4. The position of a point on a line is given by the equation s(t) = t³ — 6t² +9t - 4, where s is measured in metres and t in seconds. a. What is the velocity of the point after 2 seconds? b. What is its acceleration after 4 seconds? c. Where is it when it first stops moving? d. How far has it travelled when its acceleration is 0? e. After 2 second, is it moving toward or away from the origin?

Q: QUESTION 2 Given f(x) = x-3-²x, xo = 1. Use Newton's formula to approximate the values of 1, 2 and…

A: Introduction: Newton's approximation method is a basic method to approximate root of an equation.…

Q: Let S be the surfaced defined by the vector function R(u, v) =, u € [0, 2], v € [-1, 1]. a. Find an…

A:

Q: Problem 4 Problem 4a Problem 4b Problem 4c Find the Laplace transform or the inverse Laplace…

A:

Q: dy sin(x) dx + cos(x) y = tan(x)

A:

Q: In the diagram below ZA = 38°. Side a measures 12 cm. What is the measure of ZB? Express your answer…

A:

Q: Question 15 time (sec) 0 1 2 velocity (ft/sec) 11 19 20 12 3 1 8 feet

A:

Q: *cos(3x)sin³ (3x)dx = a. Use Simpson's rule to approximate the following integrals: (using n b.…

A:

Q: Evaluate the following integrals. ·[³ 1. 2x log 2x dr

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

Q: Define f (x,y) = 3y √1+x² a. Find the rate of change of f at the point (-1, 1) along the direction .…

A:

Q: 10. |G/H| [G:H]. *True False

A: 10. True or False: |G/H|=[G:H]

Q: Given that C = C₁ U C₂ U C3, where C₁ is the line segment from (-1, -1) to (0, 0), C₂ is the line…

A:

Q: Find the solution of the equation z=1/2(p^2+q^2)+(p-x)(q-y) which passes through the x axis

A: Given: The given equation is z=12p2+q2+p-xq-y To find: The solution of the given equation when it…

Q: 10. Using Theorem 6.4. (Gram-Schmidt process) obtain an orthonormal basis 3 v} for span(S). Then…

A: Since you post non interlinking three questions as per our guideline we can solve only first…

Q: 10. Use Green's Theorem to evaluate the integral fe y dx + 2xy³ dy, where C is the square with…

A: Introduction: By applying Green's theorem, one can determine line integral through surface integral.…

Q: In the following problems, find the mean value of the given function over the specified region R.…

A: INTRODUCTION: Numbers in the provided data set are represented by their average value. It is a…

Q: Which of the following represent the volume of the solid cut of the sphere z² + r² = 16 by the…

A:

Q: x 1 2 3 4 5 6 An exponential function. OA linear function. A quadratic function. f(x) None of the…

A: Using the given table, we need determine the function that describes this dataset.

Q: Find the general solution of the given system. X' x = (10_-5)x 8-12, X(t) =

A:

Q: If C is the unit circle x² + y² = 1 oriented counterclockwise and F(x, y) = x F. dR? -T 2π TT î 1 C…

A:

Q: f(x) = x³+1, x<1 1 x+4 Use the composite Simpson's rule to 2 S²₁ 0 n=3. approximate the integral…

A: We have, the given function fx=x3+1 ,    x&lt;11x+4,  x≥1 we get, h=b-an=2-03=0.6667 The value for x…

Q: Four students achieve the following grades on their midterm which was out of 20 marks: 4, 4, 4, 20.…

A: The mode is 4 as its is the highest occurring frequency. So it will reflect the accuracy or more…

Q: Find the inverse of the function on the given domain. f-1 (x) = f(x) = (x - 18)2, [18, ∞)

A: Inverse of function f(x)=(x-18)2 . In the interval [18, infinity) is  f-1(x)= 18+sqrt(x)

Q: Let G be the solid in the first octant bounded by the planes x = y, y = z, z = 0 and x = 1. Set up…

A:

Q: Given that P (10, 12), Q = (10.3, 12.1), f(P) = 50 and f(Q) = 57, = : approximate the directional…

A: Given that P=10, 12,   Q=10.3, 12.1,   fP=50,    fQ=57   To Approximate: The directional derivative…

Q: Consider the function f(x, y) = ax - 2y + 1 where a is a positive number. S SR ax 2y + 1 dA 45,…

A:

Q: or all x ER, it is known that Find the value of ƒ (2022) (0). Find the exact value of f(x) = +∞ 3n…

A: For all x∈ℝ f(x)=xe-x=∑n=0∞(-1)nxn+1n!

Q: Show that the given differential equation is exact and find the general solution. You must use the…

A:

Q: 56²12x³. 3 + - x² X dx a. Use the trapezoid rule to approximate the following integrals: (using n =…

A: We will divide entire interval of integral [0,2] into 4 sub intervals and then apply trapezoidal…

Q: 5. Find the conjugacy classes in D4 and write down the class equation forD4. (To get full credit for…

A: 5. Given is the table of D4.   To Find: The conjugacy classes of D4 and write down the class…

Q: Let f be a function of two variables such that and f(2,1)= 4. f(x, y) = a. If, in addition, x=r cos…

A:

Q: A chemical manufacturing plant can produce z units of chemical Z given p units of chemical P and 7…

A:

Q: A smooth curve C is defined by some vector function R(t) with R = (π,0,−2) and R'(t) = (2, √√5 csc…

A: Since you have asked multiple questions, we will solve the Question Q (1) and (2) for you. If you…

Q: b) Find the equation of the plane containing lines ₁ : x = 2+5t, y = 4+2t, z = -t and l₂: x=2-t₁y =…

A: We have to find the equation of the plane containing lines l1 : x=2+5t, y=4+2t, z=-t and l2 : x=2-t,…

Q: 8. The recurrence relation below expresses the amount owing on a reducing balance loan where…

A: Disclaimer:  Since you have posted a question with multiple sub-parts, we will solve first three…

Q: Consider the polar curves C₁ and C₂, where: • C₁ is the upper half of the circle r = cos 0. • C₂ is…

A: It is provided that: C1 is the upper half of r=cosθ and C2 is the petal of r=cos4θ. We need to…

Q: If M is linear subspace of hilbert space H then M is clos

A:

Q: 15. Evaluate the surface integral ff (x+y+z) ds, where S is the parallelogram with parametric…

A: The surface S is parametrize by R(u,v). Then the elementary surface area ds=|RuXRv|dudv

Q: 8. When a stone is thrown vertically up, its height, h m, above the ground at time t seconds is…

A: Introduction: There are many different ways to solve a quadratic equation. Since, the maximum index…

Q: Assume that the following determinant calculation is correct. 1 0 0 2 1 2 1 3 0 0 4 1 1 2 5 0 = −32…

A:

Q: 4. Solve the Cauchy problem Utt = 9uxx+cos x, (x, t) E Rx (0, ∞) u(x,0)=0, TER u(a,0)=0, x ER using…

A:

Q: Suppose that a particle moves along a straight line with velocity v(t) = 12 4t, where 0 ≤ t ≤ 2 (in…

A: For the particle moving in a straight line  Displacement 12t-2t2 Total distance travelled is 16…

Q: (7) Consider a particle that moves going from the point (-2, 2) to the point (-2, 2) along the…

A: Given: The force field, Fx,y=2x+yx2+y2,2y-xx2+y2   To show: There exists no scalar function g such…

Q: A smooth curve C is defined by some vector function R(t) with R() = (π, 0, −2) and R¹(t) = (2, √5…

A: Since you have asked multiple questions, we will solve the Question Q (1) and (2) for you. If you…

Q: 16x4+9y12 (x,y)→(0,0) 4x²+3y6 Show that lim does not exist.

A:

Q: 7. Express 55C14 + 54C14 +54C15 as a single term from Pascal's triangle.

A:

Q: 2. Let H ≤ G and define = on G by a = b iff a¯¹b € H. Show that =µ is an equivalence relation.

A:

Q: Consider the following normal form of a game. K L M OF OD no dominant strategy (2,3) OE (3,2) (4,3)…

A:

Q: Thm. Let V be an inner product Space and ждек then | 1 ≤ 11all. 1171/ further equility is hold iff…

A: Using the properties of inner product And  aā=|a|2 , for any complex scalar  ||cx||=|c| ||x||, for…

Q: quation dy/dx = (x^2 + y^2)/(xy). I follow all of its steps until this step:  (v^2)/2  =  ln (x) +…

A:

Q: Find the Fourier series for the following functions: f(t)= |sin t], -1 < t < n and The function is…

A: Given Data: Fourier series for the following functions. ft=sin t , -π&lt;t&lt;πand the function is…