Evaluate the integral by making an appropriate change of variables. ∬r6sin(49x2+25y2) da, where r is the region in the first quadrant bounded by the ellipse 49x2+25y2=1.
The integral expression [tex]\int\limits \int\limits^{}_R {\sin(49x^2 + 25y^2)} \, dA[/tex] is given as a polynomial function
The result of the integral [tex]\int\limits \int\limits^{}_R {\sin(49x^2 + 25y^2)} \, dA[/tex] is [tex]\frac{\pi}{140}(1 - \cos(1))[/tex]
How to evaluate the integral?The integral expression is given as:
[tex]\int\limits \int\limits^{}_R {\sin(49x^2 + 25y^2)} \, dA[/tex]
To transform the ellipse in the form [tex]a^2x^2 + b^2y^2 = 1[/tex], we make use of the following equation
[tex]u = ax[/tex] and [tex]v = by[/tex]
So, we have:
[tex]\int\limits \int\limits^{}_R {\sin(49x^2 + 25y^2)} \, dxdy = \int\limits \int\limits^{}_R {\sin(u^2 + v^2)|J|} \, dudv[/tex]
Where:
[tex]u^2 = 49x^2[/tex] and [tex]v^2 = 25y^2[/tex]
This gives
[tex]u = 7x[/tex] and [tex]v = 5y[/tex]
And
[tex]J = \frac{x}{u} * \frac{y}{v}[/tex]
[tex]J = \frac{x}{7x} * \frac{y}{5y}[/tex]
Evaluate the product
[tex]J = \frac{1}{35}[/tex]
Substitute [tex]J = \frac{1}{35}[/tex] in [tex]\int\limits \int\limits^{}_R {\sin(49x^2 + 25y^2)} \, dxdy = \int\limits \int\limits^{}_R {\sin(u^2 + v^2)|J|} \, dudv[/tex]
So, we have:
[tex]\int\limits \int\limits^{}_R {\sin(49x^2 + 25y^2)} \, dxdy = \int\limits \int\limits^{}_R {\sin(u^2 + v^2)|\frac{1}{35}|} \, dudv[/tex]
This gives
[tex]\int\limits \int\limits^{}_R {\sin(49x^2 + 25y^2)} \, dxdy = \int\limits \int\limits^{}_R {\sin(u^2 + v^2)\frac{1}{35}} \, dudv[/tex]
Factor out 1/35
[tex]\int\limits \int\limits^{}_R {\sin(49x^2 + 25y^2)} \, dxdy =\frac{1}{35} \int\limits \int\limits^{}_R {\sin(u^2 + v^2)} \, dudv[/tex]
The equation is in the first quadrant.
So, we have:
[tex]\int\limits \int\limits^{}_R {\sin(49x^2 + 25y^2)} \, dxdy =\frac{1}{35} \int\limits^{\pi/2}_0 \int\limits^{1}_0 {\sin(r^2)} \, rdrd\theta[/tex]
Integrate
[tex]\int\limits \int\limits^{}_R {\sin(49x^2 + 25y^2)} \, dxdy =\frac{1}{35} * [\theta]|\limits^{\pi/2}_0 * [-\frac 12\cos(r^2)]|\limits^{1}_0[/tex]
Evaluate the product
[tex]\int\limits \int\limits^{}_R {\sin(49x^2 + 25y^2)} \, dxdy =-\frac{1}{70} * [\theta]|\limits^{\pi/2}_0 * [\cos(r^2)]|\limits^{1}_0[/tex]
Expand
[tex]\int\limits \int\limits^{}_R {\sin(49x^2 + 25y^2)} \, dxdy =-\frac{1}{70} * [\frac{\pi}{2} - 0] * [\cos(1) - \cos(0)][/tex]
Evaluate the difference
[tex]\int\limits \int\limits^{}_R {\sin(49x^2 + 25y^2)} \, dxdy =-\frac{1}{70} * [\frac{\pi}{2} ] * [\cos(1) - \cos(0)][/tex]
Evaluate cos(0)
[tex]\int\limits \int\limits^{}_R {\sin(49x^2 + 25y^2)} \, dxdy =-\frac{1}{70} * [\frac{\pi}{2} ] * [\cos(1) -1][/tex]
Evaluate the product
[tex]\int\limits \int\limits^{}_R {\sin(49x^2 + 25y^2)} \, dxdy =-\frac{\pi}{140}(\cos(1) -1)[/tex]
This gives
[tex]\int\limits \int\limits^{}_R {\sin(49x^2 + 25y^2)} \, dxdy =\frac{\pi}{140}(1 - \cos(1))[/tex]
Hence, when the integral is evaluated, the result is [tex]\frac{\pi}{140}(1 - \cos(1))[/tex]
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Emma earns a \$39{,}000$39,000dollar sign, 39, comma, 000 salary in the first year of her career. each year, she gets a 5\%5%5, percent raise.
Answer: Emma earns $554,064.80 in total in the first 11 years of her career
We are to determine the future value of $39,000 each year for 11 years given the growth rate of 5%
The formula for calculating future value:
FV = P (1 + r)^n
Explanation:
In the reaction n2 + 3h2 ⇌ 2nh3, an experiment finds equilibrium concentrations of [n2] = 0. 1 m, [h2] = 0. 05 m, and [nh3] = 0. 001 m. What is the equilibrium constant kc for this reaction?
A manufacturing company produces steel housings for electrical equipment. The main component part of the housing is a steel trough that is made out of a 14-gauge steel coil. It is produced using a 250-ton progressive punch press with a wipe-down operation that puts two 90-degree forms in the flat steel to make the trough. The distance from one side of the form to the other is critical because of weatherproofing in outdoor applications. The company requires that the width of the trough be between 8. 31 inches and 8. 61 inches. The file trough contains the widths of the troughs, in inches, for a sample of n = 49. What is the t-statistic calculated from the sampled data?
The t-statistics that will ba calculated from the data about the steel housing will be -5.936.
How to calculate t-statistic?From the information given, the component part of the housing is a steel trough that is made out of a 14-gauge steel coil.
From the complete question that has the data, the t-statistic will be calculated thus:
u = 8.46
x bar = 8.422
s = 0.04
n = 49
Therefore, the t-statistics will be:
= (8.421 - 8.46) / (0.046 / ✓49)
= -5.936
In conclusion, the t-statistics is -5.936.
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Which metaphor could replace the literal sentence ""simon’s year at school was sometimes hard and sometimes easy""? simon’s year at school was a struggle. simon’s year at school was a piece of cake. simon’s year at school was a mountain. simon’s year at school was a rollercoaster.
Answer:
D
Explanation:
Some Gey
The metaphor that could replace the literal sentence is "Simon’s year at school was a rollercoaster". Therefore, option D is correct.
What is a metaphor?A metaphor is a figure of speech in which a word or phrase is applied to an object or action to which it is not literally applicable. It is a comparison between two things that are not alike but share some common characteristic or quality.
A metaphor creates a mental image in the mind of the reader or listener by describing one thing in terms of another. For example, "life is a journey" is a common metaphor that describes the experience of living as if it were a journey through time and space, with its ups and downs, twists and turns, and unexpected detours.
Other examples of metaphors include "the world is a stage," "time is money," and "love is a rose." Metaphors are a powerful tool for writers and speakers, as they can convey complex ideas and emotions in a concise and memorable way. Hence, option D is correct.
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A car traveling at a speed of 24 m/s comes to a stop at a red light. How much time will it take for the car to stop if its acceleration is –8. 0 m/s2? 3 s 16 s 32 s 192 s
Answer:
3 s
Explanation:
final velocity x first velocity / -8.0m/s2
Using technology, determine the quarterly payment on a 3 year loan of $13,010 at 5.6% compounded quarterly. round you answer to the nearest cent. a. $1,183.23 c. $1,185.34 b. $1,517.95 d. $11,832.23
The joint probability distribution of the number x of cars and the number y of buses per signal cycle at a proposed left-turn lane is displayed in the accompanying joint probability table.
The joint probability distribution combines the probabilities of x and y
The probability that there is exactly one car and exactly one bus during a cycle is 0.020
How to determine the probability from the probability table?The complete question requests that the probability that there is exactly one car and exactly one bus during a cycle be calculated.
This means that, we check the table where the values of x and y are 1.
i.e.:
P(x,y) = P(1,1)
From the complete table, we have:
P(x,y) = P(1,1) = 0.020
Hence, the probability that there is exactly one car and exactly one bus during a cycle is 0.020
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What characteristics of the mice is an adaptation that increase their fitness
Answer:
camouflage
Explanation:
hope this helps
Which factors directly affect the climatic conditions of any particular area?
Answer:
The climate of any particular place is influenced by a host of interacting factors. These include latitude, elevation, nearby water, ocean currents, topography, vegetation, and prevailing winds.
Explanation:
How did participation in other reform movements help strengthen the women's movement? women's struggles in other groups made them want to have a group where they could be in charge. women's success in reform movements made them question the limitations placed on them in society. the success of other reform programs led to the transcendentalism movement. the experience gained working on reform programs made women qualified to create the women's rights movement.
Answer:
Women's success in reform movements made them question the limitations placed on them in society
• women’s success in reform movements made them question the limitations placed on them in society.
Explanation:I took the test
Define a function print_feet_inch_short(), with parameters num_feet and num_inches, that prints using ' and " shorthand. End with a newline. Remember that print() outputs a newline by default. Ex: print_feet_inch_short(5, 8) prints: 5' 8" hint: use \" to print a double quote
The function print_feet_inch_short(), with parameters num_feet and num_inches, that prints using ' and " shorthand. End with a newline is as follows:
def print_feet_inch_short(num_feet, num_inches):
print(str(num_feet) + " ' ", str(num_inches)+"\"")
print_feet_inch_short(5, 6)
Code explanation:The code is written in python.
We defined a function named "print_feet_inch_short". The function accept two argument namely "num_feet" and "num_inches".We print the string format of our argument with the required apostrophe. Then, we finally call the function with the required parameters.learn more on python here: https://brainly.com/question/24551910
Answer:
def print_feet_inch_short(num_feet, num_inches):
print(str(num_feet) + "'", str(num_inches)+"\"")
Explanation:
Are all news and information on the internet to why or why not
Answer:
Every news article is on the internet
Explanation:
Few people use news papers now and days and every single news article is shown either on TV or maybe just an online website. So yes I think every news article is on the internet
A load having the maximum level of current sustained for three hours or more is referred to as a ____ load
Find the real solution(s) of the equation (x+10)5=70. round your answer(s) to two decimal places.
Answer: x= 4
Distribute the five, subtract fifty from both sides, divide both sides by five.
The real solution(s) of the equation (x + 10) 5 = 70 is -7.6.
What is an equation?A real solution is one that contains all the necessary constituent particles in the right ratio and has undergone the necessary dissolution. A solution is therefore referred to as a genuine solution. In algebra, a real solution is just an answer to an equation that is a real number.
There are two real solutions for x if the discriminant's value is positive, which means that the graph of the solution has two distinct x-intercepts.
There is only one actual solution for x if the discriminant's value is zero, which means that the solution's graph only has one x-intercept.
The given equation is (x + 10) 5 = 70
[tex](x + 10) 5 = 70 \\x + 10 = \sqrt[5]{70} \\x + 10 = 2.34\\x + 10 = -7.6[/tex]
Therefore, the real solution(s) of the equation (x + 10) 5 = 70 is -7.6.
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Which sentences contain examples of bias? check all that apply. all spiders are creepy. most bats are nocturnal. every artist is fascinating. many flowers are poisonous. video games are all awesome.
The sentences which contain examples of bias include the following:
All spiders are creepy.Every artist is fascinating.Video games are all awesome.What is Bias?This is the tendency to lean in a certain direction, either in favor of or against a particular thing and usually reflects partiality or preference.
The sentences above depict bias as it's one-sided and not objective which is why they were chosen as the most appropriate choices.
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Answer:
A,C,E
Explanation:
Edge
Which word best describes a scientific hypothesis?
Answer:
"educated guess" is the correct answer
What are the domain and range of the function f(x) = 3x + 5? domain: ; range: domain: ; range: domain:; range: domain: ; range:
Answer:
b
Explanation:
look at domain and range
Ch4-ch4 interactions: do the ch4 molecules appear to attract each other much? briefly describe their interaction
The CH₄ molecules appear to attract each other because it's non-polar molecule.
What is a molecule?A molecule simply means a group of atoms which are bonded together by a chemical bond.
In this case, the CH₄ molecules appear to attract each other because it's a non-polar molecule. Two CH₄ molecules attract each other with the weakest force.
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The essence of many perfumes comes from the oils in the petals of fresh flowers, such as the rose, carnation, and orange blossom. However, fragrances are not limited to the petal, but can come from the leaves of lavender, peppermint, and geranium. Also, the oils of cinnamon and balsam are derived from bark, while the oils of cedar come from its wood. The fragrance of ginger and sassafras comes from roots, whereas that of orange, lemon, and nutmeg comes from fruits and seeds. Thus, there are many sources from which to derive fragrances for perfumes
The short outlines which highlights all the important points in the given passage are as follows;
The fragrance of quite a number of perfumes comes from the leaves of some plants.Additionally, these fragrances can be derived from bark, like the oils of cinnamon and balsam; or from wood, like the oils of cedar.The fragrance can also be derived from roots, like that of ginger and sassafras.And finally, fruits and seeds are so sources of fragrance, like in the case of orange, lemon, and nutmeg.What are Fragrances?A fragrance is defined as a combination of organic compounds that produces a distinct smell or odour and is characteristically used in a perfume.
Remarks; Read the paragraph below carefully and prepare a short outline that highlights all the important points in the passage.
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The location of the "dot" is _____. 60° s latitude/30° w longitude 30° e latitude/60° s longitude 30° w latitude/60° s longitude 60° s latitude/30° e longitude
Answer:
ITS D I JUST GOT IT RIGHT!!!!!!!!!!!
Explanation:
HOPE THIS HELPS!!!!!!!!!!!
Answer:
30° E latitude/60° S longitude
Explanation:
A student measures the mass and volume of a small cube made of an unknown metal. The mass of the cube is 25. 0 g, and the volume of the cube is 3. 19 cm3. The student is told that the cube is a sample of one of the four metals listed in the table
With the density found you can use the value to map out the corresponding metal from the table
Density of metal = 1.3157 g/cm^3
Mass, Volume and DensityGiven Data
Mass of cube = 25g
Volume of cube = 19 cm^3
With the given data we can find the density of the unknown sample
Density is expressed as = Mass/Volume
Density = 25/19
Density = 1.3157 g/cm^3
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How are bodies of water represented in dry zen gardens? (site 1)
Bodies of water are represented in Dry Zen Gardens by sand or gravel that are racked to depict or give an appearance of water.
What is a Dry Zen Garden?A Dry Zen Garden is a type of Japanese Garden built mainly to help with meditative practices.
It usually comprises:
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Which phrases from the passage are oxymorons? select 2 options. True love’s hand happy dagger good juliet lips are warm timeless end
The phrases from the passage which are oxymorons are;
Happy daggerTimeless endWhat is oxymoron?Oxymoron is a figure of speech which gives two words or two phrases that are contradictory in meanings to one another.
The phrases; Happy dagger and Timeless end are oxymorons because a dagger when used depict sadness or harmful, So, it can't be a happy dagger.
On the other hand, timeless end is not possible because a end is an endpoint and cannot be timeless at the same time.
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Answer:The answers are
Explanation: B, and E
What is the best response to the following question? ¿adónde vas? voy milla. Voy mapa. Voy esquina. Voy derecho
According to the context, the correct answer to the given question is "Voy derecho", which is linked to the absence of turns or detours.
Where are you going? - I'm going straight.Translation: Where are you going? - I'm going straight.What is a way?It is a route where cars circulate or a path to travel on foot that leads to a certain place.
When a person goes straight, it means that he is going to the place moving in one direction.
Therefore, we can conclude that according to the context, the correct answer to the given question is "Voy derecho ".
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Answer:
The answer to your question is
D. Voy derecho
Two hamsters work together and move a pile of sunflower seeds in 7 1/2 minutes
It would take the first hamster 20 minutes to do it alone and the second hamster 12 minutes to do it alone.
What is an equation?An equation is an expression that is used to show the relationship between two or more numbers and variables.
Let x represent the rate of the first hamster and y the rate of the second hamster. One hamster need 8 more minutes to do it alone, hence:
x = y + 8
The Two hamsters work together and move a pile of sunflower seeds in 7 1/2 minutes, hence:
(1/x + 1/y)7.5 = 1
(1/(y + 8) + 1/y)7.5 = 1
Hence:
y = 12
x = y + 8 = 12 + 8 = 20
It would take the first hamster 20 minutes to do it alone and the second hamster 12 minutes to do it alone.
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Helena needs 3. 5 cups of flour per loaf of bread and 2. 5 cups of flour per batch of muffins. She also needs 0. 75 cup of sugar per loaf of bread and 0. 75 cup of sugar per batch of muffins. Helena has 17 cups of flour and 4. 5 cups of sugar available for baking. Which combination of loaves of bread and batches of muffins could helena bake? 2 loaves of bread and 4 batches of muffins 3 loaves of bread and 3 batches of muffins 4 loaves of bread and 2 batches of muffins 5 loaves of bread and 1 batch of muffins
Answer:
2 loaves of bread and four batches of muffins
Ants can carry food at a speed of 1 cm/s. how long will it take the ant to carry a cookie crumb a distance of 50 m from the kitchen table to the ant hill? (express the answer three different ways; in seconds, minutes and hours)
Answer:
The total time taken by the ant to take cookie crumbs from the kitchen table to an anthill is 83.33 minutes.
Explanation:
Harry's school is selling t-shirts to raise money for the archery team. The school will receive 35% of the total sales which can be modeled by the equation y = 0. 35x, where x represents the total number of sales. What is the meaning of the x-intercept in the equation?
Answer:
I think x is the number of sales graphed
Explanation:
If this is wrong im terribly sorry
The use of phrases, fragments, and punctuation can affect the pace and mood of a text. how would you describe the pace of the following passage? "of my own thoughts it is folly to speak. swooning, i staggered to the opposite wall. for one instant the party upon the stairs remained motionless, through extremity of terror and of awe. in the next, a dozen stout arms were toiling at the wall. it fell bodily." slow fast both fast and slow average
The punctuations used in the sentences help us identify the mood of the text and the pacing of the passage can be described as fast.
What is the meaning of pacing an excerpt with punctuation?Punctuation pacing tells your reader whether to speed up or slow down whilst reading your content. It highlights the fact and provides clarity.
Many authors, however, fail to accurately punctuate their sentences correctly. These errors can have a significant impact on the readability as well as clarity of published contents.
In the given passage, the pace of the passage is described as being fast through the passage.
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Answer:
B is the correct answer ( Fast )
Explanation: