Answer:
Its less than or equal to 17
Explanation:
Dark matter absorb light emit radiation and been observed directly.
Answer:
does not,
does not,
and has not
Explanation:
Dark matter doesn't absorb light, doesn't emit radiation and has not been observed directly.
What is dark matter?Dark matter can be defined as often invisible substances that are difficult to spot and observed because they don't absorb, emit or reflect light.
This ultimately implies that, dark matter doesn't affect human view because they do not interact or interfere with electromagnetic radiation.
However, humans can see through the (weakly interacting) dark matter but it has not been observed directly by scientists and astronmers.
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Use stokes' theorem to evaluate s curl f · ds. F(x, y, z) = x2 sin(z)i + y2j + xyk, s is the part of the paraboloid z = 4 − x2 − y2 that lies above the xy-plane, oriented upward.
Stokes' theorem says that the surface integral of the curl of the vector field F across the surface S is equal to the line integral of F along the boundary of S.
In this case, the boundary is a circle in the x,y-plane with radius 2. (To see this, set z = 0 and rearrange the equation for the paraboloid as x² + y² = 4.)
Then
[tex]\displaystyle \iint_S (\nabla\times\vec F)\cdot d\vec s = \int_{\partial S} \vec F \cdot d\vec r[/tex]
where
[tex]\vec r = 2\cos(t) \,\vec\imath + 2\sin(t) \,\vec\jmath[/tex]
parameterizes the circular boundary of S with 0 ≤ t ≤ 2π. Then
[tex]d\vec r = \dfrac{d\vec r}{dt}\,\dt = (-2\sin(t)\,\vec\imath + 2\cos(t)\,\vec\jmath)\,dt[/tex]
and the integral becomes
[tex]\displaystyle \iint_S (\nabla\times\vec F)\cdot d\vec s = \int_{\partial S} \vec F \cdot d\vec r[/tex]
[tex]\displaystyle \iint_S (\nabla\times\vec F)\cdot d\vec s = \int_0^{2\pi} \vec F(\vec r(t)) \cdot \frac{d\vec r}{dt}\,dt[/tex]
[tex]\displaystyle \iint_S (\nabla\times\vec F)\cdot d\vec s \\= \int_0^{2\pi} ((2\cos(t))^2 \sin(0)\,\vec\imath + (2\sin(t))^2\,\vec\jmath + (2\cos(t))(2\sin(t))\,\vec k) \cdot(-2\sin(t)\,\vec\imath + 2\cos(t)\,\vec\jmath)\,dt[/tex]
[tex]\displaystyle \iint_S (\nabla\times\vec F)\cdot d\vec s = \int_0^{2\pi} 8\sin^2(t)\cos(t) \, dt[/tex]
[tex]\displaystyle \iint_S (\nabla\times\vec F)\cdot d\vec s = \int_0^{2\pi} 8\sin^2(t) \, d(\sin(t))[/tex]
[tex]\displaystyle \iint_S (\nabla\times\vec F)\cdot d\vec s = \frac83 (\sin^3(2\pi)-\sin^3(0)) = \boxed{0}[/tex]
A bat emits a sound at a frequency of 3. 00 × 104 hz as it approaches a wall. The bat detects beats such that the frequency of the echo is 900 hz higher than the frequency the bat is emitting. The speed of sound in air is 340 m/s. The speed of the bat is closest to.
Taking into account the Doppler efect, the speed of the bat is closest to 5.02 [tex]\frac{m}{s}[/tex].
The Doppler effect is defined as the apparent frequency change of a wave produced by the relative movement of the source with respect to its observer. In other words, this effect is the change in the perceived frequency of any wave motion when the sender and receiver, or observer, move relative to each other.
The following expression is considered the general case of the Doppler effect:
[tex]f1=f\frac{v+-vR}{v+-vE}[/tex]
Where:
f1, f: Frequency perceived by the receiver and frequency emitted by the issuer respectively. Its unit of measurement in the International System (S.I.) is the hertz (Hz), which is the inverse unit of the second (1 Hz = 1 s⁻¹) v: Velocity of propagation of the wave in the medium. It is constant and depends on the characteristics of the medium. In this case, the speed of sound in air is considered to be 340 m/s vR, vE: Speed of the receiver and the sender respectively. Its unit of measure in the S.I. is the m/s ±, ∓: We will use the + sign:In the numerator if the receiver approaches the sender
In the denominator if the sender moves away from the receiver
We will use the sign -:In the numerator if the receiver moves away from the emitter
In the denominator if the sender approaches the receiver
In this case, a bat emits a sound at a frequency of 3.00×10⁴ Hz= 30,000 Hz as it approaches a wall.
The bat detects beats such that the frequency of the echo is 900 hz higher than the frequency the bat is emitting.
So, you know:
f1= 30,000 Hz + 900 Hz= 30,900 Hzf= 30,000 Hzv= 340 m/svE=vR= vbatReceiver approaches the senderReplacing in the expression is considered the general case of the Doppler effect:
[tex]30900 Hz=30000 Hz\frac{340 \frac{m}{s} +vbat}{340\frac{m}{s} -vbat}[/tex]
Solving:
[tex]\frac{30900 Hz}{30000 Hz} =\frac{340 \frac{m}{s} +vbat}{340\frac{m}{s} -vbat}[/tex]
[tex]1.03=\frac{340 \frac{m}{s} +vbat}{340\frac{m}{s} -vbat}[/tex]
1.03×( 340[tex]\frac{m}{s}[/tex] -vbat)= 340 [tex]\frac{m}{s}[/tex] + vbat
1.03×340[tex]\frac{m}{s}[/tex] - 1.03×vbat= 340 [tex]\frac{m}{s}[/tex] + vbat
350.2[tex]\frac{m}{s}[/tex] - 1.03×vbat= 340 [tex]\frac{m}{s}[/tex] + vbat
350.2[tex]\frac{m}{s}[/tex] - 340 [tex]\frac{m}{s}[/tex]= vbat + 1.03×vbat
10.2 [tex]\frac{m}{s}[/tex]= 2.03×vbat
10.2 [tex]\frac{m}{s}[/tex]÷ 2.03 = vbat
5.02 [tex]\frac{m}{s}[/tex]= vbat
In summary, the speed of the bat is closest to 5.02 [tex]\frac{m}{s}[/tex].
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brainly.com/question/17107808https://brainly.com/question/14929897A generic x by x grid has c blocks moved to create a (x-c) by (x+c) grid. Which of the following equations represents the difference of squares for this situation?.
The expression that represents the difference of squares for this situation is [tex]x^2-c^2[/tex]
Given the generic x by x grid has c blocks moved to create an (x-c) by (x+c) grid, to get the difference of two squares, we will take the product of the expressions as shown:
[tex]=(x-c)(x+c)\\=x^2+xc-xc-c^2\\=x^2 -0-c^2\\=x^2-c^2[/tex]
Hence the expression that represents the difference of squares for this situation is [tex]x^2-c^2[/tex]
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Which of the following people worked with government in the 1960s to get laws passed to help noncitizens and farm workers? Huey Newton Bobby Seale Stokely Carmichael Dolores Huerta.
Government often makes laws that aim for the betterment of its people. Cesar Chavez worked with government in the 1960s to get laws passed to help noncitizens and farm workers.
Cesar was known to be a man who use nonviolent means as used by Mahatma Gandhi and Martin Luther King Jr. in all his works.
He was known to be the founder of the National Farm Workers Association (later the United Farm Workers of America)
He won a lot of significant victories so as the pay and improve working conditions for farm workers is improve in the late 1960s and 1970s
See full question below
Which of the following people worked with government in the 1960s to get laws passed to help noncitizens and farm workers?
Huey Newton
Bobby Seale
Cesar Chavez
Dolores Huerta
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Answer:
Explanation:
Dolores huerta
How many grams of iron (density = 7. 87 g/ml ) would occupy the same volume as 96. 4 g of aluminum (density = 2. 70 g/ml)?.
Explanation:
density = mass / volume
96.4 g of aluminum / volume = 2.7
therefore,
96.4 = 2.7 × volume
volume = 96.4 / 2.7 = 35.7037037... ml
back to iron :
7.87 = mass / 35.7037037...
mass = 7.87 × 35.7037037... = 280.9881481... g
it would be 280.9881481... g of iron in the same volume.
A student runs 120 meters in 10 seconds. What is their speed?.
Answer:
12
Explanation:
speed=distance÷time
Which historical figure does old major most likely represent? tsar nicholas ii an imperial guard vladimir lenin joseph stalin.
Answer: old major is based on Karl Marx and partially Vladimir Lenin
Explanation:
The historical figure that old major most likely to represent is Vladimir Lenin. The correct option is C.
Who does old Major represent and why?The pig Snowball represents the intellectual revolutionary Leon Trotsky, while Old Major represents either Karl Marx or Vladimir Lenin.
Old Major represents Karl Marx and Vladimir Lenin, who promoted the Communist Party but died before their vision could be realized.
As a result, those who did not fully comprehend the dream were able to twist it to their advantage.
Old Major describes a dream he had the night before in which animals are free, happy, well fed, and treated with dignity in a world free of human tyranny.
He exhorts the animals to do everything possible to make this dream a reality, including overthrowing the humans who claim to be their owners.
Thus, the correct option is C.
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An entrepreneur is considering the purchase of a coin-operated laundry. The current owner claims that over the past 5 years, the mean daily revenue was $6750 with a population standard deviation of $265. A sample of randomly selected 30 days reveals a daily mean revenue of $6280. If you were to test the null hypothesis that the daily mean revenue was $6750, which test would you use?.
Based on the given value of sample size and the population standard deviation, the required test for the null hypothesis is the Z test of population mean.
The Z test of population is used to test the null hypothesis of a Normal distribution. Since, the sample size is large (>30) and the variance of the population is known, the most appropriate test of hypothesis to use is the Z test of population mean.Learn more : https://brainly.com/question/25576166
A cube with volume 8 $\text{cm}^3$ is cut in half by a plane which contains two edges of the cube. What is the area of the rectangle formed by the intersection of the plane and cube? express your answer in simplest radical form.
The area of the rectangle formed by the intersection of the plane and cube is [tex]4\sqrt{2}cm^2[/tex]
The diagram of the cube and the cutting plane is shown in the figure.
Since the cube has a volume of [tex]8cm^3[/tex], the sides are [tex]2cm[/tex] each.
From the diagram, the red rectangle is the rectangle formed from the intersection of the plane and the cube. It has an area given by
[tex]A_R=\text{side of cube}\times \text{diagonal}=2d[/tex]
and, using Pythagoras' theorem,
[tex]d=\sqrt{2^2+2^2}\\d=\sqrt{8}=2\sqrt{2}\text{ cm}[/tex]
Substituting the value of [tex]d[/tex] into the formula for [tex]A_R[/tex]
[tex]A_R=2\times d\\=2\times 2\sqrt{2}\\=4\sqrt{2}[/tex]
The area of the rectangle formed by the intersection of the plane and cube is [tex]4\sqrt{2}cm^2[/tex]
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Answer:
4 square root of 2cm
Explanation:
cool stuff
A 20~\mu f20 μf capacitor has previously charged up to contain a total charge of q = 100~\mu cq=100 μc on it. The capacitor is then discharged by connecting it directly across a 100-k\omega100−kω resistor. At what point in time after the resistor is connected will the capacitor have 13. 5~\mu c13. 5 μc of charge remaining on it?.
Answer:
10385877.377477km
Explanation:
kasi po i plas lang po
Consider the following line integral. C xy dx + x2y3 dy, c is counterclockwise around the triangle with vertices (0, 0), (1, 0), and (1, 4).
It looks like the integral is
[tex]\displaystyle \int_C xy \, dx + x^2y^3 \, dy[/tex]
Let's close the loop by adding a line integral over the line segment joining (1, 4) to (0, 0). Then the closed loop is the triangular region
T = {(x, y) : 0 ≤ x ≤ 1 and 0 ≤ y ≤ 4x}
Since the integrand has no singularities over or on the boundary of T, we have by Green's theorem
[tex]\displaystyle \int_C xy \, dx + x^2y^3 \, dy = \iint_T \left(\frac{\partial(x^2y^3)}{\partial x} - \frac{\partial(xy)}{\partial y}\right) \, dx \, dy = \int_0^1 \int_0^{4x} (2xy^3 - x) \, dy \, dx[/tex]
Compute the double integral:
[tex]\displaystyle \int_0^1 \int_0^{4x} (2xy^3 - x) \, dy \, dx = \int_0^1 \int_0^{4x} \left(128x^5 - 4x^2\right) \, dx = \frac{60}3[/tex]
From this result, we subtract the line integral over the extra line segment we added. Parameterize this path by
C' : {(1 - t, 4 - 4t) : 0 ≤ t ≤ 1}
The line integral over C' is
[tex]\displaystyle \int_{C'} xy \, dx + x^2y^3 \, dy = \int_0^1 (1-t)(4-4t)(-dt) + (1-t)^2(4-4t)^3(-4\,dt)[/tex]
[tex]\displaystyle \int_{C'} xy \, dx + x^2y^3 \, dy = \int_0^1 \left(256 t^5-1280 t^4+2560 t^3-2564 t^2+1288 t-260 \right) \, dt = -44[/tex]
so that the line integral over C alone is 60/3 - (-44) = 64.
Select the two recommendations that would decrease the margin of error of the interval.
From the options given, the only option which would result on having a reduced error margin, is to increase the sample size.
Recall :
Margin of Error = Zcritical × σ/√n
Increasing the mean would have no impact on the margin of error as it is not a part of the factors which affects the margin of error value. Increasing the standard deviation, which is the Numerator will result in an increased margin of error value. By raising the confidence level, the critical value of Z will increase, hence widening the margin of error. The sample size, n being the denominator, would reduce the value of error margin.Hence, only the sample size will cause a decrease in the margin of error of the interval.
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Write your own lyrics in english using the music/rhythm of your favorite song.
Do you ever wish your dreams could come true?
Dream of things that won't make you boo.
Dreams can come real,
just make sure you make them feel.
If it's a nightmare make sure you hide up the back stairs,
and if it's a good dream make sure you make it seen.
So I really wish dreams were real,
that way I could start to feel.
Explanation: Sorry it isn't that good I did the best I could. It's also rrrreeeealllllllyyyyy short sooo.......
Which of the following statements is true of postmodern cultural spaces.
How does the first amendment protect religious freedom for american citizens? choose exactly two answers that are correct.
Answer:
It lets people practice their faith in their own way and
It prevents the government from establishing a national religion.
Explanation:
Which of the following is a difference between phase i and phase ii of meiosis.
Answer: Phase I results in two diploid daughter cells and phase II results in four diploid daughter cells
Explanation:
i took the test
Inspectors for a hospital chain with multiple locations randomly select some of their locations for a cleanliness check of their operating rooms. The inspectors check every operating room in the hospitals that were chosen. What type of sample is this?.
Considering the situation described in the question, the type of sample Inspector used is called Simple Random Sampling
What is Simple Random Sampling?Simple Random Sampling is a random sampling technique in which participants are taken randomly from a given population.
How this situation is a Simple Random Sampling.Here, the given population is the hospital chain with multiple locations; since the inspector only randomly selects some of their locations, this is a simple random sampling.
Type of Random Sampling TechniquesSimple Random SamplingCluster Random SamplingSystematic Random SamplingStratified Random SamplingHence, in this case, it is concluded that the correct answer is Simple Random Sampling
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A cell with 10 chromosomes undergoes mitosis.
Answer:
Yes every cell undergoes mitosis
Based on the diagram, can point d be the centroid of triangle acf? explain. Yes, point d is the point of intersection of segments drawn from all three vertices. Yes, de is three-quarters of the length of the full segment. No, de should be longer than ad. No, the ratio between ad and de is 3:1.
Answer:
A is the correct answer
Explanation:
EDGE
A centroid in a triangle, is the point where all the medians meet.
now a peculiar thing about the centroid is that, it cuts all medians in a 2:1 ratio. So, if that's true, then the median AE, is being cut in two segments AD and DE and AD : DE are on a 2 : 1 ratio.
What is centroid?In a triangle, the centroid is the point of intersection of the three medians, which are line segments joining each vertex to the midpoint of the opposite side.
The centroid divides each median into two segments, with the distance from the centroid to the vertex being twice the distance from the centroid to the midpoint of the opposite side.
Let M be the midpoint of side AB, N be the midpoint of side AC, and P be the midpoint of side BC. Then, we have:
CD = 2DP
CE = 2DN
We are also given that DE = 15. Since D is the centroid, we have:
AD = BD = CD/3
AE = CE/3
DC + DP = PC
CE + DN = NE
AD + AE = DE
Using these relationships, we can find CD and CE:
CD = 2DP = 2(PC - DC) = 2((AD + DP) - (AD/3)) = 2(2AD/3) = 4AD/3
CE = 2DN = 2(NE - CE) = 2((AE + DN) - (AE/3)) = 2(2AE/3) = 4AE/3
To find AD and AE, we can use the fact that AD + AE = DE and AD = BD:
AD + BD = DE
AD + (2AD/3) = 15
5AD/3 = 15
AD = 9
AE = DE - AD = 15 - 9 = 6
Substituting these values into the equations for CD and CE, we get:
CD = 4AD/3 = 4(9)/3 = 12
CE = 4AE/3 = 4(6)/3 = 8
Therefore, CD = 12 and CE = 8.
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A gardener bought 5 rabbits.
...
Thats really nice
What is the entropy change for the freezing process of 1 mole of liquid methanol at its freezing temperature (–97. 6˚c) and 1 atm? please report your answer two points past the decimal with the unit j/molk. ∆h˚fus = 3. 17 kj/mol.
Answer:
the value of change in entropy for freezing process of 1 mole of liquid methanol is -18.07 J/mol.k
Explanation:
Entropy is defined as the measure of possible arrangement of the atoms or molecules. Entropy change for the the freezing process mole of 1 liquid methanol at -97.6 degree celcius and 1 atm will be -18.07 J/mol.
The entropy change can be calculated by the given formula:
Thus, the value of change in entropy for freezing process of 1 mole of liquid methanol is -18.07 J/mol.k
(Hope this helps can I pls have brainlist (crown)☺️)
For the freezing of 1 mole of liquid methanol, the change in entropy value is -18.07 J/mol.
What is entropy value?The measure of atoms' or molecules' potential arrangements is known as entropy. Entropy change for one mole of liquid methanol frozen at -97.6 degrees Celsius and one atmosphere is -18.07 J/mol.
The range of entropy is 0 to 1. Depending on the number of classes in your dataset, entropy can be greater than 1, but it still indicates a very high level of chaos. For the sake of convenience, the examples in this blog will have entropy values between 0 and 1.
The "information" a variable contains is measured by its entropy. Now, based on the surprise that this value of the bholds and the number of distinct values that are present in the variable, this amount is approximated.
Thus, it is -18.07 J/mol.
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If there is more than one speaker, how should they be all noted?.
Answer:
By their names. If the names are not known you should mark them as speaker 1, speaker 2, speaker 3, etc.
Explanation:
Given three consecutive integers, if the sum of the first and third integers is increased by 8, the result is 5 less than triple the second integer. Find the three consecutive integers. *
Answer:
The three consecutive integers are 12, 13 & 14
Explanation:
Let the three consecutive integers be x, x + 1, x + 2
According to the question,
If sum of the first and third integers is increased by 8, the result is 5 less than triple the second integer.
[tex] \therefore [/tex] x + x + 2 + 8 = (x + 1) × 3 - 5
2x + 10 = 3x + 3 - 5
2x + 10 = 3x - 2
10 + 2 = 3x - 2x
x = 12
So, The three consecutive integers are 12, 13 & 14
What is the equation for g, which is f(x) = 2x2 + 3x − 1 reflected across the y-axis?.
The answer to your question is:
What is an example of new technology having a positive impact on sustainability brainly.
Examples of sustainable technology include:
Electric transportation. LED light technology. Solar power.Sustainable technology is a form of technology that have a positive social, economic or environmental impact. Sustainable technologies are innovations with positive impacts with the aim of reducing the negative impact humanity have created on earth.
Examples of sustainable technology include:
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What amount of heat, in kj, would be involved in condensing 15. 8 g of ch₃oh? (∆hvap = 38. 0 kj/mol).
Considering the definition of enthalpy of vaporization, the amount of heat that would be involved in condensing 15.8 g of CH₃OH is 18.8 kJ.
When a material changes phase from solid to liquid, or from liquid to gas, a certain amount of energy is involved in this phase change.
In case of phase change from liquid to gas, this amount of energy is known as enthalpy of vaporization (symbolized as ∆Hvap).
So, the enthalpy of vaporization is the amount of energy required to change a unit of mass (for example, moles or kg) of a substance from phase liquid to phase gas at constant temperature and pressure.
In this case, you know that enthalpy of vaporization is ∆Hvap = 38.0 kJ/mol.
On the other side, you want to vaporize 15.8 g of CH₃OH. Then, being the molar mass of the compound 32 [tex]\frac{g}{mole}[/tex] (that is, the amount of mass contained in one mole), the number of moles to be vaporized is:
[tex]15.8 gramsx\frac{1 mole}{32 grams} =0.49375 moles[/tex]
Then, the amount of heat that would be involved in condensing 15.8 g of CH₃OH is calculated taking into account the enthalpy of vaporization by:
0.49375 moles× 38.0 [tex]\frac{kJ}{mol}[/tex]= 18.76 kJ ≅ 18.8 kJ
Finally, the amount of heat that would be involved in condensing 15.8 g of CH₃OH is 18.8 kJ.
Learn more:
brainly.com/question/21655944?referrer=searchResults brainly.com/question/7580155?referrer=searchResults brainly.com/question/4035699?referrer=searchResults brainly.com/question/11475740 brainly.com/question/2212655?referrer=searchResultsIn casabianca the boy's defining character trait is his (points 5).
The character trait that defines the boy in Casabianca is: his loyalty.
Casabianca is the name of the young boy who is one of the major character sin "Casabianca".
In Casabianca, the boy, out of loyalty and having a strong sense of duty, had to put up bravery to remain at his post on a French ship that caught fire during the attack of the British.
In spite of the obvious dangers, he remained at his post while waiting for orders from the captain (his dad).
Therefore, the character trait that defines the boy in Casabianca is: his loyalty.
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How did fossils help and teach scientists about the history of the earth brainly.
Answer:
Fossils helped teach scientist by giving information of the species that lived back then.
Explanation:
The fossils have clues on them help identify what they are.
Evaluate the line integral, where c is the given curve. C (x/y) ds, c: x = t3, y = t4, 1 ≤ t ≤ 4.
We have
x = t³ ===> dx/dt = 3t²
y = t⁴ ===> dy/dt = 4t³
Then with the given parameteriztion, the line integral along C of x/y is
[tex]\displaystyle \int_C \frac xy \, ds = \int_1^4 \frac{t^3}{t^4} \sqrt{(3t^2)^2 + (4t^3)^2} \, dt[/tex]
[tex]\displaystyle \int_C \frac xy \, ds = \int_1^4 \frac1t \sqrt{9t^4 + 16t^6} \, dt[/tex]
[tex]\displaystyle \int_C \frac xy \, ds = \int_1^4 \frac{\sqrt{t^4}}t \sqrt{9 + 16t^2} \, dt[/tex]
[tex]\displaystyle \int_C \frac xy \, ds = \int_1^4 \frac{t^2}t \sqrt{9 + 16t^2} \, dt[/tex]
[tex]\displaystyle \int_C \frac xy \, ds = \int_1^4 t \sqrt{9 + 16t^2} \, dt[/tex]
[tex]\displaystyle \int_C \frac xy \, ds = \frac1{32} \int_1^4 32t \sqrt{9 + 16t^2} \, dt[/tex]
[tex]\displaystyle \int_C \frac xy \, ds = \frac1{32} \int_1^4 \sqrt{9 + 16t^2} \, d\left(9+16t^2\right)[/tex]
[tex]\displaystyle \int_C \frac xy \, ds = \frac1{32} \cdot \frac23 \left(9+16t^2\right)^{\frac32}\bigg|_1^4[/tex]
[tex]\displaystyle \int_C \frac xy \, ds = \frac1{48} \left(265^{\frac32} - 25^{\frac32}\right) = \boxed{\frac{265\sqrt{265}-125}{48}}[/tex]
The line integral will be "[tex]\frac{265\sqrt{265} - 125 }{48}[/tex]". To understand the calculation, check below.
Line integralAccording to the question,
Curves, x = t³ or,
[tex]\frac{dx}{dt}[/tex] = 3t²
y = t⁴ or,
[tex]\frac{dx}{dt}[/tex] = 4t³
Now, the line integral along C will be:
→ [tex]\int\limits_C {\frac{x}{y} } \, ds[/tex] = [tex]\int\limits^4_1 {\frac{t^3}{t^4} }[/tex] √(3t²)² + (4t³)² dt
= [tex]\int\limits^4_1 {\frac{1}{t} }[/tex] √9t⁴ + 16t⁶ dt
= [tex]\int\limits^4_1 {\frac{t^4}{t} }[/tex] √9 + 16t² dt
= [tex]\int\limits^4_1 {\frac{t^2}{t} }[/tex] √9 + 16t² dt
= [tex]\int\limits^4_1[/tex] t√9 + 16t² dt
= [tex]\frac{1}{32}[/tex] [tex]\int\limits^4_1[/tex] √9 + 16t² d (9 + 16t²)
= [tex]\frac{1}{32}\times \frac{2}{3}[/tex] [tex](9+16t^2)^{\frac{3}{2} } |_1^4[/tex]
= [tex]\frac{1}{48}[/tex] ([tex]265^{\frac{3}{2}} - 25^{\frac{3}{2}[/tex])
= [tex]\frac{265 \sqrt{265 } -125 }{48}[/tex]
Thus the above approach is correct.
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