Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i, j and k. (a) Same direction as 3i + 2j. u= (b) Oppositely directed to 9i – 6j + 3k. V= (c) Same direction as the vector from the point A(-2, 0, 2) to the point B(2,1,1). W =

Q: Let f(x) = ²15 Find the critical points c that correspond to local minima. (Use symbolic notation…

A: Given :fx=xx2+15

Q: 5. Evaluate the integral. (Use C for the constant of integration.) sin³ (y)cos (y)dy

A:

Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

A:

Q: An open-top storage box with a square base has a capacity of 32 m². Find the dimensions that will…

A:

Q: A = 21° 45', a = 9.5, b = 22 se 1: = ° (smaller B-value) Case 2: B = C = C = O X (larger B-value)

A: topic:- trigonometry ratio in triangle

Q: Find the x-coordinate of the centroid of the area bounded by y (x² − 9) = 1, y = 0, x = 7, and x = 9…

A: Given: yx2-9=1

Q: Metric units only Mount Everest is 29,029 feet high. What is the height of Mount Everest in…

A: Given   Height of Mount Everest =  29029 foot

Q: 3. - 1

A:

Q: Find two unit vectors in 2-space that make an angle of 45° with 6i + 5j. NOTE: Enter the gract…

A:

Q: Professor Calderon wants to build a rectangular fence along a pond so his dogs can go for a swim; he…

A:

Q: The Laplace transform of a continuous function over the interval [0, ∞o) is defined by F(s) = [ e…

A:

Q: 8. Which of the series converge, and which diverge?: n+1 (2) Σ S 3 (c) 1 1 + ln²n (Inn)² n³ (d) n 1…

A: Disclaimer: Since you have posted multiple sub parts of question , we will solve first three sub…

Q: Q1 (a) Show that y= Ae²* + Be ³*, where A and B are constants, is the general solution of the…

A:

Q: Find the critical points c that correspond to local minima. (Use symbolic notation and fractions…

A:

Q: Evaluate

A:

Q: Find the inflection points of f(x) = 3x4 + 17x³9x² + 4. (Give your answers as a comma separated…

A:

Q: Cmin = 3 Find the critical points c for the function f and apply the Second Derivative Test (if…

A:

Q: 8. Determine if the Mean Value Theorem for Integrals applies to the function f(x) = 3 - x² on the…

A: We need to choose correct option.

Q: In some manufacture company, which sales certain product, the price function p and the cost function…

A:

Q: 31) Which of the following BEST describes the application of Cavalieri’s Principle?   a.) The volume…

A: Given ; Cavalieri’s Principle FOR 3D is states that in two 3D figure if they have same Height and…

Q: A linear model of the spread of an epidemic in a community of 1000 people is the equation: dx/dt =…

A: To find the number of people x(t) who have contracted the disease at the time oftime t.

Q: By using the substitution z = cos y, show that the differential equation dy cot y dx X can be reduce…

A: Given differential equation,dydx - cot yx = e3x cosec y

Q: Find the solution of the given initial value problem: y(4) + 2y"+y = 3t + 4; y(0) = y′(0) = 0, y″(0)…

A:

Q: You throw a ball (from ground level) of mass 1 kilogram upward with a velocity of v= 35 m/s on Mars,…

A:

Q: Find the linear least squares polynomial approximation to f(x) on the d. f(x)= e, [C

A: The solution is given below

Q: Question 2 Choose the correct answer. The average rate of change of the function f(x) = x² + 1 from…

A:

Q: Problem 1. L(x) = In 1.05 Find the linear approximation of f(x)= In x at x = 1 and use it to…

A:

Q: Use the figure to find the exact value of the following trigonometric function. tan (20) tan (20) =…

A: We can find tan(2 theta) by multiple trigonometric formula.

Q: In Exercises 1-12, sketch the graph described by the following cylin- drical coordinates in…

A: Since we are given with the multiple number of question and our guideline is solve first question…

Q: 3. Find the formula for the following sequences i. An explicit formula for 2, 6, 18, 54, 162,....…

A:

Q: (True/False) Two lines in three-dimensional space parallel to a plane are parallel to one another.

A: Given that  Is two lines in three dimensional space parallel to a plane are parallel to each…

Q: In each of the problems, apply the method of reduction of order to find a second solution of the…

A: The given differential equation is:x2y''+3xy'+y=0, x>0:The given solution is y1x=x-1=1xWe need to…

Q: y=x^3+5

A: Please refer to the image below

Q: To find the distance between a point X and an inaccessible point Z, a line segment XY is…

A: Given   In △XYZm∠Y=34°,18'm∠Z=94°,48'and z=961 m

Q: Ted is driving east at 80 km/hr and Anthony is driving north at 50 km/hr. Both cars are approaching…

A:

Q: Find the solution of the given initial value problem 88y" +19y" + y = 0, y(0) = -5, y'(0) = 6, y"(0)…

A:

Q: S 3/ 2 V x 3/2 -dx X +4

A:

Q: A farm costs f(x,y), where x is the number of pigs and y is the number of horses. There are 10 pigs…

A: Given fx(x, y) = 2x fy(x, y) = y2 f(10, 20) = 1,000,000 We have to estimate f(12, 19).

Q: 23: Solve the initial value problem 2√ = cos² (y) and y(0) = 2. lease write your answer in the form…

A:

Q: Use the Law of Cosines to solve the triangle. Round your answers to two decimal places. A= B= C= b=5…

A:

Q: Use Heron's Area Formula to find the area of the triangle. (Round your answer to two decimal…

A:

Q: (4- x - x² if x ≤ 2 2x-7 if x > 2 Calculate the following limits. Enter "DNE" if the limit does not…

A:

Q: (a) Find an equation of the tangent plane to the surface at the given point. z = x² - y², (5, 3, 16)…

A:

Q: 1) Find the extrema and possible points of inflection (if any exist) of - In X X

A:

Q: Find y as a function of a if y(0) = 8, y(0) = 4, y"(0) = 134. y(x) = y"8y" -y + 8y = 0,

A:

Q: 3. Evaluate S dA where R is the region between y = 2x and y² = x³ lying to the R left of x = 1.

A: Let's evaluate double integral.

Q: Find sets of parametric equations and symmetric equations of the line that passes through the two…

A:

Q: lim x-x 10 √x + (Inx)¹0 +5 3√x + (lnx) ¹00 + 10

A:

Q: Radar Detectors Radar detectors are either powered by their own battery or plug into the cigarette…

A: We have to find the no. Of ways of given questions.

Q: An airplane needs to head due north, but there is a wind blowing from the northwest at 80 km/hr. The…

A: