac{iP}{N}}{1-(\frac{1}{N})^{NY}}[/tex]
Therefore
[tex]R=\frac{\frac{0.024*32000}{12}}{1-(\frac{0.024}{12}+1)^{-12*5}}[/tex]
R=566.51
Hence the total payment is
T=R*N*Y
T=33990.34
By taking a loan of 29000, and applying the equation
T'=33155.77
In conclusion, it is best for Charles loans from the bank to buy a car.
Read more about loan
https://brainly.com/question/11794123
#SPJ1
How many years will Samsung galaxy 2 in 1 laptop last
Answers
Answer:
i think 6 years because i always used it
Step-by-step explanation:
make me my brainliest answer
What is the probability of drawing an ace, a 2, and a 3, without replacement?
Answers
The probability of drawing an ace will be 8 / 16575.
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
The probability will be calculated as follows:-
P = [tex]\dfrac{4}{52}\times \dfrac{4}{51}\times\dfrac{4}{50}[/tex]
P = [tex]\dfrac{8 }{ 16575}[/tex]
Therefore the probability of drawing an ace will be 8 / 16575.
To know more about probability follow
https://brainly.com/question/24756209
#SPJ1
your recipe calls for 2 over 3 cups of sugar. you are only making 2 over 4 of the recipe. how much sugar do you need? not simplified
Answers
The quantity of sugar required for 2/4 of the recipe is 1/3 cups
How to solve fraction?let
x = quantity of sugar neededRatio of sugar to recipe
2/3 : 1 = x : 2/4
2/3 ÷ 1 = x ÷ 2/4
2/3 × 1/1 = x × 4/2
2/3 = x × 2
2/3 = 2x
x = 2/3 ÷ 2
x = 2/3 × 1/2
= 2/6
x = 1/3 cups
Therefore, the quantity of sugar required for 2/4 of the recipe is 1/3 cups
Learn more about fraction:
https://brainly.com/question/11562149
#SPJ1