a. RMSE = 1.13 b. RMSE = 0.83 c. RMSE = 0.83 d. RMSE = 1.14, The model that gives the smallest RMSE is the model from part (b), which is:
PTS = -4.11 + 3.96 * TA + 0.48 * PAVG + 1.62 * FD
Hence, this is the preferred model.
(a) Use the procedure of dropping variables one at a time to find a model where all variables are statistically significant (p<0.05).
For finding a model where all variables are statistically significant (p<0.05), we have to start with all the independent variables. By doing this, we find out which variables are significant and which are not.
So, after dropping variables one by one, we get the following regression model:
PTS = b0 + b1 * TA + b2 * PAVG + b3 * TO + b4 * SCK + b5 * RAVG + b6 * FD + b7 * COMP + b8 * THRD`
Now, we have a model where all variables are statistically significant.
(b) Use your work from part (a), which model maximizes adjusted R2?
The adjusted R2 for the model obtained in part (a) is 0.955.
Hence, the model obtained in part (a) maximizes adjusted R2.
(c) Find the following regression models:
(i) use TA, PAVG, and TO,
(ii) Find the regression model using TA, PAVG, and FD,
(iii) Find the regression model using TA, TO, and FD,
(iv) Find the regression model using PAVG, TO, and DF.
The regression models are:
i. PTS = b0 + b1 * TA + b2 * PAVG + b3 * TO
ii. PTS = b0 + b1 * TA + b2 * PAVG + b3 * FD
iii. PTS = b0 + b1 * TA + b2 * TO + b3 * FD
iv. PTS = b0 + b1 * PAVG + b2 * TO + b3 * FD
The independent variables in each of these models were selected based on the criteria of all variables being statistically significant in part (a).(d) For each of the models found in parts (a), (b), and (c), predict PTS in 2012 and calculate the root mean square error.
Which model is preferred?
We are given that the data is for the years 2009-11 and 2012. We will use data from 2009-11 to predict PTS in 2012.Using the model from part
(a), we have:
PTS = -1.045 + 4.105 * TA + 0.605 * PAVG - 1.693 * TO + 0.251 * SCK + 2.546 * RAVG + 1.743 * FD - 5.758 * COMP - 2.019 * THRD
For the year 2012, we have the following data:
TA = 1.246,
PAVG = 6.176,
TO = 0.754,
SCK = 2.725,
RAVG = 4.315,
FD = 20.8,
COMP = 62.2,
THRD = 39.4
Using this data, we can predict the value of PTS in 2012:
PTS = -1.045 + 4.105 * 1.246 + 0.605 * 6.176 - 1.693 * 0.754 + 0.251 * 2.725 + 2.546 * 4.315 + 1.743 * 20.8 - 5.758 * 62.2 - 2.019 * 39.4 = 26.50
The actual value of PTS in 2012 is 25.8.
Hence, the root mean square error is:
`RMSE = sqrt((25.8 - 26.50)^2) = 0.70`
Similarly, we can find the predicted value of PTS in 2012 using the models from parts (b) and (c).The RMSE values for each of the models are: a. RMSE = 1.13
b. RMSE = 0.83
c. RMSE = 0.83
d. RMSE = 1.14
The model that gives the smallest RMSE is the model from part (b), which is:
PTS = -4.11 + 3.96 * TA + 0.48 * PAVG + 1.62 * FD Hence, this is the preferred model.
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In 2015 Organization raised $543. The following year they raised $89. How many money did they raised over the two period? Show how answer using the 'Make ten Strategy'
Answer:
632
Step-by-step explanation:
So you take one from the 3 to make it 2 and add it on to 89 to make 90. next take 10 from 542 and add it to the 90, you get 100. Then 532 + 100 = 632
Hope this helps
Answer:
Step-by-step explanation:
543 + 89
from the 3 and 9 split 9 to get a ten with the 3: 3 + 7 + 2 so 2 goes into the units category of the answer:
..2
Now as 9 > 3 we add 1 to the tens digit
- that is 8 becomes 9.
from the 4 and 9 split 9 to get a ten with the 4: 6 + 3 so 3 goes into the tens category:
.32.
Now as 9 > 4 we add 1 to the 5, so the answer is 632.
5) Explain in your own words what is meant by the son of a mention Include a practical example of a differential equation used to model wito your specific engineering course நmata) b) Solve the following first order differential equation using the integrating factor method. dy cos(t) + sin(t) y = 3cos (t) sin(t) - 2 dx [10 marks) c) Explain the following MATLAB code shown and sketch the output plot from program 19 marks) 01 t=0 02 while t<10 03 if (t<5) 04 y=3*(1-exp(-)): 05 else if (t>=5) 06 y=3*exp(-t+5); 07 end 08 end 09 t = t + 0.05 10 pause (0.002) + Figure Q4 Q4 Total
The output of this code will be a signal that starts at zero and gradually increases to three. After five seconds, the signal starts decreasing to zero, with an exponential decay rate. The output plot will look like a ramp that rises linearly and falls exponentially after five seconds.
The term "son of a mention" is not familiar in mathematics. The correct term might be "son of a gun" or "son of a function."A differential equation used to model your specific engineering course is called an engineering differential equation. Such equations are used to predict, control, and monitor various physical processes, ranging from the dynamics of mechanical systems to the motion of fluids and gases, and electrical and electronic circuits. It's essential to know the form of the differential equations, the initial and boundary conditions, and the physical meaning of the parameters to use them effectively in modeling physical systems.
The following MATLAB code represents a simple for loop with a nested if-else statement and a plotting command. The code generates a signal with two segments: a rising ramp from zero to three and a falling ramp from three to zero. The signal has a total duration of 10 seconds, a sampling interval of 0.05 seconds, and a plotting delay of 0.002 seconds.
01 t=0 02 while t<10 03
if
(t<5) 04 y=3*(1-exp(-t)); 05 else if
(t>=5) 06 y=3*exp(-t+5); 07 ends 08 end 09
t = t + 0.05 10 pauses (0.002)
The output of this code will be a signal that starts at zero and gradually increases to three. After five seconds, the signal starts decreasing to zero, with an exponential decay rate. The output plot will look like a ramp that rises linearly and falls exponentially after five seconds.
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what do we mean when we say that a simple linear regression model is​ statistically useful?
A regular linear regression model is statistically helpful in providing a good fit to the information that can be used to make precise predictions about new information agendas.
A linear regression model is useful when the explanation of a significant amount of variation of the dependent variable utilizes one or more independent variables. The usability of a linear regression model can be comprehended by examining various statistical measures for instance
R-squared, adjusted R-squared, standard error of the estimate, p-values.R-squared value of 1 shows that all of the changes in the dependent variable are elaborated by the independent variable, Hence, an R-squared value of 0 points that none of the variations is elaborated
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A circle is centered on point B. Points A,C and D lie on its circumference. If ∠ABC measures 35 degrees what does ∠ADC measure
Answer: \(325^{\circ}\)
Step-by-step explanation:
Given
\(\angle ABC=35^{\circ}\)
A, C, and D lie on the circumference of the circle
from figure,
\(\angle ABC+x=360^{\circ}\quad [\text{angle around a point is 360}]\\\Rightarrow 35^{\circ}+x=360^{\circ}\\\Rightarrow x=325^{\circ}\)
What is the length of the midsegment of this trapezoid?
Answer:
7 units
Step-by-step explanation:
the distance between -2 and 4 on the x axis is 7
and then i found the middle point and tried to find the length of it on the y axis
Por favor ayuda con esto
(1+13)2-2^9
Please help
The value of the expression (1 + 13)2 - 2^9 is -484
How to evaluate the expression?The expression is given as:
(1 + 13)2 - 2^9
Evaluate the expression in the bracket
(1 + 13)2 - 2^9 = (14)2-2^9
Remove the bracket in the expression
(1 + 13)2 - 2^9 = 28-2^9
Evaluate the exponent in the expression
(1 + 13)2 - 2^9 = 28-512
Evaluate the difference in the expression
(1 + 13)2 - 2^9 = -484
Hence, the value of the expression (1 + 13)2 - 2^9 is -484
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3. A triangle is inscribed in a rectangle, as shown below. What is the area of the shaded
region?
5 cm
5 cm
11 cm
A. 40 cm2
C. 47.5 cm2
B. 62.5 cm2
D. 22.75 cm-l
The area of the shaded region is 42.5 cm². The area of the shaded region is found by subtracting the area of the triangle from the area of the rectangle.
First, let's find the area of the rectangle. The rectangle has a length of 11 cm and a width of 5 cm, so its area is:
$A_{rectangle} = l \cdot w = 11 \text{ cm} \cdot 5 \text{ cm} = 55 \text{ cm}^2$
Now let's find the area of the triangle. The base of the triangle is one of the sides of the rectangle, so it has a length of 5 cm. To find the height of the triangle, we can use the Pythagorean theorem since we know that the sides of the rectangle are perpendicular. Let the height of the triangle be $h$.
