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  • Q1: . Sketch and find the area of the region that lies inside both curves. r^{2}=\sin (2 \theta) \text { and } r^{2}=\cos (2 \theta)See Answer
  • Q2: For a certain incompressible, two-dimensional flow field the velocity component in the y direction is given by the equation v=9 x y-x^{2} y Determine the velocity component in the x direction so that the volumetric dilatation rate is zero. Denote the x-independent constant as f(y).See Answer
  • Q3: A two-dimensional, Incompressible flow is given by u = - y and v = x. Show that the streamline passing through the point x = 10 and y = 0 is a circle centered at the origin. x^2 + y^2 =_________. exact number, no toleranceSee Answer
  • Q4:3. (a) Sketch and fully describe the surface Sph given, in terms of Cartesian coordinates (x, y, z), by Sph = {(x, y, z) : (x − xo)² + (y − yo)² + (z − zo)² = a²}, where a, xo, yo and zo are constants, and show that it can be parameterized by r(0,0) = (xo + a sin cos , yo + a sin sind, zo + a cos 0), giving the ranges of the parameters and p. (b) For the surface Sph, defined in part (a), show that a vector surface element is given by ds = a sin 0 [r - (To, yo, 2o)] dedo, and justify the sign convention associated with this normal vector. Hence evaluate the flux ƒ= $₁₂ Sph G.dS of the vector field G = (1,0, z²) out of the surface. (c) Using your answer to part (b), evaluate L = lima-03f/(4πa³). (d) State the (coordinate-invariant) integral form of the definition of divergence. By referring to your answer to part (c), demonstrate that it is consistent with the Cartesian definition of divergence in this case. (e) By applying the Divergence Theorem to the vector field u = ow, where is an arbitrary differentiable scalar field and w is a constant vector, derive the identity JI føds, where the closed surface S is the boundary of the volume V. VodV=See Answer
  • Q5:B = 5.0 53° A = 10.0 30° ter D 37° C = 12.0 60° D = 20.0 ILL 10 30⁰ F = 20.0 Given the vectors in the preceding figure, find vector R that solves equations (a) D + R = F and (b) C-2D + 5R = 3F. Assume the +x-axis is horizontal to the right.See Answer
  • Q6:Problem 1. Prove the Cauchy-Schwartz Inequality for any pair of vectors ū, v: |uv|≤|| . Hint: Recall some basic properties of the sine and cosine functions.See Answer
  • Q7:Problem 2. Let e be a fixed vector in R². Describe in geometric terms the set of vectors p such that ||pc|| = 1. Then, do the same, but for a fixed vector in R³. Hint: The quantity ||p-c=1 will represent a simple shape you are familiar with.See Answer
  • Q8:Problem 3. Determine the value(s) of a such that = ai + (a − 1)3 + 3ak is a unit vector.See Answer
  • Q9:2 Problem 4. Earth is at the origin (0,0), the moon is at (384,0), and a spaceship is at (280,90) (where distance is in thousands of kilometers). (a) What is the displacement vector of the moon relative to Earth? Of the spaceship relative to Earth? Of the spaceship relative to the moon? (b) How far is the spaceship from the earth? From the moon? (c) The gravitational force on the spaceship from the earth is 461 newtons, and from the moon is 26 newtons. What is the net gravitational force on the spaceship?See Answer
  • Q10:Problem 5. What values of a make u = aî + 2) + (5 − a)Ê perpendicular to w = 3î + ak?See Answer
  • Q11:PROBLEM SET 02: Vector Algebra OPEN 7. B-5.0 53° مرة A = 10.0 D 30 C = 12.0 D - 20.0 37" 60° с 30⁰ F = 20.0 Cookies help us deliver our services. By using our services, you agree to our use of cookies. OK Learn more Tumed in automatically when dur ENG 485See Answer
  • Q12:edfinity ← Absolute Mad Lads Raspux 00 PROBLEM SET 02 Vector Algeb x edfinity.com/assessments/64f0be977b5064003c118446 M PH 221-2A. General Physics 1 (Fall 2023) Home ? Help Center Sewind) 69°F Mostly cloudy PROBLEM SET 02: Vector Algebra OPEN 2. Practice similar. |F= 0- Submit answer Answers (in progress) A sledge is being pulled by two horses on a flat terrain. The net force on the sledge can be expressed in the Cartesian coordinate system as vector F = (-2960i +8455j) N, where i, j denote directions to the east and north, respectively. Find the magnitude and direction of the pull. Answer Enter magnitude of the vector along with direction (angle measured in degrees from the positive z-axis in a counter-clockwise direction) Help on how to format answers: units ITEMS Q Search Q I INFO degrees. Cookies help us deliver our services. By using our services, you agree to our use of cookies. D Score -/0.13 WOO Tured in automatically when due Learn more < Previous Next > ENG 11:45 PM 9/2/2021See Answer
  • Q13:Absolute Mad Lads-Rasput X 00 PROBLEM SET 02 Vector Age X edfinity.com/assessments/6410be97765014003118446 edfinity ← PH 221-2A. General Physics 1 (Fall 2023) Home ? Help Center 2 3 10 Sent: 0/4 69°F Mostly cloudy PROBLEM SET 02: Vector Algebra OPEN 3. Practice similar DD=7km D y+A+B+C+D=0 C=3.02 km 19. 10= ? 7.5⁰ A = 4.70 km Orientation: A B 16⁰° W Q Search N B = 2.48 km E ITEMS A farmer wants to fence off his four-sided plot of flar land. He measures the first three sides, shown as A, B and C in the above image, and then correctly calculates the length and orientation of the fourth side D. What is his result? Length: DL 9 INFO km Cookies help us deliver our services. By using our services, you agree to our use of cookies. degrees West of South OK O Turned in automatically when due Learn more < Previous Next > ENG de 11:46 PM 9/2/2021See Answer
  • Q14:Absolute Mad Lads-Rasput X edfinity ← PH 221-2A. General Physics 1 (Fall 2023) Home ? Help Center See M/4 co PROBLEM SET 02 Vector Algeb x PROBLEM SET 02: Vector Algebra OPEN Practice similar ITEMS INFO A particle undergoes three consecutive displacements given by vectors. All units are in mm: Ď₁=2i-1j+0k Ď₂=7i+7j-7k Ďs=-1i+7j-5k Help on how to format answers: units (a) Find the resultant displacement vector of the particle (in terms of i, j, k): mm. (b) What is the magnitude of the resultant displacement? (Include the units in your answer) Submit answer (c) How far did the particle actually travel (ie what is the sum of the magnitudes of the individual displacements)? (Include the units in your answer) Answers (in progress) Cookies help us deliver our services. By using our services, you agree to our use of cookies. OK Learn more " 09 Tumed in automatically when due 3 < Previous Next > ENG - ! 11:46PMSee Answer
  • Q15:← Absolute Mad Lads - X 00 PROBLEM SET 02 Vector Algeb X + edfinity #edlinity.com/assessments/6-4f0be977b5064003c118446 PH 221-2A General Physics 1 (Fall 2023) Home ? Help Center Rene (4) 69°F Mostly cloudy PROBLEM SET 02: Vector Algebra OPEN 5. Practice similar a= b= If Ď= (0i-4j), B=(76+45) and A = (36+05), find the unknown constants a and b such that aD + bB + Ả=ő. Submit answer Answers (in progress) Answer ITEMS Q Search .1 INFO D 0 O Score Dannet tarhnical icense Email inetni Cookies help us deliver our services. By using our services, you agree to our use of cookies. -/0.25 -/0.25 0/0.5 OK Learn more Turned in automatically when due ENG < Previous Next xt > Show desktop 11:47 PM 9/2/2003See Answer
  • Q16:edfinity + PH 221-2A General Physics Home ? Help Center PROBLEM SET 02: Vector Algebra OPEN 6. (b) Displacement D=2-7j. Unit vector: Find the unit vector of direction (in terms of i, j) for the following vector quantities: (a) Force P-5+4j. Unit vector: I (c) Velocity=-41+7j. Unit vector: Submit answer Answers (in progress) Answer ITEMS 1 INFO D 0 Score Cookies help us deliver our services. By using our services, you agree to our use of cookies. -/0.17 Learn more ENG < Previous Next > 11:47 PM CSee Answer
  • Q17:edfinity ← Home ? Help Center 1 ¢ edfinity.com/assessments/6410be97765014003188446 PH 221-2A. General Physics 1 (Fall 2023) Sonte (0/41 PROBLEM SET 02: Vector Algebra OPEN 7. Practice similar Magnitude: Direction (north of east): components. (c) Reflect and convince yourself of how to use the method of components to solve this problem. (d) What are the magnitude and direction of the displacement needed to get the ball into the hole on the first putt? Submit answer ITEMS 4. m INFO A golfer takes three putts to get the ball into the hole. The first putt displaces the ball 3.6 m exactly north. The second pur displaces the ball 2.2 m exactly southeast (i.e., 45 degrees south of east), and the third 0.8 m exactly southwest (i.e., 45 degrees south of west). What are the magnitude and direction of the displacement needed to get the ball into the hole on the first putt? (State direction as angle north of east). Suggested strategy: (a) Sketch the displacement vectors in such a way that you understand the big picture of what is happening. (b) Define a system of coordinates (i.e., the x and y axes) and redraw the displacement vectors so that it is easy to visualize their degrees Cookies help us deliver our services. By using our services, you agree to our use of cookies. OK Leam more *O! Turned in automatically when due ENG < Previous Next > 11:47 PM 9/2/2003See Answer
  • Q18:edfinity PH 221-2A. General Physics 1 (Fall 2023) Home ? Help Center M 10 Sonte mm/a 69°F Mostly cloudy PROBLEM SET 02: Vector Algebra OPEN 4. 5.0 53 A = 10.0 30 Search C-120 D-20.0 37 60 30 F-200 Cookies help us deliver our services. By using our services, you agree to our use of cookies. S Learn more Turned in automatically when due ENG 48 11:47 PM 1/2/2021 CSee Answer
  • Q19:Absolute Mad Lads - Raspux 00 PROBLEM SET 02: Vector Algeb x ←0 edfinity.com/assessments/6410be977b501400318446 edfinity ← PH 221-2A. General Physics 1 (Fall 2023) Home ? Help Center 13 10 Sensi 5 PROBLEM SET 02: Vector Algebra OPEN (b) 20-3D + 4R-6F R= Assuming the positive z-axis is horizontal and points to the right, find a vector R which solves the following equations (in terms of i, j). Use at least four decimal places when entering your answers. (a) 6Ď+4Ř= 5.F Ř= Submit answer Answers (in progress) de Answer 2 Cookies help us deliver our services. By using our services, you agree to our use of cookies. Score -/0.5 OK ㅁㅁㅁ I arn more Tumed in automatically when due ING 11:47 PM 9/2/2003See Answer
  • Q20:S.P. 2-F If A = cospâ, find the average value of A within a unit sphere centered at the origin.See Answer

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