13. Obtain the differential equation of the family of straight lines at a fixed distance p from

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A: Vertical asymptote of the rational function f(x)=p(x)q(x)is given  q(x)=0

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Q: a) How many 3-digit positive integers are there with odd digits?

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A: If f is a function of x and y then gradient of f is given by ∇f=∂f∂xi^+∂f∂yj^So, ∇fa,b is given by…

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A: The given terms of the geometric sequence,a3=123 and a6=-419

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A: (6x-1)/x(x-4) it is very simple because in numerator there us multiplication given so A/x + B/(x-4)…

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A: Find your answer below

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A: We will use critical points for calculation

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Q: lim e 0 t/ Select one True False

A: limx→0+e1xusing chain rulelet f(x) =1xg(u) =eulimx→0+ f(x) = limx→0+ 1x =∞

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A: We have to use simple derivative of the function to solve the problem

Q: If a = (3, –3, –10) and b = (-8, –4, –10) find a · b =

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Q: Complete the parametric equations for the line where the planes 8x + 13y – z = 27 and 9x + 15y – 12z…

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Q: "ind general solution for dy dy + 3 + 2y = -20 sin 2t, y (0) = 2, y' (0) = 1. dt2 dt

A: Ode

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Q: Find f. f" (0) = 2e® + 3 sin 0, f(0) = 0, f' (0) = 1 Using O for 0. O f(0)=2e^O -3sin O f(0)=2e^O…

A: Given query is to find the function f(O).

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Q: State whether the following numbers are rational or irrational. a) V4 + 7/2 b) V36 c) V11²510716

A: We have to find if the numbers are rational or irrational.   According to our guidelines we can…

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Q: At what point(s) on the curve x = 3t2+1, y= t3 -1 does the tangent line have slope?

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Q: The equation x10 – 10x2 +5 = 0 has a root in (0, 1) Select one: True False

A: We want to check true or false.

Q: 6. Differentiate y with respect to x using A-method. x-3 a. y = X b. у %3D V4x + 3

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Q: In Problems 17-20, find the indicated values of f(x, y, z) = 2x - 3y2 + 5z - 1 19. f(6, -5, 0)

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Q: Solve the differential equation. dy = 5 ex-y dx Choose the correct answer below. O A. y= 5 e* +C O…

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Q: Let a = ci +jand b 7i + 56j. Find c so that a and b are orthogonal. %3D %D C =

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Q: Which of the following are disjoint sets? * (1,3,5) and (1,3,6) O (1,2,3) and (2,3,4} ) (1,2,5) and…

A: Given query is to find the disjoint set.

Q: Determine if the following statement is true or false. The points P1(14, 8, 9), P2(7, 4, 0), P3(0, –…

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Q: Find equutiuns Ofthe followicy t. 9 tangent Aane b) The nomauf line

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A: Vector

Q: 33. f(x, y) = xr – 3xy² + 6y²

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Q: Write the form of the partial fraction decomposition of the rational expression. Do not solve for…

A: Reducing to partial fractions

Q: Find the slope of the line that is tangent to the 2x-3 graph of f (x) at P(3/2, 0)

A: Slope of the tangent to tthe curve y=f(x)  at point (a,b)  is given as m=f'(a)

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