The density of cars (in cars per mile) down a 24-mile stretch of the Pennsylvania Turnpike is approximated by 312 (2+ sin(4√x+0.2)) at a distance a miles from the Breezewood toll plaza. 1. Write a Riemann sum that approximates the total number of cars on this 24-mile stretch. To get x₁, type x_i. ΣΔ i=1 2. The total number of cars on the 24-mile stretch is equal to cars.

Q: 3) a = 222, b = 13 222 = 13 2² × (24)5 X 13 4 × 16 5 13 4 × 35 4 × 243 = = E 13 13 4 × 9 13 36 13 10…

A:

Q: B. Find the inverse Laplace transform using the following methods: 1. Using Partial Fraction…

A: Given Data: Let us consider the given data, Fs=4s+5s-12s+3. To Find: The inverse laplace transform…

Q: b) Give an easy alternative proof of the Bolzano-Weierstrass Theorem.

A: As directed in the question, answer of only part b is provided below :   (b) Bolzano-Weierstrass…

Q: Lagrange multipliers Each function ƒ has an absolute maximum value and absolute minimum value…

A: The given function fx, y=x2+y2 subject to the constraints 2x2+3xy+2y2=7. We have to find the maximum…

Q: Using the formula Ɛijk&mlk Sjk = Skj = - Sim§ji – Siljm, show that ƐijkSjk = 0 for all i if and only…

A: As per the question we are given the relationship between the Levi-Civita symbol εijk and the…

Q: If a function f(x) is continuous on (a, b) and differentiable on (a, b), then the Mean Value Theorem…

A:

Q: If α < α', show that Dα'f⊆ Dαf .

A: Let's assume that α and α' are constants such that α<α', and let f be a function that is…

Q: Give the domain and range of the function. W 2 12345 OA. Domain: (-5,5) Range: [-2,8) OB. Domain:…

A: A graph of the function is given, we have to find its domain and range.

Q: Find the inverse of AB if A-1 and = -5 -1 5 -1 1

A: we need to find (AB)-1 from the given data.

Q: can someone do d

A:

Q: (a) Tell about the convergence (conditionally/absolutely) of alternative series, which for an=1/n…

A: (a)   Alternative series ,for which an=1n                          ∑n=1∞(-1)nan≡ ∑n=1∞(-1)nn…

Q: A company needs a new mechanical device. Compute the present worth for these mutually exclusive…

A:

Q: Find the general solution of the given higher-order differential equation. d4y dx4 - 238² d²y dx² -…

A:

Q: C. Solve the initial value problem of the following DE using Laplace Transform. b.) y"" - 3y" = te³t…

A:

Q: T: R²R¹, 7(e₁)=(2, 1, 2, 1) and 7(e₂) = (-5,2,0,0). where e₁ = (1,0) and e₂ = (0, 1)

A: Rule to find standard matrix is to find matrix with respect to standard basis of both domain space…

Q: Exercise 6 Find a (real) general solution. Show each step of your w y" + 3y + 2y = 12x²

A: We will find general solution.

Q: B C D The graph of the function f, shown above, consists of two line segments. If h is the function…

A: We are given the relation that          h(x) =  ∫0x f(t)dt    for 0 ≤ x ≤ 6  Then, differentiating…

Q: The traffic flow rate (cars per hour) across an intersection is r(t) = 400 + 1000t 180t2, where t is…

A:

Q: Suppose a company has fixed costs of $300 and variable cost per unit of 2x +1460 dollars, where x is…

A:

Q: Let H be a normal subgroup of G and K a subgroup of G that containsH. Prove that K is normal in G if…

A: Assume that H is a normal subgroup of G, and that K is a subgroup of G containing H. Then, we need…

Q: Solve the given differential equation by undetermined coefficients. y" - 14y' + 49y = 35x + 2 y(x) =

A:

Q: Exercise 5K. What must be true about n so that an n x n matrix A satsifies det(-A) = -det(A)?

