Evaluate the line integral, where c is the given curve. C xy4 ds, c is the right half of the circle x2 + y2 = 4 oriented counterclockwise.

Answers

Answer 1

Parameterize C by

x(t) = 2 cos(t)   ⇒   dx/dt = -2 sin(t)

y(t) = 2 sin(t)   ⇒   dy/dx = 2 cos(t)

with -π/2 ≤ t ≤ π/2. Then the line element is

ds = √((dx/dt)² + (dy/dt)²) dt = 2 dt

and the line integral is

[tex]\displaystyle \int_C xy^4 \, ds = \int_{-\frac\pi2}^{\frac\pi2} 2\cos(t) \cdot (2\sin(t))^4 \cdot (2 \, dt) = 64 \int_{-\frac\pi2}^{\frac\pi2} \cos(t) \sin^4(t) \, dt[/tex]

Substitute u = sin(t) and du = cos(t) dt. Then

[tex]\displaystyle \int_C xy^4 \, ds = 64 \int_{-1}^1 u^4 \, du = \frac{64}5 (1^5 - (-1)^5) = \boxed{\frac{128}5}[/tex]


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Flammable gases, patient lying in standing water, combustible liquids near the victim

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Tasha has mass 20 kg and wants to use a 4. 0-m board of mass 10 kg as a seesaw. Her friends are busy, so tasha seesaws by herself by putting the support at the system's center of gravity when she sits on one end of the board. How far is she from the support point?.

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Answer:

0.67 m

Explanation:

Mass of Tasha, m1 = 20 kg Mass of the board, m2 = 10 kg

0.67 m is correct for Tasha has mass 20 kg and wants to use a 4.0-m board of mass 10 kg as a seesaw. Her friends are busy, so Tasha seesaws by herself by putting the support at the system's center of gravity when she sits on one end of the board.

(Hope this helps can I pls have brainlist (crown)☺️)

do you think the earth is round or flat

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Choose the solution(s) of the following system of equations: x2 + y2 = 6 x2 – y = 6 no solution mr001-1. Jpg mr001-2. Jpg mr001-3. Jpg infinitely many solutions mr001-4. Jpg mr001-5. Jpg mr001-6. Jpg.

Answers

The solution to the system of equations are -1 and ±√5

Given the systems of equations;

[tex]x^2 + y^2 = 6\\ x^2 - y = 6[/tex]

From equation 2;

[tex]x^2 = 6 + y[/tex]..................................... 3

Substitute equation 3 into 1 to have:

[tex]6+y+y^2=6y^2+y=6-6\\y^2+y=0\\y^2=-y\\y = -1[/tex]

Substitute y = -1 into equation 3

[tex]x^2 = 6 + y\\x^2 = 6 + (-1)\\x^2 = 6 -1\\x^2=5\\x=\pm \sqrt{5}[/tex]

Hence the solution to the system of equations are -1 and ±√5

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Solve the inequality x + 3 < 7. Which number line represents the solution?.

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Answer:

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Answer:

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x+3<7 - subtract 3 from both sides

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Write an informative essay explaining what has caused the english spoken today to be different.

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Answer:

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Some of the main influences on the evolution of languages include:

The movement of people across countries and continents, for example migration and, in previous centuries, colonisation. For example, English speakers today would probably be comfortable using the Spanish word “loco” to describe someone who is “crazy”.
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New vocabulary required for inventions such as transport, domestic appliances and industrial equipment, or for sporting, entertainment, cultural and leisure reasons. For example, the original late 19th-century term “wireless” has become today’s “radio”.
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Answer: 200

Explanation: 90 + 50 = 140

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An angle measures 4. 3 radians. To the nearest degree, what is the measure of the angle? degrees.

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Im pretty sure this is it-

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So, let's look at 4.3/6.28, which turns out to be equal to 0.685; i.e., it is equal to 0.685 of a full circle of 360 degrees; i.e., it is equal to 246.6 degrees. Thus your angle lies in the third quadrant of the (x,y) plane.

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Answer:

4(x + y)

Explanation:

Have a nice day

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Answer:

B if your question is same as mine

Explanation:

the definition of ! ( factorial ) is

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6 = 6 × 5 × 4 × 3 × 2 × 1 = 720

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Which of the following is NOT a possible tax or deduction that could show up on your paycheck?

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I think the y intercepts would be -9 and -3

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O The FDIC has adopted regulations that incorporate IESBA independence rules.

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1) What is The Full form Of WWW ?
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2nd question is little confused .
plz Don't Spam .​

Answers

WWW is an abbreviation for World Wide Web ...

Corporation, Customer, Competitors (3C's) Model is a business model that focuses on the three key factors needed for success. This model was conceived by the famous business strategist, Kenichi Ohmae.

Answer:

• Full form of WWW :-

World Wide Web

WWW is an abbreviation for World Wide Web and it is commonly called the WEB. It is a system that is used to store documents and is accessed using URL(Uniform Resource Locator) which are accessible through Internet .

• The full form of 3 Cs :-

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(3C's) Model is a business model that focuses on the three key factors needed for success. This model was conceived by the famous business strategist, Kenichi Ohmae.

Explanation:

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Crane chose to present this account in a short story form. Which of the following is an aspect of "The Open Boat” that would be most difficult to convey in a painting depicting the same scene?

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Evaluate the surface integral. S y2 ds s is the part of the sphere x2 + y2 + z2 = 36 that lies inside the cylinder x2 + y2 = 9 and above the xy-plane.

Answers

Parameterize S in cylindrical coordinates by the vector function

r(u, v) = (x(u, v), y(u, v), z(u, v))

with

x(u, v) = u cos(v)

y(u, v) = u sin(v)

z(u, v) = 36 - u²

with 0 ≤ u ≤ 3 and 0 ≤ v ≤ 2π. Take the normal vector to S to be

[tex]\vec n = \dfrac{\partial r}{\partial u} \times \dfrac{\partial r}{\partial v} = (2u^2\cos(v),2u^2\sin(v),u)[/tex]

so that the surface element is

[tex]dS = \|\vec n\| \, du\,dv = u \sqrt{1+4u^2}\, du\, dv[/tex]

Then the surface integral is

[tex]\displaystyle \iint_S y^2\,ds = \int_0^{2\pi} \int_0^3 u\sqrt{1+4u^2} \, du\, dv[/tex]

[tex]\displaystyle \iint_S y^2\,ds = 2\pi \int_0^3 u\sqrt{1+4u^2} \, du[/tex]

[tex]\displaystyle \iint_S y^2\,ds = \frac{2\pi}8 \int_0^3 8u\sqrt{1+4u^2} \, du[/tex]

[tex]\displaystyle \iint_S y^2\,ds = \frac\pi4 \int_0^3 \sqrt{1+4u^2} \, d(1+4u^2)[/tex]

[tex]\displaystyle \iint_S y^2\,ds = \frac\pi4 \cdot \frac23(1+4u^2)^{\frac32} \bigg|_0^3 = \boxed{\frac\pi6 \left(37^{\frac32}-1\right)}[/tex]

A ratio estimates the risk associated with investing in a firm.

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A ratio which estimates the risk associated with investing in a business firm is called: solvency ratio.

Solvency ratio can be defined as a key metric that is typically used to measure the ability of a business firm to meet its long-term debt obligations.

Basically, a solvency ratio measures the financial position of a business firm and the extent to which its assets cover long-term debt obligations (commitments), especially for future payments and the liabilities.

In conclusion, a ratio which estimates the risk associated with investing in a business firm is called solvency ratio.

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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.

Answers

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 sender

Replacing 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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The square root of a number is between 8 and 9 which of these could be that number.

Answers

9

9 is a square root because when u multiply 3×3=9

My mom suggested keep the surroundings clean and green.

Answers

This is the correct sentence:

My mom suggested keeping the surroundings clean and green.

It's correct to say keeping and not keep because you have to form the sentence using suggest + the verb with ing (keep + ing: keeping).

I was able to find the instructions to complete the exercise online: Write sentences using suggest + V-ing or suggest + clause with should.

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A cell with 10 chromosomes undergoes mitosis.

Answers

Answer:

Yes every cell undergoes mitosis

Excessive smoking, substance abuse, and sleep disorders are all examples of ________ symptoms of stress.

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Excessive smoking, substance abuse, and sleep disorders are considered to be behavioral symptoms of stress.

It should be noted that behavior-related stress symptoms include absence and turnover, changes in productivity, changes in eating habits, increased consumption of alcohol, and smoking.

In a case where an individual who doesn't usually drink alcohol or smokes before starts drinking alcohol, it's known as behavioral symptoms of stress. In such a situation, stress leads to a change of behavior.

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Which of the following theorems cannot be used to prove two lines are parallel?.

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How are we supposed to answer this question without the theorems mentioned in the question????

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