During an experiment in which you are investigating the acceleration changes due to force changes, what value must stay constant during these trials?
a. Force
b. Velocity
c. Acceleration
d. Mass
Answers
During an experiment of acceleration changes, the value that must stay constant during these trials is d. Mass
Inertia, a basic characteristic of all matter, may be measured quantitatively using mass. When a force is applied, an item effectively provides resistance to changes in velocity or position. The change brought about by an applied force is less the more mass an item has. According to Newton's second law of motion an object's acceleration is inversely proportional to its mass and directly proportional to the net force that has been applied to it. It may be expressed mathematically as F = ma.
The goal of this experiment is to see how variations in force impact acceleration. It is crucial to maintain the mass constant throughout the trials in order to isolate the impact of force on acceleration. Any observable variations in acceleration may be entirely attributable to variations in the applied force by maintaining the mass constant.
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Related Questions
Trapezoid EFGH is inscribed in a circle, with \(EF \parallel GH\). If arc GH is 70 degrees, arc EH is x^2 - 2x degrees, and arc FG is 56 - 3x degrees, where x > 0, find arc EPF, in degrees.
Answers
Answer:
Arc EPF is 240°
Step-by-step explanation:
Since the quadrilateral, EFGH is a trapezoid and EF is parallel to GH, we have;
∠HGF + ∠GFE = 180°
∠GHE + ∠GFE = 180°
∠HGF + ∠HEF = 180°
∴∠HEF = ∠GFE
In ΔHEF and ΔGFE
∠EHF = ∠EGF (Angles subtending the same segment)
With side EF common to both triangles and ∠HEF = ∠GFE , we have;
ΔHEF ≅ ΔGFE (Angle Angle Side rule)
Hence, side FG = EH
For cyclic trapezoid side FG = EH
The base angles subtended by GH = 70
Arc EH = x² - 2·x
Arc FG = 56 - 3·x
Therefore;
70 + x² - 2·x + 56 - 3·x + arc EPF = 360 .............(1)
Also since the equation of a circle is (x-h)² + (y-k)² = r², where the center of the circle is (h, k), then as EF is a displacement of say z from GH, then arc EH = FG which gives;
x² - 2·x = 56 - 3·x
x² - 2·x - 56 + 3·x = 0
x² + x - 56 = 0
(x - 7)(x + 8) = 0
Therefore, since x > 0 we have x = 7
Plugging in the value of x into the equation (1), we have
70 + 7² - 2·7 + 56 - 3·7 + arc EPF = 360 .............(1)
70 + 70 + arc EPF = 360
arc EPF = 360 - 140 = 240°.
The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 9.5 to 24 on the number line. A line in the box is at 15.5. The lines outside the box end at 2 and 30. The graph is titled Burger Quick.
Which drive-thru typically has more wait time, and why?
Burger Quick, because it has a larger median
Burger Quick, because it has a larger mean
Super Fast Food, because it has a larger median
Super Fast Food, because it has a larger mean
Question 2
The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the number line. A line in the box is at 19. The lines outside the box end at 10 and 27.
Which of the following is the appropriate measure of center for the data, and what is its value?
The mean is the best measure of center, and it equals 19.
The median is the best measure of center, and it equals 4.
The median is the best measure of center, and it equals 19.
The mean is the best measure of center, and it equals 4.
Question 3
A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
5, 5, 6, 8, 10, 15, 18, 20, 20, 20, 20, 20, 20
A graph titled Donations to Charity in Dollars. The x-axis is labeled 1 to 5, 6 to 10, 11 to 15, and 16 to 20. The y-axis is labeled Frequency. There is a shaded bar up to 2 above 1 to 5, up to 3 above 6 to 10, up to 1 above 11 to 15, and up to 7 above 16 to 20.
Which measure of variability should the charity use to accurately represent the data? Explain your answer.
The range of 13 is the most accurate to use, since the data is skewed.
The IQR of 13 is the most accurate to use, since the data is skewed.
The range of 20 is the most accurate to use to show that they have plenty of money.
The IQR of 20 is the most accurate to use to show that they need more money.
Question 4
The circle graph describes the distribution of preferred transportation methods from a sample of 400 randomly selected San Francisco residents.
circle graph titled San Francisco Residents' Transportation with five sections labeled walk 40 percent, bicycle 8 percent, streetcar 15 percent, bus 10 percent, and cable car 27 percent
Which of the following conclusions can we draw from the circle graph?
Together, Streetcar and Cable Car are the preferred transportation for 168 residents.
Together, Walk and Streetcar are the preferred transportation for 55 residents.
Bus is the preferred transportation for 45 residents.
Bicycle is the preferred transportation for 50 residents.
Question 5
The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 1 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 1 and 2. There are two dots above 8. There are three dots above 6, 7, and 9.
Which of the following is the best measure of variability for the data, and what is its value?
The range is the best measure of variability, and it equals 8.
The range is the best measure of variability, and it equals 2.5.
The IQR is the best measure of variability, and it equals 8.
The IQR is the best measure of variability, and it equals 2.5.
Question 7
At a recent baseball game of 5,000 in attendance, 150 people were asked what they prefer on a hot dog. The results are shown.
Ketchup Mustard Chili
63 27 60
Based on the data in this sample, how many of the people in attendance would prefer mustard on a hot dog?
900
2,000
2,100
4,000
Question 8
The number of milligrams of Vitamin C from 100 different gummy vitamins sold in the world was collected.
Which graphical representation would be most appropriate for the data, and why?
Box plot, because the median can easily be determined from the large set of data
Stem-and-leaf plot, because you can see the shape of the data
Histogram, because it shows each individual data point
Bar chart, because the data is categorical
Answers
Burger Quick, because it has a larger median.
How to explain the informationBurger Quick typically has more wait time because it has a larger range (30-2=28) compared to Super Fast Food (27-3=24) and also has a larger interquartile range (IQR) (24-9.5=14.5) compared to Super Fast Food (15.5-8.5=7), indicating more variability in the wait times. The fact that Burger Quick's median (15.5) is larger than Super Fast Food's median (12) reinforces this conclusion.
Therefore, the correct answer is: Burger Quick, because it has a larger median.
Answer 2: The appropriate measure of center for this data is the median, which is represented by the line in the box at 19. This is because the data is skewed, with a longer tail to the right, and the median is less sensitive to extreme values compared to the mean. Therefore, the correct answer is: The median is the best measure of center, and it equals 19.
Answer 3: The measure of variability that the charity should use to accurately represent the data is the IQR (Interquartile Range), which is the range of the middle 50% of the data. The reason for this is that the data is skewed to the right, with many values concentrated in the upper range of the data, and the IQR is less sensitive to outliers compared to the range.
The IQR for this data is 20-10=10, which represents the spread of the middle 50% of the data. Therefore, the correct answer is: The IQR of 20 is the most accurate to use, since the data is skewed.
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The table shows three functions and their output values for different values of x. Which equation represents h(x)? h(x) = (f(x))(g(x)) h(x) = f(x) – g(x) h(x) = f(x) + g(x)
Answers
The equation that represents h(x) is h(x) = (f(x))(g(x)).
To determine which equation represents h(x), we need to analyze the given table and understand the relationship between the functions f(x), g(x), and h(x).
Since h(x) represents the output values obtained by multiplying f(x) and g(x), we should look for values in the table where h(x) is the product of the corresponding values of f(x) and g(x).
Let's examine the table and compare the values:
x | f(x) | g(x) | h(x)
1 | 3 | 4 | 12
2 | 5 | 2 | 10
3 | 2 | 6 | 12
From the table, we can see that the values in the h(x) column are the products of the corresponding values in the f(x) and g(x) columns. Therefore, the equation that represents h(x) is h(x) = (f(x))(g(x)).
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Answer:
It's B.
Step-by-step explanation:
Edge 2020.
the angle below has a measure of 5.8 radians. determine the exact coordinates of the terminal point ( x , y ) .
Answers
Exact coordinates of the terminal point (x, y) are (-3.40, 4.71).
Let's dive deeper into the details below.
The angle below has a measure of 5.8 radians. The exact coordinates of the terminal point (x, y) can be determined by using trigonometry.
First, we must remember that the formula for the x-coordinate is x = r cos θ, where r is the length of the radius and θ is the measure of the angle. Therefore, we can calculate the x-coordinate by plugging in the radius (which is given) and the measure of the angle (5.8 radians) into the formula:
x = 5.8 cos (5.8) = 5.8 × -0.5806 = -3.40
Now, we must use the formula for the y-coordinate which is y = r sin θ. Plugging in the radius and the measure of the angle, we can calculate the y-coordinate:
y = 5.8 sin (5.8) = 5.8 × 0.8139 = 4.
Therefore, the exact coordinates of the terminal point (x, y) are (-3.40, 4.71).
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Select the correct graph.
Which graph is the graph of function
f(x) =4^x
Answers
Answer:
the question on top is right
Step-by-step explanation:
Triangle fgh is an isosceles right triangle with a hypotenuse that measures 16 units. an altitude, line segment g j, is drawn from the right angle to the hypotenuse. what is the length of line segment g j? 2 units 4 units 6 units 8 units
Answers
The square of the altitude is equal to the product of the base of the triangles
Triangular altitude theoremThe square of the altitude is equal to the product of the base of the triangles. The length of line segment GJ is 8units
According to the theorem;
GJ² = HJ*JF
Determine the value of x using the pythagorean theorem
\(x^2+x^2=16\\2x^2=16\\x^2=8\\x=\sqrt{8}\\x=2\sqrt{2}\)
According to the theorem;
GJ² = HJ*JF
HJ + JF = 16
Since HJ = JF, hence
HJ = JF = 8
Substitute
GJ² = HJ*JF
GJ² = 8 * 8
GJ² = 64
GJ = 8units
Hence the length of line segment GJ is 8units
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Answer:
8
Step-by-step explanation:
Tony made $90 for 5 hours of work.
At the same rate, how much would he make for 12 hours of work?
Answers
Answer: $216
Step-by-step explanation:
If you divide 90 by 5 then you get 18 so 18 multiplied by 12 is 216.
write each ratio in simplest form: 1 day to 54 minutes
need help asap
Answers
Answer:
80:3
Step-by-step explanation:
1 day × 24 hours / day × 60 minutes / hour = 1440 minutes
1 day : 54 minutes =
= 1440 minutes : 54 minutes = 1440:54 = 240:9 = 80:3
Answer: 80:3
Hi Geovannie, when you submit this form,
Required
1. Solve the equation:
-(1+4x)=4(1-x)-5*
(5 Points)
Answers
Steps to solve:
-(1 + 4x) = 4(1 - x) - 5
~Distribute both sides
-1 - 4x = 4 - 4x - 5
~Combine like terms on the left side
-1 - 4x = -1 - 4x
~Add 4x to both sides
-1 = -1
~Add 1 to both sides
0 = 0
Therefore, all real numbers are solutions.
Best of Luck!
Griffin says the birds height above and the fish’s depth below sea level are opposites. Is this possible? Explain.
Due-March 7
Answers
the length of a basketball pitch can be divided into 12 parts which 25 centimetres on how much parts it's 20 centimetres long can be obtained from the pitch
Answers
Answer:
the number of parts is going to be
= 15 parts
Step-by-step explanation:
A basketball pitch can be divided into twelve(12) parts , each part of equal length of twenty five (25) centimeters.
The initial and total length of the basketball pitch = 12*25
The initial and total length of the basketball pitch = 12*25
The initial and total length of the basketball pitch = 300 cm
So if it's now divided into parts of each 20 cm ,
the number of parts is going to be
= 300/20
the number of parts is going to be
= 15 parts
Find the power set for the following sets (Write 3 examples of each)
a) Two sets A & B both having any 2 elements
b) Two sets A & B both having any 3 elements
c) Two sets A & B both having any 4 elements
Answers
Given statement solution is :- a) Power set for two sets A and B with any 2 elements:
Set A: {1, 2}, Set B: {3, 4}
Power set of A: {{}, {1}, {2}, {1, 2}}
Power set of B: {{}, {3}, {4}, {3, 4}}
b) Power set for two sets A and B with any 3 elements:
Set A: {1, 2, 3}, Set B: {4, 5, 6}
Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}
Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}
c) Power set for two sets A and B with any 4 elements:
Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}
Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}
Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},
a) Power set for two sets A and B with any 2 elements:
Set A: {1, 2}, Set B: {3, 4}
Power set of A: {{}, {1}, {2}, {1, 2}}
Power set of B: {{}, {3}, {4}, {3, 4}}
Set A: {apple, banana}, Set B: {cat, dog}
Power set of A: {{}, {apple}, {banana}, {apple, banana}}
Power set of B: {{}, {cat}, {dog}, {cat, dog}}
Set A: {red, blue}, Set B: {circle, square}
Power set of A: {{}, {red}, {blue}, {red, blue}}
Power set of B: {{}, {circle}, {square}, {circle, square}}
b) Power set for two sets A and B with any 3 elements:
Set A: {1, 2, 3}, Set B: {4, 5, 6}
Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}
Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}
Set A: {apple, banana, orange}, Set B: {cat, dog, elephant}
Power set of A: {{}, {apple}, {banana}, {orange}, {apple, banana}, {apple, orange}, {banana, orange}, {apple, banana, orange}}
Power set of B: {{}, {cat}, {dog}, {elephant}, {cat, dog}, {cat, elephant}, {dog, elephant}, {cat, dog, elephant}}
Set A: {red, blue, green}, Set B: {circle, square, triangle}
Power set of A: {{}, {red}, {blue}, {green}, {red, blue}, {red, green}, {blue, green}, {red, blue, green}}
Power set of B: {{}, {circle}, {square}, {triangle}, {circle, square}, {circle, triangle}, {square, triangle}, {circle, square, triangle}}
c) Power set for two sets A and B with any 4 elements:
Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}
Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}
Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},
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results of a random survey showed that 15 out of 25 students plan to vote for Stacy for class
president. Based on this survey, about how many votes will Stacy receive if 225 students cast votes?
Answers
165 votes
So we know that there would be 225 votes.
Explanation:
225 divide 25=11
Then lastly multiply 15 with 11.
Final Result: 165 votes
Solve using determinants
X/Δ1 = -y/Δ2 = z/Δ3 = 1/Δ0
Please show working and verification by plugging in
values in equation.
Answers
Using determinants and Cramer's rule, we can solve the system of equations and express the variables in terms of the determinants. The solution is:
X = Δ0/Δ1, y = -Δ2/Δ1, z = Δ3/Δ1.
To solve the system of equations using determinants and Cramer's rule, we need to compute the determinants Δ0, Δ1, Δ2, and Δ3.
Δ0 represents the determinant of the coefficient matrix without the X column:
Δ0 = |0 1 1|
|1 0 -1|
|1 -1 1|
Expanding this determinant, we get:
Δ0 = 0 - 1 - 1 + 1 + 0 - 1 = -2
Similarly, we can compute the determinants Δ1, Δ2, and Δ3 by replacing the corresponding column with the constants:
Δ1 = |1 1 1|
|-1 0 -1|
|1 -1 1|
Expanding Δ1, we get:
Δ1 = 0 - 1 - 1 + 1 + 0 - 1 = -2
Δ2 = |0 1 1|
|1 -1 -1|
|1 1 1|
Expanding Δ2, we get:
Δ2 = 0 + 1 + 1 - 1 - 0 - 1 = 0
Δ3 = |0 1 1|
|1 0 -1|
|1 -1 -1|
Expanding Δ3, we get:
Δ3 = 0 - 1 + 1 - 1 - 0 + 1 = 0
Now, we can solve for X, y, and z using Cramer's rule:
X = Δ0/Δ1 = -2/-2 = 1
y = -Δ2/Δ1 = 0/-2 = 0
z = Δ3/Δ1 = 0/-2 = 0
Therefore, the solution to the system of equations is X = 1, y = 0, and z = 0.
To verify the solution, we can substitute these values into the original equation:
1/Δ1 = -0/Δ2 = 0/Δ3 = 1/-2
Simplifying, we get:
1/-2 = 0/0 = 0/0 = -1/2
The equation holds true for these values, verifying the solution.
Please note that division by zero is undefined, so the equation should be considered separately when Δ1, Δ2, or Δ3 equals zero.
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Could someone help me find how to extract the root from this equation?2y ^ 2 - 8 = 6 - 2y ^ 2
Answers
Answer:
y = ± √ 7/2
Step-by-step explanation:
2*y^2-8-(6-2*y^2)=0
(2 • (y2)) - 8) - (6 - 2y2) = 0
(2y2 - 8) - (6 - 2y2) = 0
Pull out like factors :
4y2 - 14 = 2 • (2y2 - 7)
4.2 Factoring: 2y2 - 7
difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
2 • (2y2 - 7) = 0
5.1 Solve : 2 = 0
5.2 Solve : 2y2-7 = 0
Add 7 to both sides of the equation :
2y2 = 7
Divide both sides of the equation by 2:
y2 = 7/2 = 3.500
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
y = ± √ 7/2
Susan collected 89 stickers for 28 weeks. How many stickers did she collect in total round off your answer to the nearest hundred answer for free
Answers
Answer:
2500 ( nearest hundred)
Step-by-step explanation:
Given that :
Number of stickers collected per week = 89
Number of weeks for which stickers were being collected = 28
To obtain the total number of stickers collected, we take the product of the number of weeks for which the stickers were beug vcilled and the number of stickers collected per week
The number of stickers collected :
89 * 28 = 2492
2492 = 2500 ( nearest hundred)
Please help me and explain thank u
Answers
The solution to this expression (√5 - 3√2)(√5 + 3√2) is equal to -13.
What is a difference of two (2) squares?In Mathematics and Geometry, the standard form for a difference of two (2) squares is modeled or represented by this mathematical expression:
a² - b² = (a + b)(a - b).
Where:
a and b represent numerical values (numbers or numerals).
Based on the information provided, we have the following mathematical expression:
(√5 - 3√2)(√5 + 3√2);
By comparison, we have the following:
(√5 - 3√2)(√5 + 3√2) = (a + b)(a - b)
a² - b² = (√5)² - (3√2)²
a² - b² = 5 - 18
a² - b² = -13.
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Use the Chain Rule to find the indicated partial derivatives.u = √r2 + s2, r = y + x cos t, s = x + y sin t∂u/∂x, ∂u/∂y, ∂u/∂t when x = 4, y = 5, t = 0∂u/∂x = ∂u/∂y = ∂u/∂t =
Answers
The partial derivatives of u with respect to x, y, and t when x = 4, y = 5, and t = 0 are ∂u/∂x = 9, ∂u/∂y = 9 and ∂u/∂t = 36/41
To find the partial derivatives of u with respect to x, y, and t, we will use the chain rule. The chain rule is used to find the derivative of a composite function, where one function is inside another function. In this case, u is a composite function of r and s, and r and s are functions of x, y, and t.
First, we will find the partial derivative of u with respect to x:
∂u/∂x = (∂u/∂r)(∂r/∂x) + (∂u/∂s)(∂s/∂x)
To find ∂u/∂r and ∂u/∂s, we can use the power rule:
∂u/∂r = (r^2 + s^2)^(-1/2) * 2r
∂u/∂s = (r^2 + s^2)^(-1/2) * 2s
To find ∂r/∂x and ∂s/∂x, we can use the product and chain rules:
∂r/∂x = cos(t)
∂s/∂x = 1
Plugging in the values for x, y, and t, we get:
∂u/∂x = [(5 + 4cos(0))^2 + (4 + 5sin(0))^2]^(-1/2) * 2(5 + 4cos(0)) * cos(0) + [(5 + 4cos(0))^2 + (4 + 5sin(0))^2]^(-1/2) * 2(4 + 5sin(0)) * 1
Simplifying, we get:
∂u/∂x = (41/41) * 5 + (41/41) * 4
∂u/∂x = 9
Similarly, we can find the partial derivatives of u with respect to y and t:
∂u/∂y = [(5 + 4cos(0))^2 + (4 + 5sin(0))^2]^(-1/2) * 2(5 + 4cos(0)) * 1 + [(5 + 4cos(0))^2 + (4 + 5sin(0))^2]^(-1/2) * 2(4 + 5sin(0)) * sin(0)
∂u/∂y = (41/41) * 5 + (41/41) * 4
∂u/∂y = 9
∂u/∂t = [(5 + 4cos(0))^2 + (4 + 5sin(0))^2]^(-1/2) * 2(5 + 4cos(0)) * (-4sin(0)) + [(5 + 4cos(0))^2 + (4 + 5sin(0))^2]^(-1/2) * 2(4 + 5sin(0)) * 5cos(0)
∂u/∂t = (-40/41) * 5 + (200/41) * 4
∂u/∂t = 36/41
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For the Transformation T write the T-1
T: (x, y) = (x + 4, y + 3)
Т-1 (x, y) -
(x+3, y + 2)
(x-4, y-3)
(x+, y + 3)
Answers
Answer:
(T - 1)(x, y) = (x - 4, y - 3)
Step-by-step explanation:
For a given transformation:
T(x, y) = (x', y')
the inverse transformation is defined by:
(T - 1)(x', y') = (x, y)
So, if our transformation is:
T(x, y) = (x + 4, y + 3)
Then for the inverse transformation, we should have:
(T - 1)(x + 4, y + 3) = (x, y)
So the inverse transformation reduces the x-value by 4, and reduces the y-value by 3.
Writing the inverse transformation for a generic (x, y) point, we get:
(T - 1)(x, y) = (x - 4, y - 3)
what is a point-slope equation of the line with slope -12 that goes through the point (5,3)?
Answers
Answer:
y-3=-12(x-5)
Step-by-step explanation:
y-y1=m(x-x1)
y-3=-12(x-5)
Estimate the solution of the following IVP on the interval t=1 to t=5: tx' + 2x = t2 - t+1 x(1) = } Use Euler method and RK4 with a timestep of 0.1s. Compare your solutions to the results of using ode45 in Matlab as well as the analytical solution: x(t) = 1 1 1 t + + 3 2 12t2 • Display one plot with 4 curves (Euler, RK4, ode45 and analytical solution) • Display the percent difference between the 3 solution methods and the analytical solution at t=2,3,4,5 seconds (12 numbers total) and explain the changes in error. Display the total computation time for the 3 solution methods (Euler,RK4, ode45) .
Answers
The solution of the given initial value problem (IVP) was estimated using the Euler method and RK4 with a timestep of 0.1s.
To estimate the solution of the given initial value problem (IVP), we will use the Euler method and RK4 with a timestep of 0.1s. We will compare the solutions obtained from these numerical methods with the results obtained using the ode45 solver in MATLAB and the analytical solution.
First, we will implement the Euler method and RK4 to approximate the solution over the interval t=1 to t=5. Using the given initial condition and the differential equation, we can iteratively calculate the values of x(t) at each timestep.
Next, we will use the ode45 solver in MATLAB, which is a more advanced numerical solver that adapts its timestep to achieve accurate results. This will serve as a benchmark for comparison with the other methods.
To visualize the results, we will create a plot that displays the four curves: Euler method, RK4, ode45, and the analytical solution given by x(t) = (t + 1)/(2t^2 + 3).
To assess the accuracy of the numerical methods, we will calculate the percent difference between the numerical solutions (Euler, RK4, and ode45) and the analytical solution at specific time points (t=2, 3, 4, 5). This will allow us to quantify the error and analyze the changes in error between the methods.
Additionally, we will measure and display the total computation time for each solution method (Euler, RK4, and ode45). This will provide insights into the efficiency of the different methods in terms of computational resources required.
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Evaluate x-y = -11 and y =26
Answers
x= 15
Step-by-step explanation:Hi there !
x - y = - 11
replace y = 26
x - 26 = - 11
x = 26 - 11
x = 15
Good luck !
I need help immediately!!!
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The limit as x approaches one is infinity.
\(lim_{x\to1}\frac{x + x {}^{2} + {x}^{3} + ... + {x}^{100} - 1000}{1 - x} =\infty\)
What is the limit of a function?The limit of a function, f(x) as x approaches a given value b, is define as the value that the function f(x) attains as the variable x approaches the given value b.
From the given question, as x approaches 1,
substituting x into 1 - x,
the denominator of the function approaches zero, because 1 - 1 = 0 and thus the function becomes more and more arbitrarily large.
Thus, the limit of the function as x approaches 1 is infinity.
Therefore,
The limit (as x approaches 1)
\(lim_{x\to1}\frac{x + x {}^{2} + {x}^{3} + ... + {x}^{100} - 1000}{1 - x} = \infty \)
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help this is urgent hurry pls
Answers
Answer:
Step-by-step explanation:
You're right; it's 97 degrees. The angles of a triangle add up to 180, so to solve for each triangle's unknown angle value, subtract the known angles from 180. For the left triangle, that's 33 and for the right triangle it's 50. Those missing angles plus the one the question is asking for should add up to 180 degrees as well. Hence, 180 - 33 - 50 = 97.
What is the value of sin 2900 + cos 2900 ?
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Answer:
-1.25737973739
Step-by-step explanation:
plz make it brillent ans
3-1 The roof area of a fable roof is made up of two rectangles. (True or False)
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Given statement "The roof area of a gable roof is made up of two rectangles"
The given statement is True.
Because, A gable roof consists of two sloping roof surfaces that meet at the top, forming a triangle shape on both ends of the building.
Each of these sloping surfaces can be represented as a rectangle, and the combined area of these two rectangles represents the total roof area.
Area is a measure of the amount of space inside a two-dimensional (2D) or three-dimensional (3D) shape.
It is typically measured in square units, such as square meters, square feet, or square inches.
For similar question on area.
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The length of a rectangle is 2 inches more than twice its width, and its perimeter is 60 inches. Find the length and width
of the rectangle.
If w = the width of the rectangle, then the length equals
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Answer:
no
Step-by-step explanation:
What is 116.52 plus 8% as tax
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Answer:
125.84
Step-by-step explanation:
116.52(0.08)=9.32
116.52+9.32=125.84
Answer:
The total is $125.84.
Step-by-step explanation:
The total is equal to the original value (100%) + the tax amount (8%) which equals 108%. To multiply it, we move the decimal two to the left to get our figure (1.08) then multiply that times 116.52. So, 116.52x1.08=125.8416; for dollars I rounded to the nearest cent: $125.84.
n + 5 ≥ 25
Which inequality represents the solution set for this situation?
A) n ≥ 20
B) n ≤ 20
C) n ≤ 30
D) n ≥ 30
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Sally has two pieces of fabric that are 128 inches long. She needs to cut each piece of fabric into multiple pieces that are 6 inches long. How many pieces will she have after she cuts both pieces of fabric?