A 3 kg object is attached to a spring and will stretch the spring 29.4 cm by itself. A forcing function of the form F(t) = 10 cos(wt) is attached to the object and the system experiences resonance. The object is initially displaced 14.5 cm downward from its equilibrium position and given a velocity of 7 cm/sec upward. Assume there is no damping in the system and displacement and velocity are positive downward. Use g = 9.8 m/s². Keep the coefficients in your answer exact or round them off to at least five decimal places. a) What is the differential equation of the motion. y' = y y = b) Solve the differential equation to find the displacement as a function of time (t). y(t)

Q: Use the Midpoint Rule with n = 3 to approximate the integral .9 (10x + 10x²) dx 3

A: Given function  f(x) = 10x+10x2Now Lower limit (a) = x0 = 3n = 3Upper limit (b) = x3 = 9

Q: 1 A tank originally contains 100 gal of fresh water. Then water containing - Ib of salt per gallon…

A:

Q: 1. The following matrix 13 row echelon form of the matrix A= 1 O T (a) Find (5) Find (c) Let 3 = -2…

A:

Q: is said to have a horizontal asymptote if either the limit at infinity exists or the limit at…

A:

Q: sketch roughly the given argle and trigonometric functions the -1215° o six = determine the values…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Draw a line that passes through the blue dot and cuts the square in half. • Is the line you…

A:

Q: др др Draw a dependency diagram, and write a chain rule formula for and where p = g(u,v,w), u…

A:

Q: Show that U22 is cyclic. Find all of the generators of U22 and explain how you know that each…

A:

Q: How do I solve this initial value problem? dy/dt=((y^2)-1)^(1/2) at (-1,-2)

A:

Q: For the given function and interval, find the smallest value of n such that the remainder estimate…

A:

Q: 7. Find the area of the parallelogram whose vertices are (1,-2), (7,-1), (-2,1), (4,2).

A: "Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Doing my last lab question just need some help!

A: Given information:Data on height and shoe length is provided in a table.Height values:…

Q: Find the missing number to complete this part-part-whole model. 1,20 3,649

A: A table in which the part-part model is given.The objective is to identify the whole.

Q: Given f(x) = 3x and g(x) = 3x – 1, which of the following accurately describes the end behavior the…

A:

Q: 2. Given the functions: h(r) = 9/1-rl + x and Determine the value(s) for the following: a) h(4) b)…

A:

Q: Find all the hole(s), horizontal and vertical asymptote(s), if any, of the graph of the ollowing…

A:

Q: Suppose det (A - A) = 0. (Show using Theorem 3, which is Let A be nxn matrix. Then the folllowing…

A: Given that . The objective is to show that there exists  such that .

Q: The volume bounded by plane: x + 2 y = z--2 and quadric surface. 1-x² z - 4-y² (a) set up intergal…

A: Given information:The plane  and quadratic surface .To find:Set up an integral to find the…

Q: 2. Assume U= Z, and let A = {..., -6, -4, -2,0, 2, 4, 6, ...} B = {...,-9, -6,-3, 0, 3, 6, 9,...} с…

A: According to guidelines we can solve only first three subparts.given , U=Now

Q: lim X-1 хех xex-e x-1

A:

Q: How many free variables does each augmented matrix have? a. Choose b. Choose c. Choose ✓ d. Choose V…

A:

Q: Question 1 An object is pulled along the ground by exerting a force of 25 pounds a rope that makes a…

A:

Q: Verify that the given differential equation is not exact. (x² + 2xy - y2) dx + (y2 + 2xy - x2) dy =…

A:

Q: Explain the difference between a periodic function and a sinusoidal function. Include an image or…

A: The difference between a periodic and sinusoidal function is shown below in tabular form:

Q: List three mathematicions. for each Foreece mathematical and list Contribution. of ancient

A: Pythagoras ( c. 570 - c. 495 BC )    2. Euclid           ( fl. 300 BC )    3. Archimedes ( c. 287 -…

Q: The following matrices are used in Exercises 35-45. 31 A-1 - - - - - - - - [19] [3₂2]· [ B = 12 21 =…

A:

Q: Find all units, zero-divisors, and nilpotent elements in the following rings: c) Z₁ Z₂.

A:

Q: Write and solve an equation to answer the question. A box contains orange balls and green balls. The…

A:

Q: In Exercises 40-45, express the given vector b as a lin- ear combination of v₁ and v2, where v₁ and…

A:

Q: 5.21 Given a probability space (S,F,P) and a random variable X. Let A be a sub-o-field of F, and…

A: Given that:Let A be a sub--field of F.To show:i)  if  is an A-measurable random variable.ii) Let Y…

Q: -1-9 cos² 6t + 12 sin 6t cos 6t -12 sin² 6t+ 9 sin 6t cos 6t y' = that has periodic (therefore…

A:

Q: If gcd(m,n) = 1 is a given condition, how can you prove that the congruences x ≡ a (mod m) and x ≡ b…

A: The congruences have a solution when .

Q: Given a demand curve of P = 218 - 4Qd and supply of P = 58 +2Qs, find the equilibrium price (Pe),…

A:

Q: solution. Determine whether the following system has no solution, an infinite number of solutions or…

A: According to bartleby guidelines we solve only first question and rest question can be reposted…

Q: Subgroups of Z. We will show that the only subgroups of Z are the subgroups of the form nZ = {nk : k…

A:

Q: A company estimates that 0.7% of their products will fail after the original warranty period but…

A:

Q: et L1 be the line that passes through (2, 1,0) in the direction of (1, -1,2) and L2 be the line that…

A:

Q: Using Discrete Mathematics and language. 33. Is it possible to have a combination of nickels, dimes,…

A: Definitions: n is divisible by d if and only if there exists some integer k such that: n=dkSolution…

Q: Consider the following optimization problem (P) min 21 s.t. x² + ax ≤1 1₂ ≤ 1 where a is a parameter…

A: IntroductionWe consider the optimization problem defined as:minx1  s.t. x12+αx22≤1 x2≤1where is a…

Q: Compute each matrix sum or product if it is defined. If an expression is undefined, explain why. Let…

A:

Q: The doubling time of a bank account balance is 9 years. By what factor does it grow in 36 years? In…

A:

Q: Let P(2,3,1), I be the line that passes through Q(1,0, -1) in the direction of (1,1,2) and P:…

A:

Q: 15. Assume that the vector space R³ has the Euclidean inner product. Apply the Gram-Schmidt process…

A:

Q: In Exercises 9-12, verify that the given matrix A does not have an inverse. [Hint: One of AB = I or…

A:

Q: First verify that the given vectors are solutions of the given system. Then use the Wronskian to…

A: Here we have to verify that x1, x2, x3 are the solutions of x'=Ax.

Q: Let x and y be functions of t. Find the general solution of the system of equations below by first…

A: The objective is to find the general solution.

Q: Use a calculator to compute the left, sum, midpoint sum, and right sum for the function f, using a…

A:

Q: 4.3-1 Use the substitution method to show that each of the following recurrences defined on the…

A: The substitution method for solving recurrences consists of three steps:Guess the form of the…

Q: Evaluate the limit lim x→0+ In cos x X

A:

Q: 1. Analyze the following equation graphically. Sketch the vector field on the real line, find all…

A: The differential equation is .To Find:a) Sketch the vector field.b) Fixed points.c) Stability of…