The position of a particle in the xy-plane at time t is r(t) = (t – 3) i + (t² + 3) j. Find an equation in x and y whose graph is the path of the particle. The equation for the path of the particle is y =

Q: 6. If x(t) = e' +1 and y=2e²ª are the equations of the path of a particle moving in the xy-plane,…

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Q: The position function of a particle is given by r(t) = ⟨-3t2, 5t, t2 - 4t⟩ At what time is the…

A: rt=-3t2, 5t, t2-4t To find the velocity, differentiate the position function with respect to t, we…

Q: Find the length of the curve on y=2x^(3/2) from x=0 to x=1

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

Q: Find 2 for the curve dx x²y³ – 2xy = 6x² + 2y3 + 1

A: Topic = Derivative

Q: Suppose f(x, y, z) = In(7x + 9y+7z). Find an equation for the level surface of f that passes through…

A: Given Data: The level of the curve for fx,y,z=In 7x2+9y+7z2 is of the form,…

Q: Find a direction in the xy-plane in which f(x, y) = e¹-xy has zero change at the point P(1.0. e).

A: We know directional derivative formula Du→fa, b, c=∇fa, b, c.u^ Lets say u→=cosθ, sinθ be the…

Q: Find the equation in the xy-plane whose graph includes x In(6t) and y = t².

A: Given  x= ln(6t) y=t2

Q: The diagram shows a sketch of the curve with equation y = -r +7x 12 1 3. -2- 8 CMA Q3 Find the…

A: For the solution follow the next step.

Q: Find the points on the curve x2 + xy + y2 = 16 which are nearest and farthest from the origin.

A: Given curve is g: x2+xy+y2=16 If x,y is any point on the curve g: x2+xy+y2=16 Then square of the…

Q: The position of a particle moving along the x - axis at time t is given by x(t) = e©os2t, 0stsn. For…

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Q: An insect is moving on the surface of a hot plate, the temperature of which at the point x units to…

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Q: Find the point in the plane x – 2y + z = 4 that is closest to the origin.

A: Solution)                   Given                           plane  x-2y+z =4

Q: Q4: A particle is moving on the curve defined parametrically by the system of equation x = 1- 2cos?t…

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Q: for the exact equation of the form M(x,y)dx + N(x,y)dy = 0 Select one: а. My= Nx b. Mx+ Ny=0 С. Mx =…

A: We will prove it using definition of exact equation

Q: The function is given in parametric form by the equations{x=t2+t−1y=t3−2t.Find the second-order…

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Q: Find the maximum height above the xy-plane of a point on r(t) = (e1 , sint, t(4 - t))

A: Maximum height above the x-y plane will be the maximum value of z .So we will take z parameter of…

Q: Express the curve by an equation in x and y given x(t) = e' and y(t) = 7 – e2'. a) O-x2 + y = 7, x 2…

A: simplify the equation and choose correct equation.

Q: The position of a moving particle is given by s = t - 8t + 15, then its speed at t = 8 is

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Q: (d) The curve y = x – x² from r = 0 to r = 2

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Q: Use the technique of variation of parameters to find a particular solution to the DE y" – 2y + y =…

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Q: Calculate the “n” of the DE with the given 6y^2dx-x(2x^3+y)dy=0

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Q: For the equation, xt+1=rxt(1-xt) for t=0,1,2,... Find the two fixed points. For which values are…

A: To find: The two fixed points, which values are the locally stable. Given: The equation is…

Q: (6) Find the points on the curve 5x2 + 6xy + 5y² = 9 which are nearest to and farthest from the…

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Q: Find the equation of the tangent to the hyperbola x² – 3y² = 1 at the point S(2,-1). A) 2x + 3y – 1…

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Q: (A) Evaluate" [(x² + y)dx + (x+1+d along the path ABCA shown in figure C(0,3) A(0,1) x=3sint y=3cost…

A: What is Line Integral: When we integrate a function along a straight line or a curve inspite of…

Q: a particle moves along a curve x = t^3+1, y=t^2, z=2t+5 , where t represents the time . its velocity…

A: Velocity is obtained by differentiating the position function

Q: Find the point on the curve y = Vx closest to the point (1,0).

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Q: Show that the equation of the tangent ine to 'the graph of the parabola at the point Pt'=(t,t²) 1s…

A: Consider the given function whose equation of tangent is required to calculate.

Q: A particle is moving with the given data a(t)= 3e^2t -2 cost, s(0)=0 and v(0)=0, find the position…

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Q: y = e*, 0<z<1.

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Q: B. Find the length of the curve y= x2 from x = 0 to x = 7.

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Q: Ql: Find y(0.5) for y'=-2x-y, y(0) = -1, with step length (h=D 0.1) using Runge-Kutta.

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Q: Match the equation with its graph. 2t r(t) = ti + In(t)j + k, 0.1 < t< 5 3

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Q: Find the length of the curve y = V- from z =1 to r = e. 3

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Q: Find C so that the line y = 4x + 3 is tangent to the curve y x2 + C.

A: The given equations are y=4x+3 y=x2+c.

Q: Find c so that the line y = 4x + 3 is tangent to the curve y= x^2 + c?

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Q: Solve for y(t) where y(t) + 2 / a – u)y[w)du = t.

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Q: 2. Find dy where y = v3x3 +4x + 1.

A: Given y=3x3+4x+1

Q: Ql: Find y(0.5) for y'=-2x-y, y(0) = -1, with step length (h= 0.1) using Runge-Kutta.

A: Since you have asked multiple question, as per our guidelines we are supposed to answer only one…

Q: Find the point on the graph of z = x2 + y2 + 10 nearest the plane x + 2y - z = 0.

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Q: (A) Evaluate" [(x² + y)dx + (x + 1) 1+ along the path ABCA shown in figure C(0,3) A(0,1) x=3sint…

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Q: Q: Find the point on the curve 4x' +a'y = 4a', 4< a < & that is farthest from the point (0,-2).

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Q: The cartesian equation of the curve x = 1-t.y vt is: (a)y = 1-x, x2 0 (b)y = 1-x .x 20 (c) x=1-…

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Q: What is the value of c such that the line y=2x+4 is tangent to the parabola y=cx^2.

A: Given that the line y=2x+4 is tangent to the parabola y=cx2. The derivative of y=cx2 is dydx=2cx.…

Q: The point on the curve x? + 2y = 0 that is nearest to the point (0,-;) occurs where y'is A) 0 B)…

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Q: trace the path of the curve f(t) = (3e', 4e24)

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Q: The curve x = t - 3t, y = Vt intersects the y-axis when x = 0, which occurs when t = 0 and t = y 3-…

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Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.