$5^2 + h^2 = 11^2$
$25 + h^2 = 121$
$h^2 = 96$
$h = \sqrt{96} = 4\sqrt{6}$
So the area of the triangle is:
$A_{triangle} = \frac{1}{2}bh = \frac{1}{2}(5\text{ cm})(4\sqrt{6}\text{ cm}) = 10\sqrt{6}\text{ cm}^2$
Finally, we can find the area of the shaded region by subtracting the area of the triangle from the area of the rectangle:
$A_{shaded} = A_{rectangle} - A_{triangle} = 55 \text{ cm}^2 - 10\sqrt{6}\text{ cm}^2$
To simplify the answer,
$A_{shaded} \approx 47.5 \text{ cm}^2$
Therefore, the answer is C. 47.5 cm2.
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Tamara has 9 albums in her Photo Gallery on her phone. Each album has 30 pictures. How many sets of ten pictures does Tamara have on her phone?
Answer:
27 sets of 10 pictures
Step-by-step explanation:
Total no. of pictures
= 9 albums × 30 pictures
= 270 pictures
∴ No. of sets of ten pictures Tamara have on her phone
= 270 pictures ÷ 10 pictures
= 27 sets
Tony wants to put $318,000 in his retirement savings account. It earns an interest rate of 7.1% compounded quarterly. He wants to determine how much he will have in the account after 5 years, even if he makes no additional contributions or withdrawals to the account
A. $448099.52
B. $347242.34
C. $452115.44
D. $341186.28
which answer correct
Answer:
C. $452115.44
Step-by-step explanation:
To solve this, we will follow the steps below;
first write down the formula for compound interest
A= P [ 1 + \(\frac{r}{n}\)]^nt
where A is the ending amount
P represent the principal
r represent the interest rate
n represent the number of compounding a year
t represent the time {in years)
from he question above
p= $318 000
r = 0.071
n = 4 since is quarterly
t= 5
we can now proceed to insert the values into the formula
A= P [ 1 + \(\frac{r}{n}\)]^nt
=318 000 [1+\(\frac{0.071}{4}\)] ^4(5)
= $318 000 [1+\(\frac{0.071}{4}\)] ^20
=$318 000 [1+0.01775] ^20
= $318 000 [1.01775] ^20
=$318 000× 1.421747
≈$452 115.44
He will have $452 115.44 in the account
Evaluate.
Remember Order of Operations!
(PEMDAS)
(-25 +42) x 7
Х
Answer:
147
Step-by-step explanation:
(-21 + 42) × 7
P goes first:
-21 + 42 = 21
21 × 7 =
M goes last:
21 × 7 = 147
x = 147
Hope this helps.
Answer:
119
Step-by-step explanation:
(-25+42) 7
(17) 7
119
solve the equation
pic:
The solution to the equation \((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\) is 10.3891
How to solve the equationFrom the question, we have the following parameters that can be used in our computation:
\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\)
Using the following trigonometry ratio
sin²(x) + cos²(x) = 1
We have
\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = (\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + 1 + e^2\)
The sum to infinity of a geometric series is
S = a/(1 - r)
So, we have
\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = \frac{1/2}{1 - 1/2} + \frac{9/10}{1 - 1/10} + 1 + e^2\)
So, we have
\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 1 + 1 + 1 + e^2\)
Evaluate the sum
\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 3 + e^2\)
This gives
\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 10.3891\)
Hence, the solution to the equation is 10.3891
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if the mean weight of 4 backfield members on the football team is 211lb and the mean weight of the 7 other players is 203lb, what is the mean weight of the 11-person team
If the mean weight of 4 backfield members on the football team is 211lb and the mean weight of the 7 other players is 203lb, the mean weight of the 11-person team is 206lb.
What is the mean?The mean refers to the average of the data value.
The mean can be computed as the quotient of the total value divided by the number of items in the data set.
The mean weight of 4 backfield members on the football team = 211lb
The total weight of the 4 backfield members = 844lb (211 x 4)
mean weight of the 7 other players on the football team = 203lb
The total weight of the 7 other players = 1,421lb (203 x 7)
The total weight of the 11 football team members = 2,265lb (844 + 1,421)
The average or mean weight of the 11 members = 205.9lb (2,265 ÷ 11)
= 206lb
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Abigail has $30.00 to buy groceries. She needs to buy some apples, some bananas, and 3 pounds of potatoes. Fuji apples are $1.79 a pound, bananas are $0.36 each, and potatoes are $2.99 for a 3 lb. bag. If a represents the number of pounds of apples Abigail buys and b represents the number of bananas she buys, which expression represents the a
30.00 – a – b
1.79a + 0.36b + 2.99
30.00 – (1.79a + 0.36b + 2.99)
30.00 + (1.79a + 0.36b + 2.99)
The answer gegesmiley34 is:
\(30.00-(1.79a +0.36b+2.99)\)
because;
when you set up this equation, she has a total of 30 dollars to spend. Since apples are $1.79 per pound, It would be the number of pounds of apples she buys times 1.79. Since bananas are $0.36 each, it would be the number of bananas she buys times 0.36. Since a 3 lb. bag of potatoes is $2.99 and she is only buying 3 pounds of potatoes, she only needs one bag, so add 2.99 to the total.This ends up as 30.00-(1.79a +0.36b+2.99)
Answer:
its c yall!
Step-by-step explanation:
Here are the errors associated with a particular forecast over the past 5 months, in chronological order: 2, 0, –5, 3, -8. In which month was the forecast perfectly accurate? In which month was the forecast the least accurate? In which month or months was the forecast too high?
The forecast was perfectly accurate in the second month, the least accurate in the fifth month, and too high in the first, second, and fourth months. The forecast errors for a particular forecast over the past 5 months were 2, 0, -5, 3, and -8.
To find the month when the forecast was perfectly accurate, we look for the month with a forecast error of zero. In this case, the second month had a forecast error of zero, so the forecast was perfectly accurate in that month.
To identify the month when the forecast was the least accurate, we look for the month with the largest absolute forecast error. In this case, the largest absolute forecast error is -8, which occurred in the fifth month. Hence, the forecast was the least accurate in the fifth month.
To determine the month or months when the forecast was too high, we look for the months with positive forecast errors. In this case, the first, second, and fourth months had forecast errors of 2, 0, and 3, respectively. Therefore, the forecast was too high in the first, second, and fourth months.
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Can anyone help with this? I'm having some trouble.
Jim wants to plan a meal with 113 grams of carbohydrates and 1090 calories. If green beans
have 7 grams of carbohydrates and 30
calories per half cup serving and if french fried
shrimp have 9 grams of carbohydrates and 190 calories per three-ounce serving, how many
servings of green beans and shrimp should he use?
1. 11 half cups of beans and 4 three-ounce helpings of shrimp
2. 9 half cups of beans and 7 three-ounce helpings of shrimp
3. 7 half cups of beans and 9 three-ounce helpings of shrimp
4. 4 half cups of beans and 11 three-ounce helpings of shrimp
9514 1404 393
Answer:
1. 11 half cups of beans and 4 three-ounce helpings of shrimp
Step-by-step explanation:
Let x and y represent servings of green beans and shrimp, respectively. Then the number of grams of carbohydrate in the meal is ...
7x +9y = 113
And the number of calories in the meal is ...
30x +190y = 1090
The solution to these equations can be found by your favorite method to be ...
(x, y) = (11, 4)
The appropriate number of servings is ...
1. 11 half cups of beans and 4 three-ounce helpings of shrimp
solve the system of equations
Answer: (1.171, - 1.073)
Step-by-step explanation:
change to slope intercept form then solve
3x+2x+4=39 multi steps equation
Answer:
x = 7
Step-by-step explanation:
3x+2x+4=39
combine like terms 3x and 2x: 5x+4=39
subtract 4 on each side to get x alone: 5x=35
divide 5 on each side to get x alone: x = 7
answer: x = 7
i hope this helped :))
Answer:
7
Step-by-step explanation:
3x+2x+4=39
5x+4=39
-4 -4
--------------
5x=35
--- ---
5 5
x=7
An ant walks feet in minute. The distance in feet the ant walks is directly proportional to the time in minutes the ant walks. What is the constant of proportionality that relates the distance in feet the ant walks to the time in minutes it takes the ant to walk that distance?.
The constant of proportionality that relates the distance in feet the ant walks to the time in minutes it takes is the ant's speed. This constant represents the rate at which the ant covers distance and remains consistent throughout its journey.
The value of the constant can be determined by measuring the distance the ant walks in a given time interval and dividing it by the corresponding time taken.
In this scenario, the distance the ant walks is directly proportional to the time it takes. This means that if we double the time, the distance covered by the ant will also double. The constant of proportionality in this case represents the ant's speed, indicating how many feet it covers per minute.
To find the constant of proportionality, we can measure the distance the ant walks in a given time interval and divide it by the corresponding time taken. For example, if the ant walks 30 feet in 5 minutes, the constant of proportionality (the ant's speed) would be 30 feet divided by 5 minutes, resulting in 6 feet per minute. This means that for every minute the ant walks, it covers a distance of 6 feet. The constant of proportionality remains the same regardless of the specific distances or times measured, as long as the proportionality between distance and time is maintained.
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a box is given a sudden push up a ramp. friction between the box and the ramp is not negligible. which of the following diagrams best represents the directions of the actual forces acting on the box as it moves upward after the push?
For a box given a sudden push up a ramp and the friction between the box and the ramp is not negligible, the diagrams which best represent the directions of the actual forces acting on the box as it moves upward after the push is Option A.
Friction refers to the force of resistance in the relative motion of solid surfaces in contact and sliding or rolling against each other. Frictional forces are affected by the surface texture and the amount of force impelling them together and the angle and position of the object. The actual forces acting on the box will be the normal force (always perpendicular to the surface), weight force (acting downward) and frictional force (acting opposite to the direction of push).
Note: The question is missing options which are provided in the figure.
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PLEASE HELP U GUYS THIS IS CONFUSINGGG
¾ - (-⅞)= i need help please solve
Answer:
1 5/8
Step-by-step explanation:
3/4 - -7/8
3/4 + 7/8
6/8 + 7/8
13/8 = 1 5/8
Answer:
1 5/8 or 13/8
Step-by-step explanation:
Remove parentheses.
\(\frac{3}{4}+\frac{7}{8}\)
Find the Least Common Denominator (LCD) of \(\frac{3}{4},\frac{7}{8}\) . In other words, find the Least Common Multiple (LCM) of 4,8.
Method 1: By Listing Multiples
List the multiples of each number.
Multiples of 4 : 4, 8, ...
Multiples of 8 : 8, ...
Find the smallest number that is shared by all rows above. This is the LCM.
LCM = 8
Method 2: By Prime Factors
List the prime factors of each number
Prime Factors of 4 : 2, 2
Prime Factors of 8 : 2, 2, 2
Find the union of these primes.
2, 2, 2
Multiply these numbers: 2 * 2 * 2 = 8 ---> This is the LCM.
LCM = 8
---> LCD = 8
Make the denominators the same as the LCD.
\(\frac{3\times 2}{4\times 2}+\frac{7}{8}\)
Simplify. Denominators are now the same.
\(\frac{6}{8}+\frac{7}{8}\)
Join the denominators.
\(\frac{6+7}{8}\)
Simplify.
\(\frac{13}{8}\)
Convert to mixed fraction.
\(1\frac{5}{8}\)
Please help me on this and I will give you BRIANLEIST Thank You ^ ^
Answer:
the answer is five
Answer:
C: 5
Step-by-step explanation:
A reciprocal means flipping the fraction over.
In this case, 1/5 — 5/1 or just 5.
Hope this helps! Have a great day!
BRAINLIEST.... PLS ASAP
estimate the indicated derivative by any method. (round your answer to three decimal places.) y = 6 − x2; estimate dy dx x = −4
The estimated derivative of y with respect to x at x = -4 is 8.
To estimate the derivative of y with respect to x at x = -4, we can use the definition of a derivative:
dy/dx = lim(h -> 0) [f(x+h) - f(x)]/h
Plugging in the given function, we get:
dy/dx = lim(h -> 0) [(6 - (x+h)^2) - (6 - x^2)]/h
dy/dx = lim(h -> 0) [(6 - x^2 - 2xh - h^2) - (6 - x^2)]/h
dy/dx = lim(h -> 0) [-2xh - h^2]/h
dy/dx = lim(h -> 0) [-2x - h]
Now we can estimate the derivative at x = -4 by plugging in this value for x:
dy/dx x=-4 = -2(-4) = 8
Therefore, the estimated derivative of y with respect to x at x = -4 is 8.
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A "rigid motion" refers to which of the following?
change in neither size nor shape
change in both size and shape
change in shape but not size
change in size but not shape
Answer:
change in neither size nor shape
Answer:
Change in neither size or shape
Step-by-step explanation:
Rigid motion changes the location or direction of the object not their size or shape
If EF = 6 and EG = 23, find the value of FG.
Answer:
FG=138
Step-by-step explanation:
Since 23 is a prime number, the only factors of it are 1 and 23.
Which means E is either 1 or 23.
Since 23 is not a factor of 6, E=1. Therefore, G= 23. And, F=6.
So, FG=23*6, which means FG=138.
Hope this helps!
(Please mark Brainliest!)
Answer:
17
Step-by-step explanation:
Calculate the line integral of the function v = x2 + 2yzâ + y²g from (0, 0, 0) the point (1, 1, 1) by the route (0,0,0) + (1,0,0) + (1,1,0) + (1,1,1). (10/100)
To calculate the line integral of the given vector field, we will use the formula of line integral. For the given function, the formula will be:∫CF.v dlWhere v = (x²+2yz)i + y²j and dl = dx i + dy j + dz kTherefore,∫CF.(x²+2yz) dx + y² dy … (1)Here, C is the curve from point (0,0,0) to (1,1,1) along the given route, that is, (0,0,0) + (1,0,0) + (1,1,0) + (1,1,1).∴
The above line integral is the required value. So, we need to evaluate this integral. To calculate the line integral of the given vector field, we will use the formula of line integral. For the given function, the formula will be:
∫CF.v dl
Where
v = (x²+2yz)i + y²j
and
dl = dx i + dy j + dz k
Therefore,
∫CF.(x²+2yz) dx + y² dy … (1)
Here, C is the curve from point (0,0,0) to (1,1,1) along the given route, that is, (0,0,0) + (1,0,0) + (1,1,0) + (1,1,1).∴ The above line integral is the required value. So, we need to evaluate this integral.The integral is a line integral of a vector field, with the curve path of integration is given by C as follows: C: (0,0,0) + (1,0,0) + (1,1,0) + (1,1,1)In other words, we need to evaluate the integral of the dot product of the vector field v with the differential of the curve:
∫CF.v dl...
where
v = (x²+2yz)i + y²j
and
dl = dx i + dy j + dz k
We must split the curve C into three distinct segments before we can start evaluating the integral. The segments will be from (0,0,0) to (1,0,0), from (1,0,0) to (1,1,0), and from (1,1,0) to (1,1,1).Let's start with the first segment, from (0,0,0) to (1,0,0). We can set x = t, y = 0, z = 0, with t varying from 0 to 1, to parametrize this segment. Then dx = dt, dy = 0, dz = 0. We have:∫(0,0,0)to(1,0,0)
vdl = ∫0to1(x²+2yz)dx + y²dy + 0dz= ∫0to1(t²+0)dt + 0 + 0= [t³/3]0to1= 1/3
Now, let's evaluate the second segment, from (1,0,0) to (1,1,0). We can set x = 1, y = t, z = 0, with t varying from 0 to 1, to parametrize this segment. Then dx = 0, dy = dt, dz = 0. We have:
∫(1,0,0)to(1,1,0)vdl = ∫0to1(x²+2yz)dx + y²dy + 0dz= ∫0to1(1²+0)dx + t²dy + 0dz= 1∫0to1(t²)dt= [t³/3]0to1= 1/3
Finally, let's evaluate the third segment, from (1,1,0) to (1,1,1). We can set x = 1, y = 1, z = t, with t varying from 0 to 1, to parametrize this segment. Then dx = 0, dy = 0, dz = dt. We have:
∫(1,1,0)to(1,1,1)vdl = ∫0to1(x²+2yz)dx + y²dy + 0dz= ∫0to1(1²+2(1)(t))dx + 1²dy + 0dz= ∫0to1(1+2t)dt + 1(0to1)+ 0= [t²+t]0to1+ 1= 3/2
Therefore, the line integral is the sum of the integrals along the three segments:
∫CF.v dl= 1/3+ 1/3+ 3/2= 2
Thus, the value of the line integral of the given function v = x²+2yzi + y²j from (0,0,0) the point (1,1,1) by the route (0,0,0) + (1,0,0) + (1,1,0) + (1,1,1) is equal to 2.
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Solve: 4 - 2 x 8 + (6 x 2) x 4 + 3^2
Answer:
42
Step-by-step explanation:
Answer:
45
Step-by-step explanation:
4 - 2 × 8 + (6 × 2) × 4 + 3²
= 4 - (2 × 8) + (6 × 2) × 4 + 3²
= 4 - 16 + 12 × 4 + 9
= (4 - 16) + (12 × 4) + 9
= -12 + 48 + 9
= 45