Let z(a, y) = 7x – 6y where x = - 7s – 4t & y = – 2s + 8t. %3D %3D az Calculate as az by first finding at ду and using the at ds as' at az as az %3D at Check Answer

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

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Q: 20) Let y=7x+5x Then compute dy and Ay for X= -7 and dx =0.4. dy =? and Ay = ? Gounded 6o 4 decimal…

A: Derivative: - The derivative of the function is the equation that we find. The instantaneous rate of…

Q: If f(x, y) = 2x² – 8y², then the total differential of f at x = 1 and y = -2 is : - O df = 32 dx + 4…

A: In total differential take the derivative of each terms, put the given values and simplify.

Q: xy dx (x² + 3y) dy = 0 -

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Q: Differentiate with respect to t. y = 7sin(x - t) -(7sin(x-t)) = dt

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Q: FIND 2 DIFFERENT (LINEARLY IN DE PENDËNT ) SOLUTION S POR THE D.E y"_x² y'- 3 xy = O *y'-3xy%3D0

A: Step:-1 Given that y''-x2y'-3xy=0 ---(1) This is second order differential equation with variable…

Q: (c) Show that (d/dz)z does not exist anywhere,

A: See the attachment

Q: JK = 4x + 8, %3D KL = 5x + 6, and JL = 86, %3D Find KL. J K L

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Q: -3dk + (xy²– x²) dy = 0, -2 -2 x*)dy = 0, Integrating Factor = x

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Q: Verify that [(y- 2x \dx +(2xy +x*dy = [S -川- dA where C is the bounda ôy R defined by y = 0, x = 1,…

A: See the details solution in below

Q: Let y 4 Find the change in y, Ay when ax = 0.2 4 and Ar Find the differential dy when 4 and da 0.2 =

A: Change in y is,

Q: Let w(x, y, z) = x² + y² + z² where x = sin(7t), y = cos(-3t), z = e-4t. dx dy dz dw dt dt' dt dt…

A: Given problem:- wx,y,z=x2+y2+z2,x=sin7t,y=cos-3t,z=e-4t Find dwdt

Q: dz Suppose that z = x³ – 3y?, x = 4(t³ – 1), and y = Int. Find using the Chain Rule. dt %3D -

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

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Q: Find the total differential. w = (3x + 4y)/(y + 3z)

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Q: Let y = 4x. %3D Find the change in y, Ay when x = 5 and Ar = 0.4 Find the differential dy when x = 5…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 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

A: differentiate the given function with respect to 't' 2x dx/dt +2y dy/dt +2z dz/dt =0 Now substitute…

Q: Q6. If w = y²z² + xy and x = t³ – 1; y=t² + 2; z= 3t , find the total dw at t = 2 dt differential

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Q: . Determine the solution of y dt + (2yt + 1) dy = 0given that given that y (-1) = Q Call

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Q: 4. Suppose that z = x³y, x= t², and y = t³, find . dt = 12t11 dt 11t10 b) = 10t° dt d) = 9t® dt

A: This question is related to differentiation, We will solve it using given information.

Q: Eliminate the arbitrary constants y Iny = C,e "+ C, X-

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Q: if U=4xy2 +yz3 + 10xz…

A: Given- U=4xy2+yz3+10xz x=4t+5 y=1t and z=6t2

Q: [-+] 5t dy 3.1는-51%3D-y dt

A: This is a linear 1st order differential equation.

Q: What is the integrating factor of 6y²dx (2a + y) dy = 0 %3D

A: A non-exact Differential equation becomes exact when we multiply it by an Integrating factor.

Q: Find dy/dr by differentiating implicitly if z +ry- 6r = 2.

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Q: Eval S fCx,y,z)dV Por f auel regien W M, fory2)= 2x W: x'+ y? < zs 4

A: The region W : x2+y2≤z≤4, and f(x,y,z)=2x, we have to evaluate the value of ∬∫Wf(x,y,z)dV.