A:

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A:

Q: Problem 1: Let n > 1 be an integer with the property that whenever n divides the product ab of two…

A: Given: Whenever integer n divides the product ab of two positive integers a, b then n divides a or n…

Q: 1. Let an = Σ where n is a positive integer. 2⁰ i=1 (a) Find a₁, a2, a3 and 4. (b) Guess a simple…

A: (a)   Given that an = ∑i=1n 2 i - 12i        put   n = 1    ⇒  a1 = ∑i=11 2 i - 12i = 2-12=12…

Q: singular value decomposition of a matrix -0.5 0.5 0.5 -0.5] [10 0.5 0.5 0.5 0.5 0 -0.5 -0.5 0.5 0.5…

A: with the help of svd we find matrix A  then we find its norm

Q: (c). Use cylindrical coordinates and the set-builder notation to describe E, and set up, but DO NOT…

A: The given solid region is E that is below the xy-plane and above both paraboloids z=-x2-y2 and…

Q: Find the Midpoint M of the line segment joining the points Q=(-6,5) and D=(0,-3)

A:

Q: Consider the ODE y = f(u), where the graph of f(y) is given below: f(y) Use the above picture to…

A:

Q: Graph f(t)= S cos(A)6(A-2) + A2 (A-4)dA. Justify your graph.

A:

Q: Is the following linear transformation injective? Surjective? (Justify both with full sentences). T…

A: The given linear transformation Tx, y=x+3y, y-2x, y. We have to check T is injective, or surjective.

Q: Find the solution of Non linear higher order partial differential equation…

A:

Q: Compute the volume occupied by revolving a circle of radius 3 m from the axis about 10 m radius away…

A: Sol:- To compute the volume of revolution, we can use the method of disks. We can slice the solid…

Q: Modulo Rules. Find the remainders. a= 3³1; ; b = 17

A: Given: a=331, b=17. We have to find the remainder using modulo rules.

Q: Find the solution of Non linear higher order partial differential equation…

A: Given partial differential equation is                     D2-4D'2z=x3   ⟹ ∂2z∂x2-4∂2z∂y2=x3     For…

Q: (Schr¨oder–Bernstein Theorem). Assume there exists a1–1 function f : X → Y and another 1–1 function…

A: Given: The existence of 1-1 functions f: X→Y and g: Y→X To prove: X~Y

Q: Modulo Rules. Find the remainders. ; b = 11 30 a = 13 Answer!

A:

Q: In how many ways can six people boarding a bus be seated if the bus has nine vacant seats?  ways

A: The number of vacant sets in the bus = 9 . we have to find the number of ways of 6 people can sit in…

Q: Solve the Bernoulli IVP, x²y' - 2xy = 3y¹, y (1) NIT 2

A:

Q: 1. Find the general solution y(x): (a) y + 3y + 2y = 4 e−3x (b) y + 4y = 2 cos 3x. (c) y + y2y = 4x…

A: Q1(f) asked and answered.

Q: 3. Find the unique sequence (an) of real numbers with Σk-0 akan-k = 1 for all n ≥ 0.

A:

Q: 1. If x[n] is given below, sketch the functions listed. a. x[n+4] b. x[3-n] c. x[n]u[n] d.…

A:

Q: Let U = {1,2,3,4,5), A = {1,3,5}, B = {1,3,4), and C = {2,3,5). (a) Find A U (BUC). (b) Find (AUB)…

A:

Q: determine the Laplace transform of the following: f(t)=t+u(t) s+1 OF (s) = 5+¹ OF (s) == OF (s) =…

A:

Q: #1] Let f: R²2 IR and suppose that lim fexys = 5. What can you say about the value (x,y) => (1, 3)…

A:

Q: The equations for free fall at the surfaces of Venus and Jupiter (s in meters, t in seconds) are s =…

A:

Q: 1. Let R be a commutative ring with unity a. Let ✅ be a collection of ideals in R. Prove that ea is…

A:

Q: QUESTION 3 Let f(x) = ³1. (a) Find the average rate of change over [1,2]. (b) Find the average rate…

A:

Q: Calculate Vf using suffix notation and the chain rule: ƒ(r) = 3(a ⋅r)² − a²r² (a is a vector…

A:

Q: Problem 2: Simple questions 2-1) write the solution set of the given homogeneous system in…

A: