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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Students in ms. King's science class are researching the history of the cell theory and will write a blog to show what they have learned. Which of the following is the best choice for the introductory sentence?
Answer:
My name is....... then you say topic of yhe blog
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
If δdef and δmno are two triangles such that de ≅mn and ef ≅ no, which of the following would be sufficient to prove the triangles are congruent?
The information that would be sufficient to prove that both triangles are congruent by the SAS congruence theorem is: ∠E ≅ ∠N.
What is the Side-angle-side Congruence Theorem (SAS)?When two sides and one included angle in a triangle is congruent to two corresponding sides and an included angle in another triangle, both triangles are congruent to each other by the SAS congruence theorem.
Thus:
ΔDEF and ΔMNO have:
Two pairs of congruent sides: DE ≅ MN and EF ≅ NO.
Therefore, the information that would be sufficient to prove that both triangles are congruent by the SAS congruence theorem is: ∠E ≅ ∠N.
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The owner of a bookstore buys used books from customers for $1. 50 each. The owner then resells the used books for 400% of the amount he paid for them
Answer:
6.00
Explanation:
Harmony is currently producing 100 units of a necessary component part by incurring p60,000 in direct materials, p12,500 in direct labor, p22,500 in variable overhead, and p15,000 in fixed overhead. Harmony can purchase the component externally for p95,000 and only p2,500 of fixed manufacturing costs cannot be avoided (the rest are avoidable). How much savings will harmony realize in buying instead of making the component?
By taking the difference between the two costs, we conclude that buying instead of making the component, she saves $12,500
How much will she save?If she makes the components, the cost is:
$60,000 + $12,500 + $22,500 + $15,000 = $110,000
On the other hand, if she buys the components, the cost will be:
$95,000 + $2,500 = $97,500
To find how much did she saves, we need to find the difference between the two costs. That is just:
$110,000 - $97,500 = $12,500
This means that by buying instead of making the component, she saves $12,500
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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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Tomé un taxi para ir al cine. Antes, me puse los lentes. 1 of 1
The correct sentence, using the Pluperfect Tense in Spanish is:
Hubiera tomado un taxi para ir al cine. Antes, me hubiera puesto los lentes.Pluperfect Tense in SpanishThis verb tense is used to mention events that occurred in a certain period of time in the past, it is used with the main verb in past participle, that is, ending in -ado or -ido, as well as the verb "haber" with the following conjugations:
Yo: hubieraTú: hubierasUsted: hubieraÉl: hubieraElla: hubieraEllo: hubieraNosotros / Nosotras: hubiéramosUstedes: hubieranEllos / Ellas: hubieranTo identify the appropriate conjugation in each sentence, you must identify the noun in the sentence, replace it with the appropriate personal pronoun, and finally use the corresponding conjugation with the help of the guide above.
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In the context of the passage, "coarse" (sentence 1) is best interpreted as
In the context of the passage, "coarse" is best interpreted as crude.
Fetters and headsmen.In the passage, it was stated by the author that tyranny formerly employed Fetters and headsmen and they were described as coarse instruments; however, their current civilization has perfected despotism itself, though it seemed to have nothing to learn.
Based on the excerpt, the author's use of the word "coarse" is best interpreted as crude because they were unrefined in their thinking and manner approach to work. Thus, they didn't learn anything new with respect to the civilization of their time.
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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
You want to measure the height of an antenna on the top of a 125 foot building
In a 125-ft tall building, if you measure the angle of elevation to the top of the building to be 68° and the angle of elevation to the top of the antenna to be 71°, the height of the antenna is 21.7 ft.
What is the tangent of an angle?In trigonometry, the tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.
Step 1: Calculate the distance to the builiding (x).We will use the tangent of 68°, being the height of the building (h1 = 125 ft) the opposite side.
tan 68° = 125 ft / x
x = 50.5 ft
Step 2: Calculate the height of the building and the antenna (h2).We will use the tangent of 71°, being the distance to the building (x = 50.5 ft) the adjacent side.
tan 71° = h2 / 50.5 ft
h2 = 146.7 ft
Step 3: Calculate the height of the antenna.h2 - h1 = 146.7 ft - 125 ft = 21.7 ft
In a 125-ft tall building, if you measure the angle of elevation to the top of the building to be 68° and the angle of elevation to the top of the antenna to be 71°, the height of the antenna is 21.7 ft.
The complete question is:
You want to measure the height of an antenna on the top of a 125 foot building. From a point in front of the building, you measure the angle of elevation to the top of the building to be 68° and the angle of elevation to the top of the antenna to be 71°. How tall is the antenna, to the nearest tenth of a foot?
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For people applying for 9th grade, do they have to take the ISEE with the SSAT. Or just the SSAT
Answer:
Typically, schools with grades 9-12 will prefer the SSAT
Explanation:
the choice of tests is often decided by schools' admissions policies
Hope it helps!!!brainliest pls!!!Answer:
schools with grades 9-12 will prefer the SSAT
Explanation:
Find the exact value of \cos acosa in simplest radical form
cosA = 1/2
cos Φ = adjacent over hypotenuse
cosA = 14/16
cosA = 7/8
[tex] hope \: its \: helpful \: to \: you[/tex]
In the final sentence of the passage, the divinity-student's "mild short cough" highlights a tension between
In the final sentence of the passage, the divinity-student's "mild short cough" highlights a tension between his tormented thoughts and his subdued physical reaction.
What is the divinity-student's about?
The Divinity Student is known to be a famous book that was written by Michael Cisco.
The book is known to be very brief but powerful, as it is said to be a neo-gothic novel that was depicted by Harry O. Morris who was said to have used present tense to make the reader have a kind of hallucinatory journey from humanity to spiritual transcendence.
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One container has 28 kilograms of flour and another has 4 kilograms. How many kilograms of flour must be taken from one container and transferred to the other so each of the containers has equal amount of flour?
Answer:
12 kilograms have to be taken from the first one to the second one
Why grade 12 learners should write their nbts as early as possible
Answer: help to interpret your NSC results and can be used by universities in different ways. so these are two reasond.
Explanation:
Gracias por llamar. Talking visiting taking calling
Answer:
CALLING
Explanation:
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:
According to the graph, which of the following occupations has the highest employment level? cashiers registered nurses waiters and waitresses customer service representatives
According to the Occupations with the Highest Employment Levels, May 2013 graph, the highest employment level is the Cashier.
What is the employment level?The employment level can be defined as the number of persons engaged in productive operations and activity in an economy. This notion applies to both employees and self-employed people.
The two most common employment measurements are:
The number of people employed andEmployees number
From the graph, the Employment level is calculated as follows:
[tex]\mathbf{= \dfrac{employed \ people }{total \ labor \ force } \times 100\%}[/tex]
We realize that the Cashier has the highest employment level, since it has the peak number in the graph.
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Answer:
Cashier
Explanation:
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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What is the the total area under the standard normal distribution curve?
Answer:
1.
Explanation:
Simply 1.
Answer:
The total area under the standard normal curve is 1
What is the impact of piercy beginning the poem, "barbie doll" with details about the girlchild being born and presented with dolls and other "girly" toys?
The impact of Piercy beginning the poem, "Barbie Doll" with the given information is that; It causes the reader to visualize the girlchild growing up with the things that all little girls play with.
What is the impact of Imagery?Imagery is the use of figurative language that aids the reader in properly visualizing what the writer is trying to communicate.
Now, in the given poem, Piercy used Imagery to communicate the kind of playthings that the girlchild grew up playing with. Thus, we can conclude that the impact of piercy at the beginning is that It causes the reader to visualize the girlchild growing up with the things that all little girls play with.
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Green light has a frequency of about 6. 00×1014s−1. What is the energy of a photon of green light?
Answer:
If you mean 6.00 x 10^14 s^-1 then your answer is 3.98^-19 Joules
Explanation:
use this equation Ephoton=hν
where h=6.626×10^−34J⋅s Planck's constant and ν = frequency
so Ephoton=(6.626×10^−34J⋅s )(6.00 x 10^14 s^-1 )
the reciprocal seconds and seconds cancel each other out , multiply teh remaining and use joules as your unit
A stop sign in the shape of a regular octagon is inscribed in a circle. find each measure
The measure of arc NPQ is 180° while the measure of m<AOB is 69°.
How many sides does the shape of an octagon have?An octagon is known to be a type of polygon that is said to have up to 8 sides.
It is often consist of eight angles. The term Octagon connotes the addition of Octa + gon. The octa signifies eight and gon implies sides.
When you look at the image, you will see that NPQ is 180° while the measure of m<AOB is 69°.
See full question below
A stop sign in the shape of a regular octagon is inscribed in a circle.
What is the measure of arc NPQ?
M
A. 45°
B. 90°
C. 135°
D. 180°
2. In the figure at the right points A, B, C are on 00, and m<ACB = 690
What is the m<AOB?
A. 69°
B. 138°
C. 2780
D. 360°
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Javier works each weekend at an animal shelter where he earns $8 an hour. He is saving his earnings to go on a ski trip that costs $190
Answer:
24 hours
Explanation:
(im gonna assume you mean how many hours will he need to work)
he will need to work 24 hours because
8 x 24 = 192
Two sustainable ways in which businesses could assist school leavers
Answer:
businesses could provide internships for them or prep them for getting a job in the real world.
Explanation:
mr clean
One beaker contains pure water and the other beaker contains pure methanol at the same temperature. Which liquid has the higher surface tension and viscosity?
The water has a higher viscosity and surface tension compared to the methanol.
What is Surface Tension?Surface tension can be defined as the force that acts on the surface of a liquid to give it am elastic skin that is stretched.
Thus, because of the strong intermolecular hydrogen bonding in water and it's high melting and boiling point than methanol, the surface tension and viscosity of water is higher than that of methanol.
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The pulley in the figure (figure 1) has radius r and a moment of inertia i. The rope does not slip over the pulley, and the pulley spins on a frictionless axle. The coefficient of kinetic friction between block a and the tabletop is μk. The system is released from rest, and block b descends. Block a has mass ma and block b has mass mb
The speed of block B in terms of the distance (d) it has descended is [tex]V=\frac{2gd(m_B-\mu_k m_A)}{m_A \;+\; m_B \;+\;\frac{I}{r^2}}[/tex]
How to determine the speed.In order to determine the speed of block B in terms of the distance (d) it has descended, we would apply the work-energy theorem as follows:
[tex]Work=\Delta KE=KE_f-KE_i[/tex]
The work done due to gravity is given by:
[tex]W_g=(m_B)gd[/tex]
The work done due to friction is given by:
[tex]W_f=-\mu_k (m_A)gd[/tex]
The angular velocity of pulley is given by:
[tex]\omega = \frac{V}{r}[/tex]
Applying the work-energy theorem, we have:
[tex]W_g+W_f= KE_f-KE_i\\\\(m_B)gd-\mu_k (m_A)gd=\frac{1}{2} m_A V^2+\frac{1}{2} m_B V^2+\frac{1}{2} I\omega^2-0\\\\gd(m_B-\mu_k m_A)=m_A V^2+ m_B V^2+\frac{1}{2} I(\frac{V}{r} )^2\\\\2gd(m_B-\mu_k m_A)=(m_A + m_B +\frac{I}{r^2} )V\\\\V=\frac{2gd(m_B-\mu_k m_A)}{m_A \;+\; m_B \;+\;\frac{I}{r^2}}[/tex]
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A car travels 20. Meters east in 1. 0 second. The displacement of the car at the end of this 1. 0-second interval is
Answer:
Displacement is the word we use for the distance covered so in this case when a car travels 20 meters east in 1 second, at the end of that 1-second interval a car travels a distance of 20 meters.
And the distance covered is the displacement, so it means that displacement of the car after 1 second is 20 meters east.
What does number 8 wire mean to New Zealanders?
Answer:
Accordingly, the term "number 8 wire" came to represent the ingenuity and resourcefulness of New Zealanders, and the phrase "a number 8 wire mentality" evolved to denote an ability to create or repair machinery using whatever scrap materials are available on hand.
Explanation:
What is the moral dilemma affecting brutus in this passage? he is blaming himself for cassius’s death. he is trying to decide whether, upon his victory, he should kill antony or let him live. he has to choose between honoring his friend’s death and winning a battle. he has to choose between giving cassius’s position to labio and giving it to flavio.
Answer:
c. He has to choose between honoring his friend’s death and winning a battle.
Explanation:
trust me
Based on this passage, the moral dilemma affecting brutus is that: C. he has to choose between honoring his friend’s death and winning a battle.
What is an inference?In English literature, an inference is a strategic process through which a reader deduce the meaning and message that is associated with a passage or sentence (statement) in a literary work, especially through induction.
Based on the excerpt, we can infer and draw a logical conclusion that the the moral dilemma affecting brutus is that he has to choose between honoring his friend’s death and winning a battle.
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