25 45 10 15 30 20 40 4 3 7 10 Ix :195 TY : 47 Ixy : 1410 2 2 8 75 Iť=355 2 SSLY) 3 sS CXY) 4 f 5 Interfleter ļ Slore Find ! sscx) Z vintercert 8 Line of best fit 1 fur Y=5 find X

Q: 10. Differentiate y = xV A. y = xV (n) 2+In 2 va B. y' = xv (* + C. y' = x* (+ D. y-x" (프+ Im) E.…

A: We need to find differentiation.

Q: 3) If A = 2x²i – 3yzj + xz?k and ¢ = 2z – x³y, find A - Vo and A x V¢ at the point (1,-1,1). ww. 4)…

A: A=2x2 i-3yz j+xz2 kA(1,-1, 1)=(2, 3, 1)ϕ=2z-x3y∂ϕ∂x=-3x2y∂ϕ∂y=-x3∂ϕ∂z=2∇ϕ =∂ϕ∂x i +∂ϕ∂y j+∂ϕ∂z k∇ϕ…

Q: 6. Given that z = u' + 2v – x + 3y; u = r´ - s', v = r´ + s´, x = 2rs, y = 4. Find 2 =r dz(r, s, h,…

A: Given, z=u2+2v2-x2+3y2u=r2-s2 v=r2+s2x=2rsy=2rsTo find: dz(r,s,h,k)

Q: y dy Find ·S- using the substitution +5=√√√y+2 √√y+2 (√x+2-5)(-5√/y+2+y+21) + C © ²/(√x+2-5)…

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Q: Find (a) ker(T) and (b) range(T).T: R4→R3, T(w, x, y, z) = (2w + 4x + 6y + 5z, −w − 2x + 2y, 8y +…

A:

Q: Copy and complete the proof of Theorem 2-5: If two lines formcongruent adjacent angles, then the…

A: Given: In figure ∠1≅∠2. To prove: l⊥n

Q: 14. Find the distance between the two skew lines. x = 2+t x = 4+s y = 3-t y=1+s z = 4t z = 2- 2s

A: Given query is to find the the distance between two skew lines.

Q: 34. 13 75° 17 35. 16 9. 22 %3D 36. In AXYZ, mZX = 96°, XZ = 15, and XY = 24. Find YZ.

A: The law of cosines states that c2=a2+b2-2abcosC.

Q: Which of the following represents the distance between (X. (X2. Y2) O A. d = 2 / (x2 +1) + (y2 +Y1)…

A: Given two points, A(x1,y1) B(x2,y2) distance d=?

Q: (2wv – tan w) dv + (v² – v sec² w) dw = 0 C = y²v – w tan v Option 4 None of the choices C = yv+ w…

A: A differential equation is exact if it is of the form ux(x,y)dx+uy(x,y)dy=0.   Observe that if an…

Q: | 25. Use a Linear Approximation of f(x,y,z) = /x²2 + y2 + z to |estimate /7.12 + 4.92 + 69.5.…

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Q: Let f(z, y) — (-(г + ))5. Then | 20(-(x+y))^3 dzðy dzðydz dz²dy

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Q: 15. f(x, y) = xy /x² + y V9 – x² – y? 16. f(x, y) ▪ x + 2y + y? x² – y? 17. f(x, y) *

A: 1.  fx,y=xyx2+y2.  fx,y=9-x2-y2x+2y3.  fx,y=x2+y2x2-y2

Q: 5. Find rob lein 20Ounimo sad dw (a) ду dw (b) dy at the point (w, x, y, z) = (4, 2, 1, – 1) if w =…

A: point(w,x,y,z)=(4,2,1,-1)

Q: | Find fe(x² + y)i + 4y' j) dr where C consists of the three line segments from (4, 0, 0) to (4, 5,…

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Q: 20. Evaluate J Vx + 2y ds, where C is a. the straight-line segment x = t, y = 4t, from (0, 0) to (1,…

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Q: A line can combine unites of inputs Cx) to produce processing units of output cy such trat there is…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

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Q: 10. y = x2 + 3 ve y = 11 – x² eğrileri tarafından sınırlanan bölgenin alanı aşağıdakilerden…

A:

Q: Given 3 2 SSS 0 0 0 Then, A = Blank 1 and B = Blank 2 C = Blank 3 and D=√4-x² E = Blank 4 and F =…

A: To Change the order of integration from dxdydz to dzdydx

Q: Ju ox Əv oy 으 0x1 10/24 0 어 xiye Ug xzty? zi @u + v = oxy UXO u ox + Ju ag - = U - (x+y? +c)2c +…

A: Differentiate partially with respect to x and y

Q: 19 5. Evaluate F. d R where F = yî + xz°j– zy°k, C is the circl x? + y? = 4, z = 1.5 Ans. TC C 2

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Q: 4. Find x in ASTU. 17 А2 C V32 D V514 -T В 8 15 5. Which set of measures could represent the lengths…

A: 4.B. 8 Given that, ?STU is a right angle triangle.  Then we apply Pythagoras theorem to find the…

Q: ) s how that the line af intersection f the Planes X+2y-22%= 5 and 5x-2y-Z=0 is Paraliel to theline…

A: Solution is written in below steps.

Q: 28. The values of y for various values of x are given in the table below. | 2 3 4| 5 6 3 3 4.2 5.2 6…

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Q: التكن كل من R.Q علاقة معرفة كالاتي R={(x,y)|(x,y) EN*N|x +y= 5} Q={(X,Y)|(x.v) EN*N[ 2x - y= 4} RUQ,…

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Q: Thanks for the help.

A: According to the given information, Let R be a rectangle with corners at (a,a), (-a,a), (a,-a), and…

Q: um.minimum.and.Saddl .puints.e. fxクり).ニ.4.-2X.m4ymx..y b. fiang) = Xy+12. Kay ..C. f(xyy). 2. X...…

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Q: 14 Které číslo se ukrývá v obálce? a) M. (5 + 1) = 36 %3D b) 8. (5 + = 56 c) 4. X+7) = 40 %3D d) 7.…

A: a)    __·5+1=36__·5+1=36__·6=36__=366__=6∴ 6·5+1=36

Q: Find an equation of the line L.

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: Stan"(w}sec°(w)ax u )کب + 27 + ه-)J ب)ا 20 - )J No appropriate Match au)کی - 207 - ه-)J du )قی + 27…

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Q: H.W let f:AC, 9: B D be two fanctin. sit flx)= 96 VxE AAB hz fug: AUB CUD defied by s then XEA g),…

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Q: 3 If U<xy+ yZ +Z X Find d Ce, y,2) y it bcist. V =X +Y+Z, W=)X YZ %3D

A: Given : u= xy + yz +zx , v= x+y+z , w = xyz To find: ∂(x,y,z)∂(u,v,w) Solution: Let   A = u- xy - yz…

Q: 27. || x sec?y dA, R={(x, y) | 0 < x< 2,0 < y< /4} R 28. || (y + xy-2) dA, R={(x, y) | 0< x < 2, 1 <…

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Q: Find y dy ·S= using the substitution u +5=√√y+21 Vy+2 ²/(√√y+2-5) (5√√y+2+y+24) +C…

A:

Q: Find ((x? + 4y)i + 4y j) · dr where C consists of the three line segments from (3,0, 0) to (3, 5,0)…

A:

Q: w = f(x,y), x(s,1) = . y(s, t) And that fx(1,1) = 3, fy(1,1) = 4, fx(2,2) = 5, fy(2,2) = 6 Find the…

A:

Q: Find ((x + 4y)i + 4y j) · dr where C consists of the three line segments from (3,0, 0) to (3, 5,0)…

A:

Q: 2. (a) {(x, y) | y = Vx + 1} (b) {(x, y) | y = Vx² - 1} (c) {(x, y) | y = VI – x} (d) {(x, y) | x² +…

A: If a line parallel to y-axis cuts the graph of the function at most once, then it is a function…

Q: dz 4. Let r - y – 23 = 6ryz, then the value of is dr %3D 22 + 2ry (d) 코- 2yz 2 + 2yz y? – 21z (c) 22…

A: We are given: x3 -y3-z3=6xyz we need to find the derivative of z with respect to x. This can be done…

Q: y dy Find ·S- using the substitution +5=√√y+2· Vy+2 ²(√y+2−5)(5√/y+2+y+21)+C 3…

A:

Q: 2 10 Which one is equal to S zf(1,y) dz dy? 0 y O VY) O EIY O EIY)X=x] for 10 > x > y O VIX] O…

A:

Q: (a) F(r, y, 2) = 7+ 27 + 3K. (b) F(r, y, 2) = i + 25 + zk. (c) F(r, y, z) = xỉ+ yj+ 3K. (d) F(r, y,…

A:

Q: R 1.5 7) Line QT || Line RS; PQ = 6, QR = 1.5, PT = 1.2. Find ST. Q 6. 12

A:

Q: 10. Evaluate Sc(x – y + z – 2) ds where C is the straight-line segment x = t, y = (1 – t), z = 1,…

A: Given: f(x, y, z)=x-y+z-2, where C is the straight line segment x=t, y=1-t and z=1 from (0, 1, 1) to…

Q: 27. x sec'y dA, R= {(x, y) | 0 < x < 2, 0 < y < T/4} R 28. (y + xy-) dA, R = {(x, y) | 0 < x < 2, 1…

A: For the double integral, ∫ab∫cdf(x, y) dxdy, the limits of integration corresponding to the…

Q: az au əz əv əz ?w 11 11 || z = x² + xy³, əz əz du av az aw x = uv³ + w², y = u + vew when u = 1, V =…

A:

Q: If F(x,y, z) = (5x – y + az)î + (bx + 2y + 5z)ĵ + (2x + cy – z)k is irrotational then find the value…

A: Explanation of the answer is as follows

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.