(-5t -2st5-1 Given that f (t) ={2At– 2B, -1

Q: Find sets of parametric equations and symmetric equations of the line that passes through the given ...

A: To find the parametric equation of a line that passes through a point (-4,0,2) and is parallel to th...

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Q: The plane that contains the points (-2, 1, 0), (1,0, – 1) and (0, –1, 1) is orthogonal to which vect...

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Q: 8. Simplify. Show your work. (V27 + V12 – V32 - V18)(V12 + v3 – V50 – V32)

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Q: Verify that the two planes are parallel. -x + 6y + 3z = 6 1 -x + 2y + z = 7 Find the normal vector, ...

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Q: ind the indicated partial derivatives of: z = Vx2 + y? Dz

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Q: 5. (a) Complete the following unit circle. 0 or 27 11T 6 klo . 프

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Q: (b) f(z)= (4 – 5e*)³ x² + 1 (c) f(r)= ez %3D (d) f(z) = e=²–5z+4 ez-5x+4 (e) f(x)=xe² – e² = re² – e...

A: We can solve this as follows:

Q: Determine whether the lines intersect, and if so, find the point of intersection. (If an answer does...

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Q: b) y = (-x – 1)2 + 2 3 1 -5 -4 -3 -2 -1 1 2 -1 -2 -3 -4 Vertex: Left: Right: 4) 4, 2.

A: The given function,     y=-x-12+2

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Q: 2 -1 se s? +4 .2

A: Given:       L-1se-π2ss2+4 Apply inverse transform rule:       if L-1Fs=ft then L-1e-asFs=Ht-aft-a w...

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Q: Find the area of the shaded region. y-2 y- 2áin(rox)

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Q: 16 – x2 – 4y2 Use a change of variables to evaluate fSS, zdV; where D is bounded by the paraboloid z...

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Q: Pat made the substitution x – 4 = 5 sint in an integral and integrated to obtain f (x) dx = 12t – 2 ...

A: integrate

Q: 2. Determination of integrating factors: 2y(x - y+ xdx+(x² - 2ydy 0

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Q: S 2xln(1+ x)dx

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Q: Sketch the curve x^2+ x^2y^2 = a^2y^2, a > 0. Enumerate the steps in your solution

A: Given curve, x²+x²y²=a²y²....a>0 So, x²(1+y²)=a²y²

Q: 2. S(Vã+ v3)°dx

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Q: B. Provide a short proof. 5. Show that f cot 0 d0 is equal to In|sin 0| + C .

A: We know, d/dθ (sinθ)= cosθ ∫dx/x = ln|x|     

Q: Write 1.24123 1.24123123123123123123... as a ratio of integers using geometric series. %|

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Q: 8y3–1 dy 5. S 2у+1

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Q: Determine whether u and v are orthogonal, parallel, or ne u = (cos(8), sin(0), 3) v = (sin(0), -cos(...

A: We will check if they are parallel or orthogonal. 

Q: Find an equation of the plane with the given characteristics. The plane passes through the points (4...

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Q: Determine whether the planes are parallel or identical. -5x + 3y –8z = 5 15x - 9y + 24z = 14 O The p...

A: Two planes A1x+B1y+C1z =d1  and    A2x+B2y+C2z =d2  are parallel if                      A1A2 = B1B2...

Q: - Given y= ela's -x²-In'r, what is y'?

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Q: 5. (2xy² – 1)* – 3x²y³ – 1 = 0, find y' -

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Q: In the differential equation (xy +1)dx + x(x+4y- 2)dy = 0, the integrating factor is

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Q: Let a = ci + jand b = 7i + 35j. Find c so that a and b are orthogonal. C = i

A: Dot product of two vectors

Q: (c) Determine the definiteness of the quadratic form q(x) = x} + 2V6x,Xz + 2x3

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Q: A baseball diamond is a square, 90 feet on each side. The instant a runner is halfway from home to f...

A: Rate of change

Q: Solve each problem A segment has a midpoint at (10. 5, –0.5) and the endpoint at (6, 11). What are t...

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Q: Obtain the particular solution satisfying the initial conditions indicated. 1. e* (3x°y-x)dx+e" dy =...

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question fo...

Q: 3. In the differential equation (y -x -4r-1dy + 2y(x+y+2)dx = 0, 心

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Q: | by inspection: (3y° + xy kdx + (x°y² – 2}kty = 0 1. Integrating factors found

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Q: Find a set of parametric equations of the line with the given characteristics. (Enter your answers a...

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Q: Given the following inormation about the hyperbola, find both its standard and general form: Foci: ...

A: To solve the following problem

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given ...

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Q: hort proof. 5. Show that cot 0 d0 is equal to In|sin 0| + C.

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Q: SS, (x + y)e**-y´dA where R is the rectangle enclosed by x – y = 0,x – y = 2, x + y = 0, and x + y =...

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Q: Question 4 Find the points on the curve y = tan æ, where the 2 2 tangent is parallel to the line y 7...

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Q: (-x- 3 if x 2 A) -1 B) does not exist. C) 6 D) 00

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Q: Suppose f is differentiable on (a, b). If c E (a, b) and f' (c) = 0, thenf (c) is either the maximum...

A: Given f is differentiable on (a,b). and c lies in (a,b) such that f'(c)=0.

Q: Determine whether the planes are parallel or identical. -6x + 4y – 9z = 5 18x - 12y + 27z = 14 O The...

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Q: Determine whether the lines given by the symmetric equations x - 1 y - 2 z - 3 %3D 2 3 4 and x +1 y ...

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Q: ∫(x2dx) / (√1+ x)

A: We know, ∫xndx =xn+1n+1+C, C is a constant.

Q: . The exact differential d(xy)= xdy + ydx, what is the d( = 4x²y'dy+2xy*dx.

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Q: 2 sin (3x) d%

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Q: sin "x cos“x dx cos²a 4.

A: We will use simple Integration technique to solve this question.