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Q: Q4) Find the deviva tives of the follocoing (9) y = ( In xe) %3D (b) Sec ( ²+1 %3D

A: Part A -  We can observe that the power in the expression on the right-hand side contains the…

Q: Find the convolution between x(t) = 2 rect and h(t) =rect() %3D

A:

Q: Let C C R? be the path from (3, –2) to (3, 2) along the graph of the curve x – 5x?y? – 7x2 = 0.…

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Q: What is the MRS of U(x, y) = x4y4? Calculate MRS where good x is on the x-axis. O a. MRS = y/3x O b.…

A: If you like the solution then please give it a thumbs up... The Answer is :   MRS = y/3x So, Option…

Q: Use the chain rule to find where First the pieces: End result (in terms of just t): = 历 内 z = x²y +…

A: Here given that                       z=x2y+xy2,  x=3-t3,  y=3-t6 We have to find dzdt by using…

Q: Consider the path r(t) = (4t,2t 2 ,2lnt) defined for t > 0. Find the length of the curve between the…

A: Given the path r(t) = (4t, 2t2, 2ln t), t>0. Find the length of the curve (4, 2, 0) and (20, 50,…

Q: Find the oades and degsee ot e"y" - 3(y) + 22y =xeX and waite tie diffes ential equation in nosmal…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Q6. Given M = {(x, y), 1 < a² + y² < 4} c R². (a) Determine dM and aM. (b) Is M connected? Pathwise…

A: On the set M, we have to find the following results.

Q: Q4) Compute f z'dz, where C is the path formed by the line segment from -3 to 3 and the semicircle…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: the followms lineer pgramming Poblem: 3x, + Xe t 213 s.t. ズ」 X +2X3 s 20 2文,+ X』 Xる く(o 20. て apply…

A:

Q: The grades on a history midterm at Santa Rita are roughly symmetric with u = 76 and o = 3.0. Ben…

A: Given, mean μ = 76 Standard deviation, σ = 3 sample mean, x = 71 X ~ N(μ, σ)

Q: iven T: R2 -> R2, where T(x,y) = (x,y2), Is T linear? Explain.

A: Given: To explain the given statement as follows, R2 + R2, where T(x,y) = (x,y2).

Q: Q3. Let A = {(r, y), 4x² + 9y² < 36} C R² Is A connected? pathwise connected? Justify your answer.

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Q: Q21: show that the line x=-1+t,y:3+2t, 2=-t dud the plone 2x-24-z=-3 are paralle . Find the diitance…

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Q: Evaluate ſc(x – y) ds over the path C: F(t) = 4tỉ + 3tj for 0 <t< 2.

A: Given: The curve C: r→t=4ti→+3tj→ for 0≤t≤2 To Evaluate: The integral∫Cx-yds

Q: Show that the function (x2+y2 t224이) is a Solution of Loplace's equation d2u dy?

A: It will be solution of given Laplace equation only when, it will satisfy it.

Q: Hwi Sind the vecter Paralle I to the line metersell bet ween the flanes and X+y=2 2) X-2y+47-2 and…

A: Two non parallel planes meet at a line. The direction of this line is perpendicular to the normal of…

Q: Find the length of the curve. r(t) = 4ti + 8t3/2j + 9t2 k, 0st<1 %3D

A: Please see the answer below

Q: Find thearea at the reabn eying behween the x-oxis and the curve y=en(2x)-1to the right ed the line…

A: Area of region ∫e/2eydx             =∫e/2elog2x-1x2dx             =∫e/2elog2xdxx2dx-∫e/2e1x2dx…

Q: where Projuct of in tegra tion SÃr dR A-zi-xj-YK and =dxi +arj +dzK dR and %3D the seguent of the…

A: Use line integral

Q: Evaluate I = (sin(x) + y) dx + (7x + y) dy for the nonclosed path ABCD in the figure below, where A…

A:

Q: Ue langrange multipliars to fined the Shortest distancé fam the to the pGine x+g+Z=1. point (7,0,)

A:

Q: Compute the length of the path r(t)= (t, 4t3/2, 2t3/2) over the interval 0<t<8.

A:

Q: C3. Find the length of the of the curve x= 1 from y = 1 to y = 2 %3D 4 8y?

A:

Q: Reckless Rebecca decides to take up skydiving and jump from an acrobatic plane flying along the path…

A: The path of the plane is given by the below equation. rt=4t,3,3t2

Q: a find theistance fron. the Point P(2,17 to the Line yzメ+22L

A: Line :- x+2-y=0  Point (2,1)

Q: SUppOrE THAt y VEIES DIRECTLY WITH X ANO y =9' WHEN X = 18 X HUIM WRITE A DIRECT RAATES. VAQMOW…

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Q: Q3: A. Find Wer if W = f(x, y) {x = reost, y = rsint W₁,

A: From chain rule we know if w=f(x,y) and x=g(r,t) and y=h(r,t) then, ∂w∂r=∂w∂x∂x∂r+∂w∂y∂y∂r

Q: Frd he e of teepkan in the at quectert baurded on he let ty he ydx, bebw by tte carve x- boletby…

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Q: 5) find S, frdr usrng the green's theonum pl f= La?-Hy, Sx t2 31= where right tricagle uith vertizes…

A: Since you have asked multiple questions, we have answered the first question. If you want the second…

Q: -E- x2 and S: R2 → R², 4. Let T : R² → R², x-y (a) Find (SoT)(u) where u := E R?. (b) Find a…

A:

Q: O Find All the ASymploles of the Cerve 3x3 +22y-7ay²+2y"-14x4+7y²+4x+5 =0-

A: Total Asymptods are 3 .

Q: 2. For what value(s) of h, y belongs to Span {v1, v2, v3}? Where 5 -3 V2 = -4 V3 ,and y = 3 h

A:

Q: {(x, y), 4.x2 + 9y² < 36} C R2 ected? pathwise connected? Justif

A: Connected and path connectedness

Q: Evaluate f.y ds where C is the upper half of circle x? +y² = 9, traversed in the counterclockwise…

A:

Q: Q- show that yo+(?) sy + (2) B²y_₁ = y + (1) DY...+ (1²¹) Ay -

A:

Q: Q6. Given M = {(x, y), 1 < x² + y² < 4} C R². (a) Determine dM and aM. (b) Is M connected? Pathwise…

A: Given that M={(x,y),1≤x2+y2&lt;4} (a) Given M is a region enclosed between open circle of radius 2…

Q: Q3: Let L: x-2+3t, y 2t-1, z-4t and M: x+2y+z-11, and let (p) be thus point of intersection. Find…

A: given line is                                                         L1: x=2+3t, y=2t-1, z=4tM:…

Q: The ordeng and transportation Cost C Cin hundred of dollars) for automobrle dealership is modeled by…

A:

Q: Q3. Fjnd the, equationud of The tange and momal lin te given J poit lines, Tto the at the of the…

A: Differentiation w.r.t to t

Q: 27 hPlans that pas Ses through the Point C60,27 and contains the like メt4-2t)ソ= 34st) Zzス+4t 7.

A: Recall: General equation of a plane :     An equation for the plane through (x0, y0,z0 ) and…

Q: Let Q = 4x? + 6xy+ 4y². The points on the curve Q = 7 which are closest to the origin are:

A:

Q: Q3: Let L;: x-2+33t, y 2t-1, z-4t and M: x+2y+z-11, and let (p) be thus point of intersection. Find…

A:

Q: The x, y, zER, subject to the condition yz + zr + xy = 12. Then greatest value of ryg is (a) 6 %3D…

A:

Q: Use the given information to find Ax, Ay, and dy. 1 :x decreases from 2.5 to 2. х — 1 y = Ax = Ay =…

A: Given: y=1x-1; x decreases from 2.5 to 2

Q: Use the chain rule to find where First the pieces: End result (in terms of just t): d = 江 西 血麵| 2 =…

A:

Q: oves from origin at the curved Path -³x) m

A: Concept used: Velocity is the derivative of position with respect to time. Acceleration is…

Q: find thearea f the reabn eying behueen the x-axis and the curve y= en (2x)-1 to the righte the ene…

A: We have to use integration by parts.

Q: The formula for the midpoint of (x1, y1) and (x2, Y2) is: M =| O True O False

A:

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.