Given z = 11t – 48 and y = 121 sint dy dæ dy dz²

Q: Given x = 14t + 12 and y = 70t? + 145 dx (i) dt dy (ii) dt dy (ii) dx the simplified answer) (write…

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Q: Given x = 8t - 21 and y = 64 sin t dy (i) dx dy (éi) dx?

A: I am attaching image so that you understand each and every step.

Q: Given z = 64 sint + 19 and y= 4096 cost-9 %3D %3D d (i) dt %3D dy (ii) dt dy (iii) (write the…

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Q: 2. (- x) dx + 2r y dy = 0

A: Disclaimer: Since you have posted multiple question, we will will answering teh question number 2…

Q: Given x 4t – 13 and y = 16 sin t dy dx a²y dx2 ||

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Q: Given a = 5t – 30 and y = 25 sin t dy (i) da dy (ii) dr?

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Q: || (2? + y*) cos(zy) dz dy? R

A: Here the Cartesian coordinates (x,y) are converted into (u,v) by substitution method as xy=u, x2-y2…

Q: Given x = 12t + 42 and y = 66t2 + 143 dx (i) dt dy (ii) dt dy (ii) dx ||

A: The derivative is defined as the rate of change of one quantity with respect to another. In order to…

Q: Given æ = 13t – 49 and y = 169 sin t dy dx dy dx? ||

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Q: Given a = 8t- 39 and y= 64 sin t %3D RA dy %3D dx dy %3D da2

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Q: Given x 14t – 24 and y 196 sin t - dy dx d²y dx?

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Q: Find a particular solution yp = Yp(x) of the following DE d'y dx? 16y = 48x + 16x + 26

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Q: 1- Sz x?e*y dxdy 2 exy 3

A: Since you have posted multiple questions I can do first question as per our company guidelines…

Q: the following dy Sove D.E VI+x dy + XCI+y) XP

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Q: Given x = 20t + 33 and y = 80t2 + 149 dx (i) dt dy (ii)- dy (write the simplified answer) (iii) dæ…

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Q: Given x = 2t - 35 and y = 4 sin t dy (i) dx dy (ii) dx2

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Q: Given r = 3 ln(t) and y= 9 t then find dy da dy da2

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Q: Given x 13 In(t) and y = 169 t² then find dy dx

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Q: Given a = 32t + 28 and y = 20812 + 110 da (*) dt dy (é). dt dy (é6) da

A: Topic = Derivative

Q: If y = tant and t = 4x³ + x, then dy dx 11

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Q: Given a = 7t – 15 and y = 49 sin t dy (i) dr dy (ii) dr?

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Q: d y then is dx? x=1-8t Suppose y = 5t* +2

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Q: dy b) If y = sec (sint), and t = Vx + 4 find dx

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Q: If x =1 +1 and y = 21, find 4. dy dx a. 3t b. 61? 612 с. 61? d. 1? +1 (r* +1)*

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Q: X = Sint ond y = et If the while t = 0. AIO Bl -I c) -3

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Q: Given x 30t + 37 and y = 75t2 + 105 dx dt dy (éi). dt dy (éii) (write the simplified answer) dx

A: Solve the given

Q: Given x = 36t + 3 and y = 144t² + 119 dx (i) dt dy (ii) dt (iii: (write the dx simplified answer)

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Q: Find the solution of the following BVP given that y(0)=2 and y(1)=0. d’y_12dy. dx +36y = 0 dx

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Q: Given z = 11t - 48 and y = 121 sint dy da dy dx2

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Q: Given z = 6t - 45 and y = 36 sin t dy dr dy dz?

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Q: b) Eiven that x -t'+ 3t² and y=tt- 8t? 2. Find dy i) Find when t=1 dz

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Q: dy If y = sin(5x – 7), then dx II

A: Given that, y=sin(5x-7) We have to find first derivative of the given function.

Q: Given z = 7t - 43 and y = 49 sin t dy (i) de to (ii) (1₂)

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Q: dy 5. If y = e3+1 sin(1 – a²), then Find da

A: We have given y=e3x+1sin1-x2 We have to find dydx.

Q: y"'+4y"+9y'+10y=e^-d(sind)

A: Explanation of the solution is given below....

Q: If x = t+1 and y = t2 - 2t +3, then find t - 1 dx

A: We can find the answer using required rules as below.

Q: If y = 3 t2 – 4 t – 6 and x = dy sin (4 t) , find dx

A: Given, y=3t2-4t-6andx=sin4t To find the value of dydx.

Q: If the substitution m = y - x was applied to the DE: =1 – 3(y–), the resulting DE dz would be: dm =m…

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Q: Given I 20t +32 and y= 80t2 +143 da (i) dt dy (ii)- dt dy (iii. (write the simplified answer) dx

A: Functions area given by x = 20t+32 and y = 80t2+143 To evaluate : i dxdt ii dydt iii dydx

Q: Given æ = 8t + 34 and y = 20t² + 102 dr (i) dt dy (ii)- dt dy (iii). dx - (write the simplified…

A: Given,           x=8t+34  and  y=20t2+102

Q: Given a = 12 ln(t) and y = 144 t2 then find %3D dy dz &y dz2

A: x=12ln(t)y=144t2

Q: If x = 5t +4 and y = 3t-7 , then find dy at t = 2. dx а. 1 O b. 2

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Q: Given * = 11t – 25 and y = 121 sin t %3D - dy (*) da dy (é) da2 ||

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Q: ‏Solve it quickly please

A: dy/dx=(dy/dt)/(dx/dt).

Q: Given x = 13t – 6 and y = 169 sin t dy dx d²y dx? ||

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Q: Given x = 30t + 44 and y = 105t2 + 100 dx (i) dt dy (ii) # dt dy (iii): (write the simplified…

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Q: dy If y = (tane) V20 +1 find ,then choose the correct answer: dx

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Q: Given = 22t + 10 and y = 143t2 + 138 da (i) dt dy (ii)- dt dy (iii) dx (write the simplified answer)

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Q: Given a = 12t -31 and y = 144 sin t dy (*) 12cos(t) da dy (6) da?

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Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.