Q: Calculate the LOS of y = x² + 2x + 8 LOS is x = a is b is cis

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Q: Given z=200st+17 and y=9sint dr dt dy dt dy da %3D

A: First of all we will differentiate the given equations with respect to t

Q: If f(r, y) = 3x2 – 8y, then the total differential of f at z = 1 and y=-2 is: %3D O df = 6 dx + 32…

A: we can find the total differential as below using the properties of partial derivative

Q: Suppose that n # 0 and n # 1. Show that the sub- stitution v = y!-" transforms the Bernoulli…

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Q: Let z(x, y) 2x2 – 3y? where a 2s – 4t & y = 9s + 8t. he at dy dx az Calculate ds dz by first finding…

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Q: Show that 3x f(x, y) = (5x³ – 4y³)ey + 4xy? is homogeneous.

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Q: If x2 + y2 = z2, find dy/dt when x = 3, y = 4, dx/dt = 2, and dz/dt = 2. (Enter your answers as a…

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Q: Let z(x, y) = 2x2 3y2 where x = 2s – 4t & y = 9s + 8t. | dx dy ду az Calculate ds dz & and using the…

A: We have to find all first order partial derivatives.

Q: O from the equation z = In(x² + y²) + Zyy Show that zxx %3D

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Q: If x'+y' +z-9, dx/dt = 5, and dy/dt = 4, find dz/dt when (x,y,z) (2,2,1)

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Q: If f(z,y) = 3z² - 8y, then the total differential of f at z =1 and y = -2 is: %3D O df = 6 dz + 32…

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Q: If x2 + y2 = z2, find dy/dt when x = 3, y = 4, dx/dt = 6, and dz/dt = 6.  (Enter your answers as a…

A: We would differentiate the given expression implicitly w.r.t. t, ........................(1)

Q: Find the integrating factor of the given Non-Exact DE y (4x + y) dæ – 2 (x² – y) dy = 0

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Q: Reduce the DE with linear coefficients (6x + y-9)dx + (x – 2y+5) dy =0 to a homogeneous DE. A (би +…

A: Given DE is (6x+y-9)dx+(x-2y+5)dy=0 Reduce the DE with linear coefficients to a homogeneous DE

Q: If y=7x²y+z³ +yz² A = y³ z² e^5x a_x + 4x4 zcosy a_y+ 2x4 CosySinz a_z. Find the following at point…

A: Given, ψ=7x2y+z3+yz2A=y3z2e5x ax+4x4z cosy ay+2x4cosy sinz az           Note: The expert is supposed…

Q: dw Q11- express by using the chain rule: dt w = ln(x² + y² + z²) x = cost, y = sint, z = 4√t

A: We have to express dwdtby using the chain rule:

Q: Prove that (y – æ)(y + 3x)³ = cx° is a solution to 3x2 – 2xy + 3y² )dx = 4xydy.

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Q: Given z = 3x'y + V5 cos 2y-2x, detemine the total differential o

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Q: ) Find dw if w = xe³/², x = t², y = 1 — t, and z = dt 1 + 2t.

A: Topic:- application of derivatives

Q: 1 find the total differential dz. z=xsin y + x² z = (2x² + 3y)² z=5x-7y

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Q: USE HOMOGENEOUS LINEAR HIGHER ORDER DE 4. y(4) + 50y(²) + 625y = 0 ANSWER: 4. y = (C₁ + C₂x) cos 5x…

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Q: If a and ß are positive constants, show that the particular solution of dy %3D У (В — ау) dt that…

A: Given that dydt=yβ-αy and y=y0 at t=0 We have to find the solution of the above equation.

Q: Let y(x) be the solution of y' = y − 4x such that y(1) = 1. Using a step size of 0.5, set y0 =…

A: I am attaching a picture where you will get step by step solution first I write the formula of euler…

Q: (b) If z = 9t²e 4t, find 4 dz dt

A: Given.

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.