9. Find the position function of a particle moving along a coordinate line that satisfies the given conditions. a(t) = 4 sin t - cos t, s (0) = 5, v (0) = 0

Q: dw dw + 4. = 0, -00 0, dt dx w(0, t) = sin 3t.

A: Let us use method of characteristic to solve this PDE.

Q: 2: Evaluate [G(x, y)dx, [G(x,y)dy and [G(x, y)ds on the indicated curve C. G(x, y) = x³y² + y² sin…

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Q: Use the method of Frobenius to find solutions near x =0 of the following differentia equation dy…

A: Given that x2y''+xy'-x(x+1)y=0 Divide the equation with x2, y''+1xy'-1+1xy=0 Take y=∑n=0∞anxn+r Then…

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Q: ƏT ƏT and dr 3. Find of function T = x²y – xy³ + 2; x = r cos 0 and y=r sin 0

A: We have to find derivative

Q: 4. y = c, sin wt + c, cos wt w is a parameter

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Q: 2) 1 y = ²+² x= cos(t). y = sin² (t).= =-. at t = 3 t

A: Solution of the given problem is below...

Q: Use Euler's method with h = 1/4 to compute approximate values of y(1) for t.y'= y(sint), y(0)=2.

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Q: Find the position function of the particle moving along a line that satisfies the a(t)=4 sint-cos t,…

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Q: Given z = 2 cos t + 33 and y = 8 sin²t dz (i) dt dy (ii) dt dy (iii) dr

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Q: dy Solve the initial value problem: 4( sin(t)- + cos(t)y dt = cos(t) sin (t), 0 < t < T, y(T/2) =…

A: Here the first order differential equation is given as: 4sinty' +costy=cost⋅sin7t0&lt;t&lt;π,…

Q: 4. y" + y = tan x. 5. 4y" – 4y' – 8y = 8e-t 6. y" – 2y + y = : + 3e 1+ t2 et 7. 4y" +y = cos I

A: 4. Given, y"+y=tanx

Q: 16. t 31²y = cos t, y(T) = 0 dt

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Q: 3y" (t) – / (t) = e' cos(t) + sin(t), y(0) = 0, y'(0) = 0 -

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Q: The displacement of a structure is defined by the following equation for a damped oscillation: y=9e…

A: The displacement of a structure is defined by the equation  y=9e-0.7tcos4t…

Q: I need help with 1a)

A: straight line becomes y=x

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Q: dW w. if W=3x3+2y³ ; where x= e, y= cos 2t at t=0 dt Find

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Q: 1. 5. Find the value of the line integral. (x - y) dx- 2.xy dy C:r(t)=2 cos ti + sin ti

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Q: let y(t) be a solution of (cos y + 1). dy = 2t such that y(2) = 0. dt Show that sin y + y = t2 + C.…

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Q: Let y = tan(4r + 8). Find the differential dy when a = 3 and dæ = 0.1 Find the differential dy when…

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Q: B) Find the distance traveled by the particle P (x.y) between t = 0 and t 4 if the position at time…

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Q: 1. [* sin'x cos xdx parctan3/2 3secx 2. y dy dx 3. T y xpáp X 4. [S yz dx dy dz ea/4 2cose prsine 5.…

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Q: 19. State the order and degree of the differential d y d³y equation dx dy Cosx dx +2 + dx? а. 3, 2…

A: Order of the differential equation The highest derivative in the differential equation is the order…

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A: We have given differential equation  tdvdt=v+t dvdt=vt+tt dvdt-vt=1 Comparing this with differential…

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A: Given a particle is moving in a curve rt=cos 7t i^+sin 7t j^+6t k^to find the tangential and normal…

Q: Use the method of Example 4 to compute dy/dx p at P = (2, 1) on the curve y^2x^3 + y3^x^4 −…

A: we can solve by this implicit differentiation, so,

Q: (d) +ỷ =0 dy dt (e) (f) d²y dt² d³y dt3 + sin(t + y) = sin t +t + (cos² t) y = t³ dy dt

A: To find out the order of the differential equation and also we need to write down that the…

Q: A ) Find ſ cos 5t dt dy B) If y = x² +; , x= 2t -5 then find dt

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Q: 4. Find dw/dt. 3 (a) w = 5x²y*z4; x = P; y = t z = t5 1 (b) w = 5 cos.ry- sin rz; = X pi y = t := 1?…

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Q: (1+ In xy) dx + (-)dy = 0

A: See the attachment

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Q: Given z = sin(1 - 2). x = 2 – ts and y = 2t – s - then calculate when t = -1 and s = -1. dt

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Q: H.wl: Find L St. sin 2t.dt -3t {e p1 p2

A: We find Laplace transform of given function

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Q: dz Use an appropriate form of the chain rule to find dt 1 8 cos x sin ry; y = 9t t' Enter the answer…

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Q: 25) 2 sin(y)dx+cos(y)dy 0, y(0) = z/2

A: Q 23 is incomplete as it doesnot contain dy term. and Q 25 is in next step.

Q: dy %3D 3 e*y* dx +

A: Givendydx+y3=exy4To Find:Solution of a given Bernoulli's equation

Q: If x = 2 sin* t and y = 3 cos* t, then find dy at t = %3D dx 4 а. 1.5 b. -2.5 с. -1.5 d. 2.5

A: Solution:

Q: Find the general solution of the given equations below: 1) dy dy 3+ 2y = e' sin(t) dt

A: Hello, thanks for your question but according to our policy I am answering the very first question.…

Q: Given (1 + 3x sin y) dx - x² cos y dy=0 with y(1) = 0. Using Euler method with h=0.1, compute…

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Q: 5.Express this model of an electric circuit d²y dt² dt As a pair of first order equation +6+5y=sin…

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Q: Solve the following problem dw dw + x dt 1, -00 0, %3D dx with w(x, 0) = f(x).

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Q: dw 3) Find ifw = 5 cos(xy) – sin(xy),x = ,y = t,z = t³ - %3D dt

A: Given: w=5cosxy-sinxy, x=1t, y=t, z=t3 For finding dwdt, first we find w in terms of t So, we put…

Q: 4. Find дw b. dz a. дх at the point (x, y, z) = (0, 1, T) if w = x² + y? + z? and y sin z + z sin x…

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Q: 8) Find the general and particular solution for the following separable equation dy = -.5y, y(0) = 2…

A: The solution as follows :-

Q: 18. The equation of the tangent line to 2² sin T # 0 f(x) = 0 x = 0 at r = 0 is 1 (a) y = -x (b) y =…

A: Note:Since you have asked  multiple questions ,we will solve first question for you.To get remaining…

Q: 2²y ds, C:x = cos t, y = sin t, z = t, 0 < t < a/2

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Q: Q2: find dw/dt at given value point for the following function x= cos°(1), y = sin²(1).= =-. 1 at t…

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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.