find the jacobian of the transformation x=u, y=2uv and sketch the region g: 1≤u≤2, 2≤2uv≤4, in the uv-plane.
Answers
To find the Jacobian of the transformation, we need to calculate the partial derivatives of x and y with respect to u and v:
∂x/∂u = 1
∂x/∂v = 0
∂y/∂u = 2v
∂y/∂v = 2u
So the Jacobian matrix is:
J = | ∂x/∂u ∂x/∂v |
| ∂y/∂u ∂y/∂v |
| 1 0 |
| 2v 2u |
And the Jacobian determinant is:
|J| = (1)(2u) - (0)(2v) = 2u
To sketch the region g, we need to find the values of u and v that satisfy the inequalities:
1 ≤ u ≤ 2
2 ≤ 2uv ≤ 4
Dividing both sides of the second inequality by 2v, we get:
1/v ≤ u ≤ 2/v
If we plot the lines u = 1/v and u = 2/v on the uv-plane, we see that they intersect at v = 1 and v = 2, as shown below:
| /
2/v | /
| /
| /
|/
--------------> u
/|
/ |
/ |
/ |
1/v |
Therefore, the region g is the trapezoidal region bounded by the lines u = 1/2, u = 1, u = 2, and the x-axis:
| /
| /|
| / |
| / |
----------------------> u
/|
/ |
/ |
/ |
Note that the sides of the trapezoid are the images of the lines v = 1/2 and v = 2 under the transformation x = u, y = 2uv.
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Related Questions
10.6 exponential growth and decay
1. y=7500(1+0.3)^x
2. y=(0.85)x
3. y=900(1.27)^x
Answers
If the price of a particular chocolate bar is increased by 40%, and it used to be $2, what is the new price after the increase?
Answers
Answer:
6$
Step-by-step explanation:
2+4=6
20%+40%=60%
The new price after the increase is $2.8 .
What is percent increase?Percentage increase is the difference between the final value and the initial value, expressed in the form of a percentage. In other words, it is the difference between the final value and the initial value which is divided by the initial value and then multiplied by 100.
According to the question
The price of chocolate bar = $2
The price of a particular chocolate bar is increased by 40%,
i.e
The percent increase in the price of chocolate bar = 40%
Now,
increase prize :
= \(2*\frac{40}{100}\)
= $0.8
The new price after the increase
= $2.8
Hence, the new price after the increase is $2.8 .
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Consider a sample with data values of 10,20,11,17, and 12 . Compute the mean and median. mean median ASWSBE14 3.E.002. Consider a sample with data values of 10,20,21,18,16 and 17 . Compute the mean and median. mean median [-/3 Points] ASWSBE14 3.E.006.MI. Consider a sample with data values of 51,54,71,58,65,56,51,69,56,68, and 51 . Compute the mean. (Round your answer to two decimal places.) Compute the median. Compute the mode.
Answers
The mean is the average value of a set of data. To calculate the mean, you add up all the data values and then divide the sum by the number of values in the set.
For the first sample with data values of 10, 20, 11, 17, and 12, the mean can be calculated as follows:
(10 + 20 + 11 + 17 + 12) / 5 = 70 / 5 = 14
So, the mean of this sample is 14.
The median is the middle value in a set of data when the data is arranged in order. If there is an even number of values, the median is the average of the two middle values.
For the first sample with data values of 10, 20, 11, 17, and 12, the median can be calculated as follows:
First, arrange the data in order: 10, 11, 12, 17, 20
Since there are 5 values, the middle value is the third value, which is 12.
So, the median of this sample is 12.
Now, let's move on to the second sample with data values of 10, 20, 21, 18, 16, and 17.
To calculate the mean:
(10 + 20 + 21 + 18 + 16 + 17) / 6 = 102 / 6 = 17
So, the mean of this sample is 17.
To calculate the median:
First, arrange the data in order: 10, 16, 17, 18, 20, 21
Since there are 6 values, the middle values are the third and fourth values, which are 17 and 18. To find the median, we take the average of these two values:
(17 + 18) / 2 = 35 / 2 = 17.5
So, the median of this sample is 17.5.
Lastly, let's consider the third sample with data values of 51, 54, 71, 58, 65, 56, 51, 69, 56, 68, and 51.
To calculate the mean:
(51 + 54 + 71 + 58 + 65 + 56 + 51 + 69 + 56 + 68 + 51) / 11 = 660 / 11 = 60
So, the mean of this sample is 60.
To calculate the median:
First, arrange the data in order: 51, 51, 51, 54, 56, 56, 58, 65, 68, 69, 71
Since there are 11 values, the middle value is the sixth value, which is 56.
So, the median of this sample is 56.
Please note that the mode refers to the value(s) that appear most frequently in a set of data. In the given questions, mode is not requested for the first and second samples. However, if you need to calculate the mode for the third sample, it would be 51, as it appears three times, which is more than any other value in the set.
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please help with my math
Answers
Answer:
f + g = \(\frac{x-1}{x+ 3}+\frac{x-3}{x+1}=\frac{x^{2}-1 }{(x+3)(x+1)}+\frac{x^{2}-9 }{(x+1)(x+3)}=\frac{2x^{2}-10 }{(x+1)(x+3)}\)
Step-by-step explanation:
how many ternary strings (digits 0, 1, or 2) are there with exactly 5 0s, 5 1s and 5 2s?
Answers
A ternary string is a string composed of characters 0, 1, and 2. The number of ternary strings that contain exactly n characters, each of which is one of three types, is 3^n.Exactly 5 0s, 5 1s, and 5 2s are required for the ternary string, which means that the total number of characters is 15.
Each of these characters can be one of three types (0, 1, or 2). As a result, the total number of possible strings is 3^15. This is equivalent to 14,348,907. We arrived at this conclusion by computing 3 to the fifteenth power.Explanation:When constructing a sequence of three symbols, the first symbol has three alternatives, the second symbol has three alternatives, and so on. There are n choices for each of the n characters, resulting in a total of 3^n possible sequences.Example 1:Let's assume we have to create 5-character sequences with three symbols: a, b, and c. There are 3*3*3*3*3 = 243 possible sequences since there are three choices for each symbol.Example 2:Let's assume we have to construct a 10-character sequence using three symbols: 0, 1, and 2. There are 3*3*3*3*3*3*3*3*3*3 = 59,049, a total of 59,049 possible 10-character sequences. We can perform the same calculation for 15-character strings using the same logic.
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need help pls
schoology]
![need help plsschoology]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/PtNJJjVAsppBTckBDEAlbnMvKbtMrU9h.png)
Answers
Answer:
31⁰
Step-by-step explanation:
\(a + 59 = 90\)
\(a + 59 - 59 = 90 - 59\)
\(a = 31\)
The graph of the function f(x)= -(x+3)(x-1) is shown below. What is true about the domain and range of the function?
The domain is all real numbers less than or equal to 4,
and the range is all real numbers such that -35xs1.
The domain is all real numbers such that -35xs1, and
the range is all real numbers less than or equal to 4.
O The domain is all real numbers, and the range is all real
numbers less than or equal to 4.
O The domain is all real numbers less than or equal to 4,
and the range is all real numbers.
Answers
Answer:
The domain is all real numbers, and the range is all real
numbers less than or equal to 4.
Step-by-step explanation:
The domain of a function f(x) is the set of all values for which the function is defined
We are given \(f(x)= -(x+3)(x-1)\)
f(x) is defined for all real values of x since there are no restrictions on the value of x
So,The domain of the function is all real numbers
Range of the function is the set of all values that f takes.
So, Range of given function is all real numbers less than or equal to 4.
Hence The domain is all real numbers, and the range is all real numbers less than or equal to 4.
How do you factor 3х2-8x?
Answers
Answer: 6-8x
Step-by-step explanation:
Assume an initial starting ft of 290 units, a trend (tt) of eight units, an alpha of 0.40, and a delta of 0.50. if actual demand turned out to be 278, calculate the forecast for the next period.
Answers
The forecast for the next period when the actual demand turned out to be 278 will be 294 units.
What is the forecast?The method of forecasting entails creating assumptions based on historical and current data. These might then be contrasted with what transpires.
Ft = 290, Tt = 8, α = 0.40, δ = 0.50, At = 278. Then the forecast for the next period will be
FITt = Ft + Tt
= 290 + 8
= 298 units
Ft + 1 = FITt + α(At − FITt)
= 298 + 0.40(278 − 298)
= 298 − 8
= 290 units
Tt + 1 = Tt + δ(Ft + 1 − FITt)
= 8 + 0.50(290 − 298)
= 8 − 4
= 4 units
FITt + 1 = Ft + 1 + Tt + 1
= 290 + 4
= 294 units
The forecast for the next period will be 294 units.
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pls help me on this k12 question.
Answers
Answer: The answer is A, 132 units
Step-by-step explanation:
how many groups of 5/6 are in 1
Answers
Answer:
1 1/5
Step-by-step explanation:
Want to multiply by the reciprocal to get 1.
5/6 times 6/5 is
5 times 6 in numerator which is 30
6 times 5 in denominator which is 30
So we get 30/30 which is 1.
Mark as best answer!
find slope of the line given (0,-2) and (-2, -8)
Answers
Answer:
\(3\)
Step-by-step explanation:
\(\mathrm{The\ slope\ of\ a\ line\ passing\ through\ the\ points\ (x_1,y_1)\ and\ (y_2,y_1)\ is\ given\ by:}\\\mathrm{Slope(m)=\frac{y_2-y_1}{x_2-x_1}}\\\\\mathrm{According\ to\ the\ question,}\\\mathrm{(x_1,y_1)=(0,-2)}\\\mathrm{(x_2,y_2)=(-2,-8)}\)
\(\mathrm{Therefore\ the\ slope=\frac{-8-(-2)}{-2-0}=\frac{-8+2}{-2}=3}\)
After heating up in a teapot, a cup of hot water is poured at a temperature of
20
8
∘
208
∘
F. The cup sits to cool in a room at a temperature of
6
8
∘
68
∘
F. Newton's Law of Cooling explains that the temperature of the cup of water will decrease proportionally to the difference between the temperature of the water and the temperature of the room, as given by the formula below:
T
=
T
a
+
(
T
0
−
T
a
)
e
−
k
t
T=T
a
+(T
0
−T
a
)e
−kt
T
a
=
T
a
= the temperature surrounding the object
T
0
=
T
0
= the initial temperature of the object
t
=
t= the time in minutes
T
=
T= the temperature of the object after
t
t minutes
k
=
k= decay constant
The cup of water reaches the temperature of
18
5
∘
185
∘
F after 3 minutes. Using this information, find the value of
k
k, to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the cup of water, to the nearest degree, after 4 minutes.
Enter only the final temperature into the input box.
Answers
Answer:
k ≈ 0.060T(4) ≈ 178 °FStep-by-step explanation:
The desired formula parameters for Newton's Law of Cooling can be found from the given data. Then the completed formula can be used to find the temperature at the specified time.
__
Given:\(T(t)=T_a+(T_0-T_a)e^{-kt}\\\\T_a=68,\ T_0=208,\ (t,T)=(3,185)\)
Find:k
T(4)
Solution:Filling in the given numbers, we have ...
185 = 68 +(208 -68)e^(-k·3)
117/140 = e^(-3k) . . . . . subtract 68, divide by 140
ln(117/140) = -3k . . . . . . take natural logarithms
k = ln(117/140)/-3 ≈ 0.060
__
The temperature after 4 minutes is about ...
T(4) = 68 +140e^(-0.060·4) ≈ 68 +140·0.787186
T(4) ≈ 178.205
After 4 minutes, the final temperature is about 178 °F.
Complete the square
x^2 - 2x - 14 = 0
Answers
To complete the square for the equation x^2 - 2x - 14 = 0, follow these steps:
1. Move the constant term to the right side of the equation: x^2 - 2x = 14
2. Take half of the coefficient of x, square it, and add it to both sides of the equation: x^2 - 2x + 1 = 15
3. Factor the left side of the equation as a perfect square: (x - 1)^2 = 15
4. Take the square root of both sides of the equation, remembering to include both the positive and negative square roots: x - 1 = ±√15
5. Add 1 to both sides of the equation to isolate x: x = 1 ± √15
Therefore, the solutions to the equation x^2 - 2x - 14 = 0 are x = 1 + √15 and x = 1 - √15.
what is the domain of the function f(x)=|x|
Answers
Answer:
All Real
Step-by-step explanation:
An jar contains 5 green marbles and 9 purple marbles. A marble is drawn and dropped back into the jar. Both marbles are green. If another marble is drawn, what is the probability that it will be green?
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the formula for Probability
\(Probability=\frac{number\text{ of required events}}{number\text{ of total possible outcomes}}\)STEP 2: Write the different outcomes
\(\begin{gathered} n(green)=5 \\ n(purple)=9 \\ n(Total)=5+9=14 \end{gathered}\)STEP 3: Find the probability that the third marble drawn is green
Since it can be seen from the question that the selection was done with replacement, this means that the sample space of 5 green marbles and 9 purple marbles are not affected. The probability of this outcome using the formula in step 1 will be given by:
\(\begin{gathered} P(green)=\frac{n(green)}{n(Total)} \\ \\ P(green)=\frac{5}{14} \end{gathered}\)The probability that it will be green is 5/14
WRITE THE EQUATION IN
SLOPE-INTERCEPT FORM
(1,-5) and (-2,-17)
Answers
Answer:
f(x) = 4x -9
Step-by-step explanation:
The slope-intercept form is f(x) = mx + b, where m is the slope and b is the y-intercept.
First, we need to find the slope, m.
= \(\frac{-5-(-17)}{1-(-2)}\)
= \(\frac{12}{3}\)
= \(4\)
m = 4, and now we plug it into the equation, using any given point, (1,-5) in this case.
f(x) = 4x + b
(-5) = 4(1) + b
-5 = 4 + b
b = -9
Now we find the equation: f(x) = 4x -9, and if we plug (-2,-17) in, we should get the same number as if we plug in (1,-5).
What is the probability that a student‘s favorite hobby is roller skating ?Theoretical =Experimental =
Answers
The theoretical probability is given by 1 over the number of hobbies.
If there is a total of 8 hobbies, the probability of a student having a specific hobby is:
\(P=\frac{1}{8}\)The experimental probability is given by the number of students with that hobby over the total number of students. If 3 students have the hobby roller skating among the 24 students surveyed, the probability is:
\(P=\frac{3}{24}=\frac{1}{8}\)Witch word is an antonym for the word leisurely
Answers
Answer:
barreling, bolting, breakneck, breathless, brisk, careering
Step-by-step explanation:
These are some words that are antonyms of the word "leisurely".
quick for i ready
Step-by-step explanation:
quick
Solving by Elimination
Answers
Answer:
unsolvable
Step-by-step explanation:
by elemination 14x+7y=-7 (1)
-14x-7y=7 (2)
x and y will be 0 then
– 8g–1+7g2+ – 2g+ – 10g+ – 3g2
Answers
-8g^(-1) + 7g^2 - 2g - 10g - 3g^2
Combining the like terms:
-8g^(-1) - 3g^2 - 12g
So, the simplified expression is:
-8g^(-1) - 3g^2 - 12g
Can a cylinder produce a cross section that has 4 straight sides?
Answers
Answer:
no
Step-by-step explanation:
No, a cylinder cannot produce a cross section that has 4 straight sides. A cylinder is a three-dimensional object that has a circular base and a curved surface that extends from the base to the top. Any cross section of a cylinder taken parallel to its base will produce a shape that is congruent to the base, which is a circle. Therefore, any cross section of a cylinder will be a circle or an ellipse, which do not have straight sides.
On the other hand, a prism is a three-dimensional object that has two congruent parallel bases and flat, rectangular or parallelogram-shaped sides that connect the bases. A prism can produce a cross section that has 4 straight sides, which would be a rectangle or a parallelogram.
David is making mixed candy bags for trick-or-treaters. He has 45 gummy bears and 18 jelly beans left. He wants to put the same number of both types of candy into every bag. What is the largest number of candy bags he can make?
Answers
Can someone help me with my math. Im a bit lazy to do it. Its due tomorrow.
Answers
Answer:
what type and grade level?
Approximately how much length must be added to a 25,000 mile long string that extends all the way around the earth's equator, to raise it one inch off the ground for its entire 25,000 mile length
Answers
To calculate the additional length needed to raise a 25,000-mile long string one inch off the ground for its entire length around the Earth's equator, we can use the formula for the circumference of a circle radius.
The circumference of a circle is given by the equation C = 2πr, where C is the circumference and r is the radius. In this case, the radius would be the distance from the center of the Earth to the string, which is the radius of the Earth plus one inch. The radius of the Earth is approximately 3,959 miles. Therefore, the radius for our calculation would be 3,959 miles + 1 inch (which can be converted to miles).
Using the circumference formula, C = 2πr, we can calculate the additional length needed:
C = 2 * 3.14 * 3,960 miles
C ≈ 24,867.6 miles
The approximately 24,867.6 miles must be added to the 25,000-mile-long string to raise it one inch off the ground for its entire length.
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You would need to add approximately 0.21 miles of length to the 25,000 mile long string to raise it one inch off the ground for its entire length.
To raise a 25,000 mile long string one inch off the ground for its entire length, you would need to add approximately 0.21 miles of length to the string. Here's how you can calculate this:
1. First, convert the length of the string from miles to inches. Since there are 5,280 feet in a mile and 12 inches in a foot, the total length of the string is
25,000 miles * 5,280 feet/mile * 12 inches/foot = 1,581,600,000 inches.
2. Next, calculate the additional length needed to raise the string one inch off the ground. Since the entire length of the string needs to be raised by one inch, you would need to add
1 inch * 25,000 miles = 25,000 inches of length.
3. Now, subtract the original length of the string from the additional length needed.
25,000 inches - 1,581,600,000 inches = -1,581,575,000 inches.
4. Finally, convert the negative value back to miles by dividing it by the conversion factor of
5,280 feet/mile * 12 inches/foot. -1,581,575,000 inches / (5,280 feet/mile * 12 inches/foot) ≈ -0.21 miles.
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Pita has 12 coins in her bag.
There are three £1 coins and nine 50p coins.
She takes 3 coins out of the bag at random.
What is the probability that she takes out exactly £2.50?
Answers
There are 3C2 = 3 ways to choose 2 of the £1 coins, and 9C1 = 9 ways to choose 1 of the 50p coins. The number of combinations that contain 2 of the £1 coins and 1 of the 50p coins is therefore 3 x 9 = 27.
The probability of taking out exactly £2.50 is therefore 27/220, which can be simplified to 3/22 or approximately 0.1364 (rounded to four decimal places).
Use the diagram to answer the question.
Which of the following statements are true based on the diagram?
Points B, C, and D lie in Plane N.
Points B, C, and D are on line n
Points B and D are on line n, but Point C is not.
Answers
Answer:
Points B, C, and D are on line n
Step-by-step explanation:
Answer:
лттьло. ьнеь е екбюедку к е. еккд
In a recent election, 63% of all registered voters participated in voting. In a survey of 275 retired voters, 162 participated in voting. Which is higher, the population proportion who participated or the sample proportion from this survey?
Answers
The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).
To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.
The population proportion who participated in voting is given as 63% of all registered voters.
This means that out of every 100 registered voters, 63 participated in voting.
In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.
Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .
Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).
Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.
It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.
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Which line shows non-proportional relationships?
Solve fast for 20 points brainliest
Answers
Answer:
Line A
Step-by-step explanation:
7. A company makes cylindrical cans for peaches. Each can has a radius of 4 centimeters and a height of 12 centimeters. The company plans to increase the volume each day by 25%.
A) What will the height of the new can be if the radius remains the same?
B) What will be the radius of the new can if the height remains the same?
Answers
A ) the new can will have a height of 15 centimeters.
The volume of the original can is V = πr²h = π(4cm)²(12cm) ≈ 602.88 cm³.
To increase the volume by 25%, we need to multiply the original volume by 1.25:
V_new = 1.25V = 1.25πr²h
Since the radius remains the same, we can simplify the equation to:
V_new = πr²h_new = 1.25πr²h
Dividing both sides by πr²
So the new height of the can will be 1.25 times the original height:
Therefore, the new can will have a height of 15 centimeters.
B) the new can will have a radius of approximately 5.03 centimeters if the height remains the same.
The volume of the original can is V = πr²h = π(4cm)²(12cm) ≈ 602.88 cm³.
To increase the volume by 25%, we need to multiply the original volume by 1.25:
V_new = 1.25V = 1.25πr²h
Since the height remains the same, we can simplify the equation to:
V_new = πr_new²h = 1.25πr²h
Dividing both sides by h, we get:
πr_new² = 1.25πr²
Simplifying the equation
Taking the square root of both sides
Substituting r = 4cm, we get:
r_new = 4cm√1.25 ≈ 5.03cm
Therefore, the new can will have a radius of approximately 5.03 centimeters if the height remains the same.