The position of a point at time t = 1 is (2, 4) and velocity of the point at time t is < 2t,3 >. Wha the position of the point at time t = 3? (A) (6, 3) (C) (10, 10) (B) (7, 4) (D) (8, 7)

Q: Solve the equation (y - x + xy cot x)dx + xdy = 0

A:

Q: Given the area in the first quadrant bounded by x^2 = 8y, the line y - 2 = 0 and the y-axis. What is…

A:

Q: Determine all the relative minimum and maximum values, and saddle points of the function h defined…

A:

Q: Find an explicit formula for an. 1 1 4'9' 1 1 14) 1, 16' 25

A:

Q: 2. Evaluate the following definite integral. You can assume the function is defined b the limits of…

A:

Q: 1. Find the most general antiderivative of the function 12 f(x) = ( 2r + sin(4- r) + 7e

A:

Q: dx Which of the following functions satisfy the differential equation = x? dy O x= e o y= e* O x=y O…

A:

Q: Identify whether the given is a discrete or continuous variable. 1.The number of arrivals in an…

A:

Q: Evaluate the defınite integral. i+e"j+t k)dt O el2 12-( - 1) + O el2 – 1 i+ (e-' – 1) j + k el2 – 1…

A: ∫01e12ti + e-t j + t kdt=e12t12i -e-t j + t22 k01=e12112i -e-1 j + 122 k-e12012i -e-0 j + 022…

Q: Evaluate the definite integral. Use a graphing utility to verify your result. (8t – 1)2 dt 0.

A:

Q: Find the absolute maximum/minimum value for f(x)=x² – 4x+1 on the interval [(-3, 3] 9.

A: Given: fx=x2-4x+1 and x∈-3,3   The Power law: ddxxn=nxn-1

Q: Solve the triangle. (Do not round until the final answer. Round angles to the nearest degree and…

A: sine and cosine rule

Q: dy if 6 + sin 2y = dx 2y + 3x by using implicit differentiation. 2y + 3x Find Hence, find the…

A:

Q: If 0 = Ø and R= 4/2, then F2 = %3D 4V2 F, F, V8 08 O 2 04

A:

Q: An open box is made from an 8 inch x 8 inch piece of cardboard by cutting equal squares from each…

A: Volume of the box

Q: Given line M=-ax+ by+ c, b+ 0 What is the y intercept of the function? C-M -M-C OM-c

A:

Q: A cube 3 inches on an edge is given a protective coating 0.1 inch thick. About how much coating…

A: solution:-edge of cube=3 inchescoating=0.1total edge length of cube with coating=3+20.1=3.2…

Q: 25. Compute the Riemann sums for the function f (x)=x² on the interval [0,2] associated with the…

A: See this solution in below

Q: f(x)=/1+2sin x j. f(x)=e" +4* +sinh(10x)

A:

Q: The value x = a is a critical number for f (x). Classify a as a local maximum, cal minimum or…

A: Given f(x) = x^3 -12x^2 Also given x=8 is critical point  now we have check at x=8 has maxima or…

Q: Use the graph of the parabola to fill in the table. (a) Does the parabola open upward or downwa O…

A: a.   Parabola opens downward   b. Coordinate of vertax. Is (-2,-3)

Q: 18. Sand is falling into a cylindrical tank at a rate of 15 cubic feet per minute. The radius of the…

A: Please follow the next step.

Q: P6: x2 dx x² – -2

A: We will use substitution method to solve the integral.

Q: P5: |V4- 9x?dx 4 –

A: Let's find.

Q: 25. æ sec (a²) tan(æ²) dæ | sin? x dx (Hint : cos (2x) 26. 1 27. dx 4- (ӕ — 1)? 1 dx 9x² + 25 28. dx…

A:

Q: Find the general solution of the differential equation dx = xin (xy)

A:

Q: 23. Find two numbers whose sum is 10 and the sum of their squares is a minimum.

A: Let the two numbers be  x and yx+y=10⇒y=10-xx2+y2=SS=x2+10-x2   =x2+x2-20x+100   =2x2-20x+100

Q: Which of the following differential equation has the same order and degree? [dy]6 + 5y = e* A. + 8…

A: See the answer below

Q: Find the 5th order Taylor polynomial about a = r for sin x.

A: To find Taylor polynomial for given function

Q: sin $ 3 y cos*3 ydy

A: We have to solve above integral

Q: 25 2) V1x-91

A: To evaluate first: ∫dx|x-9| Assume the positive factors and multiply the correction factors:…

Q: Evaluate this double integral. Avoid integration by parts. Hint: Can you reverse the order of…

A:

Q: dy 15. Vx eu+ Vx, dx x > 0

A: We have to solve the difference equations

Q: 6. If z = a+i is a root of the equation z² – 6z + 10 = 0, find the value of a, if a is a real %3D…

A:

Q: 4. A live oak tree casts a shadow 58 feet long, Find the height of the tree if the angle of…

A: Here is the solution:

Q: Find the length of the curve z(t) = e“ cos(t), y(t) = e“ sin(t) for 0<t<7. %3D Give an exact answer,…

A:

Q: 4x2-3 f (x) 2х3+x2+7

A:

Q: Sketch the graph and set up the integral of the area of: a). Inside r1, but outside r2 b). Inside…

A:

Q: 6. Compute and write the slope of the tangent lines to dx y - xy +6 = 0 at the point (5,2). a. b. 2y…

A:

Q: Determine C1 and C2 respectively. Determine c, and c, so that y(x) = c,e2" + cze" + 2 sin x will…

A: Given query is to find the value of c1 and c2.

Q: 7/2 SAT sin" x cos3 x dx

A:

Q: V. Determine all the relative minimum and maximum values, and saddle points of the function h…

A: h(x,y)=x^3-3x+3xy2 for critical point  ∂h∂x=0∂h∂y=0 ∂h∂x=3(x^2)-3+3y^2∂h∂y=0-0+3x(2y)for critical…

Q: 12. A force of 170 N is applied to move an object 90 m horizontally. If the force is directed 33°…

A:

Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q…

A:

Q: x(2x² – 1)" dx After substitution is performed, which of the following is equivalent to

A: Given, ∫14x2x2-17dx

Q: Find a formula for the general term a, of the sequence, assuming that the pattern of the first few…

A:

Q: 1. Which of the following integration techniques should be used to evaluate f. sec? x V4 - tan? x}…

A:

Q: f (x)= arcsin (x³)+ aretan (4x)

A: derivative

Q: 6) Shared by the circles r = 2 and r = 4 sin 0

A:

Q: 7) For each set of parametric equations, eliminate the parameter and find a corresponding…

A: