A comet passing by a star, with initial velocity (30, 60), experiences a force which causes it to accelerate according to a(t) = (-25e' – 25e¬t, 25e' – 25e-t) (in m/sec?). Find a formula for its velocity at time t.

Q: 1.Determine the formula for the nth term of the following sequences: а, 3 3, ап+1 %3D 2а, ; n 2 1 FO...

A: Given: a1=3an+1=2an ;         for  n≥1

Q: Given the angles a, B where 0 < a, B < - which of the statements is TRUE? 4 O The angle a+B is in QI...

A: Topic = Trigonometry

Q: 22. Compute the given integral. S sin (2x)dx

A:

Q: ху'- у - 5х1 — Зх? + 2х %3D 0

A:

Q: S(x, y, z) = 2x'y²z²

A:

Q: x24x+13

A: We will find the integration of the given function.

Q: Whic of the following is NOT a solution of 2 sin? t – cost - 1 = 0 if 0 <t < 2n ?

A: Follow the procedure given below.

Q: 5. Find the linear approximation (i.e. the tangent plane) of f(x, y) = Vx/y at the point (9, 4) and ...

A: The Local Linear approximation of f at (x,y) using the partial derivative f at (x0,y0) is given by  ...

Q: Find the particular solution for the differential equation: y' + xe = -2x %3D for the boundary condi...

A: Topic = Differential equation

Q: Find one or more values of each of the following complex expressions

A: We need to compute the value of the given expression.          e2tanh-1i

Q: 0.3, and fy(2,4) 6. Assuming that f(2,4) = 5, f«(2, 4) approximation for f(2.1, 3.8). -0.2, find a l...

A: Given that: f(2, 4)=5, fx(2, 4)=0.3 and fy(2, 4)=-0.2

Q: (x – 1)2 (y + 1)2 1? Which of the following lines is an asymptote of the hyperbola 9. O 3x + 2y - 1 ...

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Q: - Given: mZB = 33°; b = 12.5; m2C = 67° Find c. %3D %3D

A:

Q: 2) The limit below represents the derivative of some function f(x) at some number a. limh→02(2+h)^6...

A:

Q: Complete

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Q: Find m angle C

A: Topic:- trigonometry ratios in triangle

Q: ху (x+ Vy² + 1)dx – (y - dy = 0 2+1 4.

A:

Q: A plane flying parallel to the ground at a height of 4 km passes over a radar station R. A short tim...

A: NOTE: Refresh your page if you can't see any equations. . here we have y=4 when s=5, s'=300 km/h

Q: esin² 3y? dy csc 6y

A: The Value of the given integral is esin²3y²/6

Q: Which of the following statements is true about the equation of an ellipse that satisfies the follow...

A:

Q: [ san28 e tan 20 ,tan 28 sec 2 Bd

A:

Q: Find the standard form of the equation of the hyperbola with the given characteristics. Vertices: (±...

A: We will find the equation of the hyperbola when vertices and asymptotes are given.Below find the det...

Q: Obtain the solution of the following differential equations. 7. xy′ − y − 5x^4 − 3x^2 + 2x = 0

A:

Q: Evaluate the indefinite integral (7t)cos(10t) dt %3D + C

A: 2 cos(A)sin(B) = sin(A+B) - sin(A-B)

Q: Obtain the solution of the following differential equations. 4. y′ =x2+y2/xy

A: Since you posted multiple question in this question which are not interlinked so  have solved first ...

Q: 12. Find the first derivative of y = 2cos(2 + x?). A. -4x sin (2 + x²) B. 4x cos (2 + x*) C. x sin (...

A: Since you have posted multiple questions. As par guidelines we"ll solve first question only. If you ...

Q: 3. The disk and cylindrical shell methods for calculating the volume of a solid of revolution always...

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Q: 4. (x + Vy? + 1)dx-(y y-: dy = 0 Vy2+1, %3D

A:

Q: 1. y = x + 3V72. y = x - 3V 3. y = 3x"4. y = -5x + 25. y

A: Since you have asked multiple question, we will solve the first 3 subparts question for you as per o...

Q: Si cos°(3x)sin (3x) – cos (3x) sin°(3x) dx

A: First we common out cos7(3x) sin7(3x) and then apply the formula cos2(3x)-sin2(3x)=cos(6x)

Q: Find the average value on the interval 3, 6 of the function whose graph appears below. average value...

A:

Q: Solve the differential equation with appropriate method. Finalize answer free of logarithms and radi...

A: Here we have to solve the given differential equation.

Q: 27 4 1422 Evaluate the integral: 36 - (A) Which trig substitution is correct for this integral? Ox =...

A:

Q: Use integration by parts to show that, for n > 2, 1 cos a sin"-1 n 1 sin"-2 xdx. n - sin" xdx = x + ...

A:

Q: 2. Find the equation of the tangent line to the parabola y = x² – 8x+9 at the point (3, –6)

A: Given y=x2-8x+9 Formula: dydx(xn)=nxn-1 dydx(k)=0, where k is a constant Consider y=x2-8x+9 Differen...

Q: Find the equation of an ellipse with center at (2,-2), vertex at (7,-2) and focus at (4,-2)? O (x + ...

A: We have to find the equation of ellipse

Q: Find (with proof) all the triplets of integers a, b, c that satisfy a? + b² = 6c².

A: Note: (a,b,c) = (0,0,0) is the trivial solution. We will look for non-trivial solutions.  

Q: In the adjoining figure, point Q is the center of the top face, and R is midpoint of the segment. R ...

A:

Q: the standar form of the equation of the hyperbola with the given characteristic Foci: (0, 19); asymp...

A:

Q: 4 7 7x+25 - Error Analysis. A classmate said that the sum of r²-9 and x+3 is -9 -

A: Given,            The sum of 4x2-9 and 7x+3 is 7x+25x2-9.To find : What mistake did your classmate m...

Q: Let f(x, y) = sin(x – y). Calculate the directional derivative of f in the direction of v = (1, 1) a...

A:

Q: a? + 6x + 9 1. For the function g (a) answer each of the following questions. %3D x² + 3x (a) Evalua...

A: We need to find values of function at x values.

Q: find a standard equation of the line perpendicular to the line ax+by=c that passes throughpoint(xo,y...

A:

Q: 5e*dx V9-12e3* +4e6x

A:

Q: Find the area of the surface obtained by rotatin the curve y = Va about the y - axis for 64 < x < 10...

A:

Q: For the following equation, show solution for determining the coordinates of the point of intersecti...

A: The given problem can be evaluated as follows:

Q: x+1 dx

A: We need to integrate∫x3+1xdx

Q: Simplify f(x). х3 — 4x2 - 16х + 64 f(x) = X - 4 x² – 4 for x * 4 f(x) =

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Q: 5T is equivalent to 12 The expression csc 1- 2 sin? 12 1 Cos 6. - 1- cos 6. 5 2 cos? 6 - 2]

A: Topic = Trigonometry Correct option  csc5π12=21-cos5π6  

Q: S(x5 + 10)®x*dx 4 X.

A: