(a) Show that if seven integers are selected from the first 10 positive integers, there must be at least two pairs of these integers with the sum 11. (b) Is the conclusion in part (a) true if six integers are selected rather than seven?

Q: A fence 25 feet tall runs parallel to a tall building at a distance of 5 ft from the building as…

A: This is a problem related to height and distance part. Based on the trigonometric concepts we will…

Q: :-1 and g(x) = "- Vx +1 Let f(x)= arccos 2arctanx. (a) Find f'(x) and g'(x). V-1 *-2 arctan Vx ?…

A:

Q: Find the area of the region enclosed by y = 3.25z and z = 5 – y. 3 -2 Use horizontal strips to find…

A:

Q: Find the rate of change of the function at a given value. 1. f(x) = 2x – 3, at x = 5 2. f(x) = 2x² ,…

A:

Q: Use part I of the Fundamental Theorem of Calculus to find the deriyative of 12 १৩) | ( ) = dt f'(x)…

A:

Q: Find the curvature K of the plane curve at the given value of the parameter. r(t) = ti + j, t = 2 K…

A:

Q: Find the gradient of the function at the given point. Function Point f(x, у, 2) : x2 + y2 + z? (7,…

A: Formula for the directional derivative of the function f(x,y,z) is: ∇f = fxi +fyj +fzk Where…

Q: Work Problem 2- a) : Use the Integral Test to verify if the following series is convergent or…

A:

Q: Determine whether the given series converges or diverges. If it converges, find its sum. 8* +7 Σ *-1

A: Solve the following

Q: You are a Math tutor, one of your students asks you to explain the error in his solution to the…

A:

Q: dx Evaluate: (x2 + 4)* (2² + 4) tan- () + 2a + C 16 (22 + 4) A f (x) = (2² + 4) tan-1 (;) +x 16 (a2…

A:

Q: 3. SV1+ V1+x dx

A: Given integral ∫1+1+x  dx

Q: Find the limit algebraically by factoring the expression first. lim X-6 -8x2-56x-48 x + 6

A:

Q: Question The statement below is of the form ren de = F6x) + C. Verify whether the following…

A: Note that: ∫-4x55-5cos(x)dx=-45∫x5dx-5∫cos(x) dx=-45x66-5sin(x)+C=-215x6-5sin(x)+C

Q: Perfo Determine the antiderivatives of the following 1. S sec24x dx 2. S(tanx - 1)2²dx dx 3. S;…

A:

Q: Demand for The Secret Loves of John O, a romance novel by Margó Dufón that flopped after two weeks…

A: Let's find.

Q: Use L'Hopital's Rule to evaluate the following limits. b) lim x? sin (-) 4x²

A:

Q: A motorcycle covers a distance of 48 km per litre of petrol consump- tion. The cost of petrol is…

A: According to given, Let us take 3 variables, m for milage= 48 c for cost of petrol per liter= 20.30…

Q: Solve the following differential equations. 1. 24 – e5x -4y - dx

A:

Q: Oil from a leaking oil tanker radiates outward in the form of a circular film on the surface of the…

A:

Q: 3/2 Construct the fourth degree Taylor polynomial at x= 0 for the function f(x) = 3(1 - x)2. P4(x) =

A: Solved below

Q: c) By using the int 00 series is s c n=1 detail solution.

A:

Q: Use the method of Laplace transforms to solve the given initial value problem. Here, x' and y'…

A: Let's find.

Q: Evaluate the integral by interpreting it in terms of areas. In other words, draw a picture of the…

A:

Q: Evaluate the following integrals. Show the solution. 1. S csc? (7x + 5) dx 2. fx? sec (4x³ + 9) dx…

A:

Q: PART C dy 12. Show that dx 2 for the relation %3D V%3D10, x, y X. # 0. y

A:

Q: solution

A:

Q: Written Works Evaluate the following Integrals. 1. S sin ycosy dy 2. sin3x dx 3 1 3. Jс S cos-y dy |…

A: Given: 1). I=∫sin3ycosydy  ....(1)   As we know that; The Power rule: ∫xndx=xn+1n+1+C ; n≠-1…

Q: Use the method of Laplace transforms to solve the given initial value problem. Here, D[x] and D[y]…

A:

Q: Find the dy/dx for  y = (ex(2x2-1)5)/(x2(sqrt2x+1))

A: This question is based on two diffrentiation rule-: 1. Product rule 2. Quotient rule.

Q: The total cost of producing x instruction manuals is given by the function C(x) = 800 + 27x – 0.6x?…

A:

Q: 2. Find the most general anti-derivative of each of the following functions: a) f(x) = sin(x) b)…

A:

Q: 300 + 900t – 90t, where t is in The traffic flow rate (cars per hour) across an intersection is r(t)…

A:

Q: A sales representative for a company that produces electric mixers can sell x units of their deluxe…

A: Given

Q: d? sin? (5x + V. с. dx2

A:

Q: x 10°)(2.98 × 10-3) (2.446 x 10-3)(62.5) Express your answer using the correct number of significant…

A:

Q: Determine the values of x that causing the following series to converge. (3x- 1)n 2n n=1

A: This is a problem related to convergance of the series. Based on the general formula we will answer…

Q: Use Part I of the Fundamental Theorem of Calculus to find each of the following when f(x) = | t*dt…

A: By using Part I of the Fundamental Theorem of Calculus:f'(x)=x4

Q: Evaluate the definite integral 8 | (2x + 4)dr 2

A:

Q: A non-linear function is given by f(2) = a*-1 Where a is a constant. b) Define the perturbation…

A:

Q: Find the Maclaurin polynomial of the ninth degree for the function h(x) = ln(1+x3)

A:

Q: that has i +j and i – 18j as adjacent sides. NOTE: Enter the exact answers. ||d||= 19 ||d||=|17.12

A: Vector

Q: 9. The growth in the population of a group of rabbits is given by P(t) = 800e008 , where P is the…

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…

Q: 4. A particle moves in a straight line and has acceleration given by a(t) = 6t + 4. Its initial…

A:

Q: Find the area represented by the definite int 8. x-2 dx

A: ∫08x-2dx=∫01-(x-2)dx+∫18x-2dx

Q: Find the domain of the vector-valued function. (Enter your answer using interval notatio r(t) = V 25…

A: Solve the following

Q: please refer to the

A:

Q: Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below.…

A:

Q: Best Publishing makes and sells dictionaries. They have a monthly fixed cost of $5,976 for rent,…

A:

Q: Solve the given differential equation. All solutions should be found. 2ау + у? + 1 x² + 2xy dy dx…

A: