The displacement (in meters) of a particle moving in a straight line is given by s= t2 - 5t + 16, where t is measured in seconds. Find the average velocity from 3.1 to 4 seconds. Average Velocity = ___________ meters/second. (2 decimal places)

Q: Diagonalize the following matrix. The real eigenvalues are given to the right of the matrix. -21 1…

A:

Q: 0 Compute the integral: I alned

A: LetI=∫01xlnxdxApply integration by…

Q: Solve the following problems showing detailed solutions. Draw the complete figures for each…

A:

Q: Problem: 1. Find the area bounded by the curve y = x² and the line y = 6.

A: Given query is to find the area bounded by the curve.

Q: 1. Graph the function below Using Calculus, find the intervals where the function increases and…

A:

Q: Solve the system of differential equations. = - X1 6x1 + 2x2 X2' - 2x1 - 10x2 2, x₂(0) - 22 = x1 (0)…

A:

Q: [x³√₁-x² x2

A:

Q: M8 1 Σ n=1 h n’ + 8 +8 3

A:

Q: Evaluate the equation f Select one: a. 0.5 b. -1 Oc. 2 Qd. 1 dzdy

A:

Q: 4. Given that f'(x) = −6x² + x + 12 and f(1) = 7, find f(x).

A: Given : f'(x)=-6x2+x+12f(1)=7   To Find : f(x)

Q: 1. F(s) = 4s+2 s²+6s+34

A:

Q: Without using the graph, determine all inflection points of a + x².

A: For inflection point , set f''(x)=0.

Q: The time required for an elevator to lift a weight varies directly with the weight and the distance…

A:

Q: Use the binomial theorem to expand the expression (u - 5v)¹

A:

Q: 2 Brad wants to buy a coffee machine for his café. The advertised price is $3200 including GST. When…

A:

Q: (x-1) dy + (y-2) dx = 0

A: To solve the given differential equation

Q: A lamina occupies the part of the disk æ² + y² ≤ 1 in the first quadrant and the density at each…

A:

Q: 3 − 4 + 16 - 64 + ...

A:

Q: In 1000 5 X limx→ +00 X

A:

Q: Find the volume of the solid of revolution obtained by rotating the region bounded by y=1/x, y=2/x,…

A: This question is based on application of integration.

Q: d. lim, In 1000 x ,5

A: Here, note that the function ln1000x grows asymptotically slower than the polynomial x5.

Q: Given : f(x) = 10 -x 9(x) = x² - 4x-2 Find and simplify (fºg)

A:

Q: √x³√1-x² 2

A:

Q: Directions: apply the limit theorem 3 1. lim x-24 2. lim-45 x-2 62 3. lim x 2 3 4. lim x x-2 5. lim…

A: Please refer to the image below

Q: 1. Evaluate the given integral Q. Q a = 1₁² 1₁² ² (x - y) dx dy 2. Sketch the region of integration…

A: double integral and changing the limit

Q: 9) Find the equation of the tangent to the curve y = 1+ Int and x=t+Int when t = 2.

A: Given problem:- Find the equation of the tangent to the curve y = 1 + lnt and x=t+Int when t = 2 .

Q: 2-201 0 1 1 1 103 A = 0 1 -1 3 0 1 1 1 1 1 1 Which is the element A3,2?

A: To find the element A3,2  of the given matrix A.

Q: clnx Find the integral of ²x ye²dzdxdy

A:

Q: 6) A force, F, of 52 N is acting in the direction of a = [2,5] a) Find a unit vector in the…

A: We need to find unit vector and force.

Q: Given: f(x) = 10-X Find and simplity (fof)

A: We have to find the composite function.

Q: d. In 1000 x limx→+00 X5

A: Let's evaluate limit.

Q: 3x 4. Find the member of the curve whose slope at any point is and passes through the 4y

A:

Q: Find the critical points and sketch the graph of the function. 1. f(x) = √5 + x 2. f(x)=x²-3x³ + 3x²…

A:

Q: TC √³x² x² sin3x dx

A:

Q: Evaluate x³ dx (x4-5)4

A:

Q: Perform bisection method on approximating the root of the equation x³ + x²-x + 7 = 0. Use initial…

A:

Q: What is the period of the graph below? sto 8+ 7+ 6+ him

A: As we can see graph  Function repeat his value after every 4 point .

Q: Convert each pair of polar coordinates to rectangular coordinates 1. (1, 60 degrees) 2. (1, 300…

A:

Q: A parabola has an equation of y - 3x = 0. Compute for the surface area of the solid generated by…

A:

Q: Using vectors, find the area of the triangle with vertices P(5, -1, -3), Q(7, 2, -4), and R(6, 1,…

A:

Q: 3t4 - 6t+ 3et Let f(t) = Then f'(t) =

A:

Q: 4) (1, 150°) 120° 150° 180° 210⁰ 240 90° 270⁰ 60° 2 3 300⁰ 30° 4 330⁰ Ꭴ

A:

Q: If zs² + yt²= 1 and 2²s+y³t = ry - 4, find 0x/0s, az/at, Əy/08, Əy/ot, at (x, y, s. t) = (1, -3,2,…

A:

Q: √81.4305 Using Linear Approximation, evaluate below. Answer must be in FRACTION.…

A:

Q: Sx" xn sinx dx = −x” cosx+n n-1 cos x dx

A:

Q: Using the laplace transformation table, evaluate the following, considering any other variable other…

A:

Q: 2 2 dx 2x (V2x + 9)

A:

Q: Electric charge is distributed over the disk x² + y² ≤ 11 so that the charge density at (x,y) is…

A:

Q: Refer to the given figure, if ABCD and m/2 = m25= 70°, complete the table by finding the measures of…

A:

Q: 1. f(t) = (t5+t) (t³ - 4t+1) 2. g(x) = (+1)(3x - 1) 3. h(x)=¹

A: Topic:- function