8. Use algebra to find the point at which the line f(x) 61 intersects the line 60 %3D 3° 4 453 g(x) %3D 100 Write the values of x and y as reduced fractions or integers. y = ||

Q: dy 2. (a) Determine in terms of x and y given that dx i. x²y + 3xy3 – x = 3 ii. sin(x? y?) = x (b)…

A: Let's find.

Q: 4x Compute (2x + 4yz) dz dæ dy 1

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Q: Ca) Supposed that w= xy – x2 with x = e¯"s²t and y = r²s sin t. Find the value of when r = 0, s =…

A: Given:  w=x3y-x2     , x=e-rs2t      and y=r2s sintsubstituting x=e-rs2t      and y=r2s sint in…

Q: (a) Find the approximations T4 and M4 for 7el/x dx. (Rou T4 = %3D %3D

A: We have to find approximations T4 and M4 for the integral ∫127e1xdx Here T4 stands for trapezoidal…

Q: dy/dx = (xy + y^2 + x^2)/(x^2) Finfd the solution of the above equation using a suitable…

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Q: 2. . For what values of m does the function y = Aet satisfy the following equation? d'y dy + бу = 0…

A: find d2ydt2,dydt and substitute in the given differential equation and solve for m

Q: So, which of the following is the solution functiony(t) ? a) y(t)= sinh2t = e* %3D b) y(t) = sin2t –…

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Q: 2.2 The value of xe*dx by using the two-point Gauss quadrature is most nearly 0.2 (A) 11.672 (B…

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Q: dg If g(xy)=e²yx².sec xy³ where x(u)=u eu and y(u)=u sinu³ Find np

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Q: 2. Find the general solution. а. у' + sec x у%3D cos x. b. y' +y =(e* - e-*). c. y' +=y. d. y' = .…

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Q: F. Solve the following by Substitution Method. 1. y(x tanx + In y)dx + tanx dy = 0 dy %3D

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Q: How many of the following questions have the same answer? dy =? I. y = cos(2t), x = sint = dx II.…

A: Since you have posted a question with multiple sub-parts, we will solve the first two subparts for…

Q: Use the method of reduction of order to find a second solution to t°y" + 3ty' – 3y = 0, t > 0 Given…

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Q: Obtain the GS of: 2 (Згу — 4у + 6) dz + (23 — ва? ? — 1) dy %3D 0 - a. x³y – 2x?y3 + 3x² b. x3у —…

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Q: 4) Find dy where r and y are related by the equation r?y + r³ + 2y? = 5y.

A: Given  x2y+x3+2y2=5y Apply power rule to take derivative We know that , derivative of x is 1  and…

Q: what is the privet solution to thhe equation (6+0)ycx)= Xsin cx) (X) %3D

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Q: 1. Obtain the general solution unless otherwise instructed d²y 1. y = 10sin²x dx2 %3D - SUMMARY OF…

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Q: 3. Check for homogeneity and obtain the general solution. (Let 4C=C) (x² + y?)dx + xy dy = 0

A: We will solve the problem

Q: The general solution of (D²+2D+1)(D²+4)y=0 is A y=(C,+C,x)e+C,cos2x + C ,sin2r B) none of the given…

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Q: A bank saving account with a fixed interest rate is modeled using the following difference equation:…

A: Given: y(n) -(1+r)y(n-1) = x(n) y(n)   = x(n) + (1+r)y(n-1)     where x(0) = 1500$ , y(-1) = do not…

Q: 2 Y Sin y - yy 3=c C- %3D

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Q: The tanh (2x) sech (2x) dx is equal to sech? (2x) sech (2x) -2*) O A. 1 +C 2(e2 +e 3 10 B. tanh6…

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Q: y =/sin 8x, y = 0, 0 s x s 8 A) 27 В) 8п C) 167 D) 4

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Q: Find the linear approximation at x=0 √(7−x). Write your answer in the form y=Ax+B.

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Q: [₁₁ ) If nd f*. f(x) dx = 4 and g(x) dx = 1, what is the value of ولاء f(x)g(y) dA where D is the…

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Q: So (xs +x) dx 24.47 %3D The bet ween y = sin x and the x - axis for area

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Q: . Solve the given equation by simple substitution. (2x + y)² dx - 2dy = 0 O x + Arc tan 2x+y = C 2 O…

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Q: (ii) Assume that d = in E-coordinates and 7 in B-coordinates. y' Find a' and y' expressed in x and…

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Q: 3. _1ffx,y) = tan—1 (), then X c) (x2 +y2)2 is ܐܐܐ )b ܐ)?x +y(

A: The given function is fx,y=tan-1yx. Find the value of ∂f∂y. Here we use the following formulas -…

Q: Show clear and detailed solutions: Suppose that z is a function of x and y, and tan Vy? + x² = z*e®y…

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Q: (iii) Given that |f(x, y) = e* sin(y) + x²y² = y + 10 a² f əxəy af ax Determine dx and Type your…

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Q: 15. Find all values of the constant c so that (2x + y)dxdy = 3.

A: Given equation is Firstly, we will evaluate the integral.

Q: B شعبة a5f 1- Show that O for the following equation in less than three steps only f (x, y) = x2 +…

A: Partia derivative..Since you have posted multiple questions we will answer first one. For second…

Q: The max value of y=sin x is a.1 b.0 c.1/2 d.2

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Q: The µ(x) that converts the equation below into an exact equation x dy (x*ev ++ (2x²e" + 1) = 0 y) dx…

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Q: Solve for the general solution of (D: - 1)y = sinx using variation of parameters y = cje¯* + ¢ze*…

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Q: 19. Where is the first minimum of y = -2 sin(x - 90°) after x = 0? a. 90° b. 180° C. 270° d. 120°

A: I am going to solve the given problem by using some simple trigonometry to get the required result.

Q: Suppose that f(0) = f(2) and f (2) = 2 and f" is continouos, %3D Find the value of xf"(x)dx (a) 4…

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Q: Q1) solve all these first order diff questions with appropriate method of solutions dy _ y²+xy?…

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

Q: The general solution of the equation xdy – ydx = (x² + y²)dx is a) y = x tan e* b) y = x tan x c) y…

A: Consider the equation: xdy-ydx=x2+y2dx. Find the general solution. Solve for dydx.…

Q: Suppose z is a function of x and y. and tan Vy? + x² = 2"e6y dz dz Solve for and

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Q: 12. What is the equation of horizontal axis of the function f (x) = 2(3 sin x + 2)? a. y = 6 b. y =…

A: For the given function

Q: If a tank holds 8000 gallons of water, which drains from the bottom of the tank in 40 minutes, then…

A: Given: The capacity of tanks 8000 gallons. V=80001-t402

Q: Please

A: Apply the chain rule to find the derivative of the function f(x) = sin2(2x):

Q: C. Given that y = e* sin x, show that d?y +2y 0

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Q: 4. If f f(x)dx= 14 and f (x)dx = 10, find ſ, f(x)dx. Draw a sketch to justify your answer.

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Q: if f(2) = (x +ay-2xy)+i(bx- y + 2xy) is anal ytic, then the values ofa and b is

A: A complex function has the form fz=u+ιv, where u and v are the functions of x and y only. It is…

Q: If y1=2x+4 and y2=x^2+C, find the value of C such that y2 is tangent to y1. O A. 6 В. 5 О С. 7 O D.…

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Q: Which expression gives the length of the curve y = 4x from x=1 to x = 4 ? 4 (A) [ 4x°dx (B) |V1+4x…

A: Given query is to find the expression for length of the curve.

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.