The function f(x)=3x+2 is one-to-one

a) find the inverse of f

b) State the domain and range of f

c) State the domain and range of f^-1

d) Graph f,f^-1, and y=x on the same set of axes

a. consider the plane with equation -x+y-z=2, and let p be the point (3,2,1)in R^3. find the distance from P to the plane.

b. let P be the plane with normal vector n (1,-3,2) which passes through the point(1,1,1). find the point in the plane which is closest to (2,2,3)

The COV-19 virus has virtually changed the way we work, study and shop. People are scared and frightened of contracting the deadly virus. Traditional grocery stores such as Loblaws, Longo’s, etc. have seen fewer shoppers, who also spent less time in the stores. A survey of 500 Canadian grocery shoppers was conducted last week to find out if the scare of contracting the COV-19 virus, (very scared , VS) or (somewhat scared, SS) has affected their grocery shopping habits: whether they purchase groceries online (OL) or they purchase at a conventional grocery store (TS).The survey reported that 400 shoppers purchased online and that 150 of all shoppers were somewhat scared. The survey also reported that 75 Canadians shopped online given that the shopper was somewhat scared.

a) Construct a cross-classification (or contingency) table with joint and marginal probabilities. [or you can construct a tree diagram].

b) What is the probability that a randomly selected shopper is very scared and shops online?   

c) What is the probability that a randomly selected very scared shopper buys from a traditional grocery store?

d) What is the probability that a shopper who shops online is somewhat scared?

e) What is the probability that a randomly selected shopper is somewhat scared or shops online?

f) Are “somewhat scared” and “online” independent events or dependent events or mutually exclusive events? Your answer must include supporting probability calculations.

Show that if P;Q are projections such that R(P) = R(Q) and N(P) = N(Q), then P = Q.

A gift shop expects to sell 400wind chimes during the next year. It costs $1.20 to store one wind chime for one year. There is a fixed cost of $⁢15 for each order. Find the lot size and the number of orders per year that will minimize inventory costs.

T̶w̶o̶ ̶l̶i̶n̶e̶a̶r̶l̶y̶ ̶i̶n̶d̶e̶p̶e̶n̶d̶e̶n̶t̶ ̶s̶o̶l̶u̶t̶i̶o̶n̶s̶ ̶o̶f̶ ̶t̶h̶e̶ ̶f̶o̶l̶l̶o̶w̶i̶n̶g̶ ̶e̶q̶u̶a̶t̶i̶o̶n̶ ̶(̶1̶ ̶−̶ ̶x̶)̶ ̶y̶″̶ ̶ ̶+̶ ̶ ̶x̶ ̶y̶′̶ ̶ ̶−̶ ̶ ̶y̶ ̶ ̶=̶ ̶ ̶0̶ ̶

a̶r̶e̶ ̶ ̶y̶1̶(̶x̶)̶ ̶ ̶=̶ ̶ ̶3̶e̶^̶x̶ ̶a̶n̶d̶ ̶ ̶y̶2̶(̶x̶)̶ ̶ ̶=̶ ̶ ̶6̶x̶.̶ ̶

a̶)̶ ̶F̶i̶n̶d̶ ̶t̶h̶e̶ ̶W̶r̶o̶n̶s̶k̶i̶a̶n̶ ̶W̶(̶y̶1̶,̶ ̶y̶2̶)̶ ̶o̶f̶ ̶y̶1̶ ̶a̶n̶d̶ ̶y̶2̶.̶ ̶

(̶b̶)̶ ̶U̶s̶i̶n̶g̶ ̶t̶h̶e̶ ̶m̶e̶t̶h̶o̶d̶ ̶o̶f̶ ̶v̶a̶r̶i̶a̶t̶i̶o̶n̶ ̶o̶f̶ ̶p̶a̶r̶a̶m̶e̶t̶e̶r̶s̶,̶ ̶f̶i̶n̶d̶ ̶a̶ ̶p̶a̶r̶t̶i̶c̶u̶l̶a̶r̶ ̶s̶o̶l̶u̶t̶i̶o̶n̶ ̶o̶f̶ ̶(̶1̶ ̶−̶ ̶x̶)̶ ̶y̶″̶ ̶ ̶+̶ ̶ ̶x̶ ̶y̶′̶ ̶ ̶−̶ ̶ ̶y̶ ̶ ̶=̶ ̶ ̶2̶(̶x̶ ̶−̶ ̶1̶)̶^̶2̶ ̶(̶e̶ ̶^̶−̶x̶)̶

1. Find the general solution of the given system using the characteristic equation

dxdt=6x-y
dydt=5x+2y

1. Find the general solution of the given system using the characteristic equation

dxdt=6x-y
dydt=5x+2y

1. Test the series below for convergence using the Root Test.
∞∑n=1 (2n/7n+5)^n
The limit of the root test simplifies to lim n→∞ |f(n)| where
f(n)=   
The limit is:    
Based on this, the series

• Diverges
• Converges

2. Multiple choice question.  We want to use the Alternating Series Test to determine if the series:

∞∑k=4 (−1)^k+2 k^2/√k5+3

converges or diverges.
We can conclude that:

• The Alternating Series Test does not apply because the terms of the series do not alternate.
• The Alternating Series Test does not apply because the absolute value of the terms do not approach 0, and the series diverges for the same reason.
• The series converges by the Alternating Series Test.
• The series diverges by the Alternating Series Test.
• The Alternating Series Test does not apply because the absolute value of the terms are not decreasing.

Find the equation of a circle that passes through (1,7). (6,2) and (4,5) using a matrix.

Use two functions below for parts a and b.
 ?(?)=??−?
 ?(?)=ln(?)+ln(1−?)+3
a) Find the stationary points, if any, of the following functions and label them accordingly (local or global minima/maxima or inflection point).
b) Characterize the above functions as convex, concave or neither convex nor concave

Determine the eigenvalues and the corresponding normalized eigenfunctions of the following Sturm–Liouville problem: y''(x) + λy(x) = 0, x ∈ [0;L], y(0) = 0, y(L) = 0,

True/False

If SS is a sphere and FF is a constant vector field, then ∬SF⋅dS=0.

Part 1. Describe the boundaries of the triangle with vertices (0, 0), (2, 0), and (2, 6). (a) Describe the boundary with the top function, bottom function, left point, and right point. (b) Describe the boundary with the left function, right function, bottom point, and top point.

Part 2. Consider the triangle with vertices (0, 0), (3, 0) and (6, 6). This triangle can be described using only one of the two perspectives presented above: top-bottom or left-right. Explain which perspective can be used and describe the region using that perspective. Write and label the boundary functions and points. If you want to use the other perspective, then you’ll have to split the shape into two different parts, each of which can be described using that perspective.

Part 3. Split the triangle in the previous exercise into two triangles. Describe each triangle as a region using the perspective you didn’t use in the previous exercise.

Solve the initial value problem y’cosx = a + y where y(π/3)=a and 0

please explain how you do everything

Find the area of the surface correct to four decimal places by expressing the area in terms of a single integral and using your calculator to estimate the integral.
The part of the surface z = e^{-x^2 - y^2} that lies above the disk
x2 + y2 ≤ 49

Please write clearly and show work. I am having trouble the the rdr integral.