State what the dot product of two non-zero perpendicular vectors is. Justify your response.

Q: 4. A hockey team plays in an arena with a seating capacity of 15,000 spectators. With the ticket.…

A: Let's find set the ticket prices for maximum revenue.

Q: What is the slope of the line tangent to the polar curve r = ㅠ Ө - ? O 1 √√3 ✓ 2 T -||♡33 √√3 cos at…

A:

Q: O The series Σ7-"[2 +5¹] n=1 converges to none of the choices the above converges to converges to…

A: The above series converges to

Q: In your own language, describe the pattern of the following sequences (The sequences are given as a…

A: We draw required connection between the pattern and formulas as below.

Q: The function f(x) = max x, searches for the maximum value between a number. Prove formally that the…

A: Given; f(x)=maxi .xi

Q: Compute the missing terms in the arithmetic sequence. 72, **** 1)..., 24,

A:

Q: The table shows values of a force function f(x) where x is measured in meters and f(x) in newtons.…

A: Here, the work done is given by: W=∫018f(x) dx

Q: Let D be the region enclosed by y = eª, y = e¯ª, x = 0 and x = 2. The volume of the solid formed by…

A:

Q: Which of the following statements is correct to find the volume generated by revolving about x=0,…

A: using shell method formula of area A = 2πy∫abf(y)dy here a = 0 b = 2 A = 2πy∫02 (8-y3)dy so here…

Q: A(4) = A'(4) -

A: Integration gives area below curve area above x axis is positive area below x axis is negative A(4)…

Q: Q.3) Evaluate the following dx 1) [ x² + 10x + 30 T 2) [²√³x² 3) ² ² 1/2 dx xy y sin x dx dy dx dy

A:

Q: II. Solve the following problems. Enclose final answer. 10. At what rate is the vertex angle of a…

A:

Q: [44 408]. -4 -18 Find the eigenvalues and eigenvectors for A = [64 The eigenvalue a + bi = has an…

A: Using Matrix operation

Q: An architect is asked to design a game room in the shape of an isosceles trapezoid where the non…

A: Let's find fourth side length for maximum area.

Q: 6) Write an equation of the plane through the points P(5,3,8), Q(6,4,9), and R(3,3,3).

A: The plane passing through the points P5,3,8, Q6,4,9 and R3,3,3

Q: cscxdx 5+ cos²x sin²x

A: solution:-∫csc25+cos2xsin2xdx,    {…

Q: Find the domain of the vector function. (Enter your answer using interval notation.) r(t) =(√16-t2,…

A: Explained below

Q: Volumes By Disk Method. Find the volume of the solid generated by revolving the shaded region about…

A: Disk method,  V=π∫abf(x)2dx  (about x-axis) V=π∫cdf(y)2dy  (about y-axis) We have, a=0, b=2,…

Q: 3 2 Evaluate the iterated integral x cos y dy dx. 2 3л 2

A: Ans= 5/2=2.5 For detail go through the solution...I have solved step by step in detail

Q: arbor during a certain 24-hr period is approximated by the function 2]. + 7.9 (0 ≤ t ≤ 24) esponds…

A: The rare of change of a function f(x) at x=c is f'(c)

Q: Convert 2xy + 2 = 0 from rectangular to polar form and solve the resulting equation for r. r =

A: Given

Q: Find the gradient of f(x,y,z) = (x² + y² +z²) ¯ - 1/2 Vf(-21.-2)=(1+Dj+k (Type integers or…

A: topic - gradient of a function

Q: Answer the following. Complete Solution 1. Integrate -2 ex sinx a. dx 0 1+x² 62e

A: F = ∫02exsinx1+x2dxIt is a complex integration hence, numerical method is used.…

Q: 7.Find: 으로 xy of of z = 2x35xyz

A:

Q: Consider - 9 dx. Using rationalizing substitution, we let z = √√e*-9. √√e²-96 What will be the form…

A: The integration of the integral is √(ex-9).

Q: Find the equation of the tangent line to the curve y = √-4 at the point (5,1). Oy=-1 Oy=-1 Oy=2x-2

A: Given y=x-4       point (5,1)To find equation of tangent line:

Q: Find all the second-order partial derivatives of the following function. w=3ye 4x²-y

A: Given :w=3ye4x2-y

Q: The scale of a map measures 1 inch: 1250 miles. If the distance between two cities measures 3 inches…

A:

Q: a) Find the derivative in its simplest form for the following function 1–tanx y = tan-1 ¹

A:

Q: Consider this expression: sin (-9) Reminders: To indicate √√7, then type: sqrt(7). You must type the…

A:

Q: Consider the series an +∞ n=1 and Et bn where cos(+) an = and bn = n3 n3 Since an 2 b₁ and 1 b₁…

A:

Q: Find the eigenvalues ₁ < ₂ and associated unit eigenvectors A = 16 -8 -8 4 The smaller eigenvalue ₁…

A: We can solve this as follows:

Q: Write an equation for the transformed logarithm shown below. Your answer should include a vertical…

A:

Q: 6e at x-b First find where the two curves meet. y = 5e" meets y = 6e where b Then Area = - f(x) dx…

A:

Q: Evaluate sin(x) 1+cos(x) -dx

A:

Q: Solve the following equations by using Cramer's Rule 2x + 2y + z = 1 x-y + 6z = 21 3x - 2y-z = 4

A:

Q: Determine the one-sided limit of the function f in the figure at the given point. (Use symbolic…

A: limx→1-f(x)=3

Q: Л ST 6 77 6 EN F/3 2 3 -0 i 11 6 4) V3 2² 2 27 3 F|N 11 6

A:

Q: A company produces a special new type of TV. The company has fixed costs of $461,000, and it costs…

A:

Q: Evaluate x + 2 S -dx using rationalizing substitution. Which of the following statements is correct?…

A:

Q: 1 S √4x²-9 Ocosh-¹+C -1 -1 Osin ¹+C Osinh¹+C O None of the choices Ocos ¹+C -1 dx

A:

Q: Set up the definite integral required to find the area of the region between the graph of y= 2²-12…

A: find intersection point

Q: 5) Write the equation of the line through the points P(1,3,7) and Q(2,5,11) in: a) Vector form b)…

A: topic - equation of line through two points

Q: Find the eigenvalues λ₁ < ^₂ < 3 and associated unit eigenvectors ₁, 2, 3 of the symmetric matrix 0…

A: Solve by matrix

Q: 1- (x²1) + dy 2xy = 1 ty Cosx Ex Sinh 2- Sin(x) dy dx 3- - dy dx + 3x²y = x²x³ + 4- xlnx dy dy +y =…

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

Q: Find a point c satisfying the conclusion of the MVT for the given function and interval. X y(x) =…

A:

Q: Find the interval of convergence for The interval of convergence is a E n=1 (x − 2)" - n² 2n

A:

Q: Find the volume of the solid of revolution generated by revolving the region bounded by the graphs…

A:

Q: Calculate the integral approximations Tg and Mg for (lnx)-¹1 dx. Your answers must be accurate to 8…

A: Given problem:-

Q: 3) [₁ 10etan (e³x – 3) dx

A: