when (x, y, z) = (2, 2, 1). dt dz dy If x2 + y2 + z2 = 9, dx 8, and dt 4, find dt %3D %3D %3D dz dt

Q: dy If y = (t + 6t + 4) (3t2 + 4), find dt dy %3D dt

A: it is required to find the derivative.

Q: dz Find given: dt =ze, =t', y= 5+5t dz dt

A:

Q: If x, y, and z are lengths of the edges of a rectangularbox, then the common length of the box’s…

A:

Q: If x2+y?+z? = 9, dt dx dy = 7, find zp dt when (x, y, z) = (2,2,1). = 8, %3D %3D dt dz dt X when (x,…

A: Given x2+y2+z2=9dxdt=8, dydt=7

Q: Assume that x and y are functions of t. If y = x² + 4x and dx/dt = 4, find dy/dt when x = 1. dy dt…

A: Solve the following

Q: SupposeThat w=XYz+XY +Z+3andx=3cost, %3D Y=35int, z=27, Evaluete dwl dtt= I 2

A: solution.

Q: d²y dy dt + 81y = 0, y(0) = 9, y' (0) = 3 + 18- %3D %3D dt?

A:

Q: dy If y = (t + 2t + 8) (6t² + 6), find %3D dt dy dt

A: The given question can be solved as shown in step2.

Q: dz 2. Given z = 4x2 + y²,x = sin t, y = t², find- %3D dt

A:

Q: If  x2 +y2+z2  = 9,dx/dt  =5 , and dy/dt  =4, find dz/dtwhen (x,y,z) =(2, 2,1).

A:

Q: Solve the DE as follows: d²y dy +3+ +2y=24 y(0) = 10 and y'(0) = 0 dt? dt

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Q: dx – x = 4y, UTM dt dy + x = y + 3e', dt

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Q: at (x, y) = (1, 2) and z? = x2 + y² if dt dx = 4 and dt dy = 3. dt dz %3D %3D Find dz dt II

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Q: d?z dz +3- 2z = te-2t dt z(0) = 0 ; z'(0) = -2 dt2

A: Given differential equation is, 2 z'' + 3z' - 2z = te-2t z(0) = 0; z'(0) = -2

Q: dz Find given: dt z = xe", x = t°, y = 3+2t

A: Given,         z=xe3y , x=t5 , y=3+2t

Q: If x2 + y? + z2 = 9, dt dy = 9, find dt dz when (x, y, z) = (2, 2, 1). = 4, and %3D dt %3D

A:

Q: dy If y (t+ 2t + 6) (7t + 6), r find dt dy dt

A: Given  y=t2+2t+67t2+6y=7t4+6t2+14t3+12t+42t2+36y=7t4+14t3+48t2+12t+36

Q: dx If x2 + y2 + z2 = 9, dt dy 6, and dt dz when (x, у, z) %3D (2, 2, 1). dt 3, find %D %3D dz dt II

A:

Q: Calculate dy/dt using the given information. x^4/3+y^4/3=2; dx/dt=6, x=1, y=1

A:

Q: (a) dy/dt = 3y(y – 1) (b) dy/dt = y² – 6y – 7 (c) dy/dt = y cos(y) 1 (d) dy/dt : Y – 2 (e) dy/dt =…

A:

Q: da dy at z = – 5 if y = 3x2 – 3 and - 1. Find at x = %3D - dt dt dx %3D dt ||

A: given y=3x2-3 ........(1)

Q: If y = 3x3 + 2x and dx 5, find dy when x = 2. %3D %3D dt dt dy dt %3D

A: Given, y=3x3+2x  and dxdt=5 We have to find dydt when x=2

Q: Suppose that w = xe"/, where x = t², y = 1 – 6t, and z =1+ 4t. dw Find dt

A: w=xeyz, where x=t2 , y=1-6t and z=1+4t

Q: Suppose that x = x(t) and y = y(t) are both functions of t. If x2 + y2 = 25, and dx = 2 when x = 3…

A: Given that x=x(t) and y=y(t) are both functions of t . If  x2+y2=25           ..(1) Differentiate…

Q: Solve for x and y where dx/dt = x^2 + xy, dy/dt = y^2 + xy subject to condition x = 1, y = 2 at t =…

A: Non linear system of differential equations

Q: Suppose x(t) and y(t) satisfy da = y? – 1 , dt dy = 2 – 2x. dt - - d (3x2 – 6x 0. + y³ – 3y) = Show…

A:

Q: Find the general solution to dx = x + y – z dt dy 2y dt dz = y – z dt

A: Given,  dxdt=x+y-z . . . .. . . .1dydt=2y . . . . . ............2dzdt=y-z . . . . . . . . . . . 3…

Q: If x2 + y2 + z² = 9, xp 6, and dy = 9, find dt dz when (x, y, z) = (2, 2, 1). dt dt dz dt

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Q: dw Find where w(x, y, z) = xyz + xy, with x(t) = e", y(t) = e¯24 and z(t) = e-9t dt

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Q: d?y + 4 + 4y(t) = 2e-tu(t) , y(0) = 3, y(0) = 0 dy dt2 dt

A:

Q: If y is a function of t and z= 4y²+y• find dz/ dt when y=2 and dy/ dt = – 1 %3D

A: z=4y2+y, dy/dt=-1

Q: Use the Chain Rule to find dz/dt. z = x2 + y?, x = cost + sin t, y = cos t – sin t. -

A:

Q: z = √xy, dz dt t², y = -t² then 2 2 2t²) =?

A: We have to choose the correct option from the given options according to the given information

Q: Q4. Find dz/dt where z = 2xy - x² y² and x = 2t, y = t²

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Q: dy If y = (t + 5t + 6) (2t² + 4), find dt dy %3D dt Submit Question

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Q: dz Use the Chain Rule to find dt for z = x? + y? + xy, x = sin t, y = et.

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Q: Use the Chain Rule to find dz/dt. z = x2 + y2 + xy,    x = sin(t),    y = 3et

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Q: dz/dt = -Bz(1 – vz), z(0) = 1. %3D

A:

Q: Find given that dt x² + y² = 2x+4y, x = 3 y = 1, and dy dt i dx dt

A: SOLUTION-

Q: dy Find given that dt x² + y² = 2x + 4y, x = 3 y = 1, and dy = | dt dx dt = 6

A:

Q: Employ the classical fourth-order Runge-Kutta (RK) method to integrate dy = y – t² + 1 dt

A:

Q: Find dz/dt dz/dt given:  z=xe2y, x=t6, y= -1+5t

A: Given,         z=xe2y    , x=t6     ,    y= -1+5tWe know that,            ∴dzdt=∂z∂x·dxdt+∂z∂y·dydt

Q: 2,d'y(0) = -2 dt? d'y(t) , dy(t) dy0) - + 3 dt = sec(t), y(0) = 2, dt %3D %3D dt

A: Answer

Q: Can you help me step by step?

A: The given function is

Q: Assume x and y are both differentiable and functions of t. dy when x dt dx = 3? dt If y = x², what…

A: Explanation of the answer is as follows

Q: dy x2 + y2 if dx Find at (x, y) = (5, 6) and z? dz dt = 9 and = 7. dt dt dz dt Additional Materials

A: To determine the derivative.

Q: If+y = 25 and dz/dt = 5 , find dy/dt when y is positive and %3D %3D (a) z = 0 dy/dt = 0 (b) z=1…

A:

Q: dz 2) Find if z = xy² + x?y, y = ln x %3D dt

A:

Q: dz dt || z = cos(x + 3y), x = 8t³, y = 9/t

A: By the use of chain rule we need to find the required derivative.

Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.