Given two planes 2x - y + z = 7 and x + 3y - 4z = 1.
(a) Give an orthogonal vector to each plane.
(b) Do the planes intersect? Why or why not?
(c) If they intersect, find the parametric equation of the intersection line, if not, find the distance of both planes.
In: Advanced Math
Let G be a simple undirected graph with n vertices where n is an even number. Prove that G contains a triangle if it has at least (n^2 / 4) + 1 edges using mathematical induction.
In: Advanced Math
Use induction to prove that for any positive integer n, 8^n - 3^n is a multiple of 5.
In: Advanced Math
1. Find the quotient and remainder when 74 is divided by 13.
2. Use the Euclidean Algorithm to find the GCD of 201 and 111.
3. Express your answer to #2 as a combination of 201 and 111.
4. In Z7 compute the following: a. 4+6, b. 4. 6, c. 35.
In: Advanced Math
For the given functions f and g, complete parts (a)-(h). For parts (a)-(d), also find the domain.
f left parenthesis x right parenthesis equals StartFraction 7 x plus 9 Over 9 x minus 7 EndFractionf(x)=7x+99x−7;
g left parenthesis x right parenthesis equals StartFraction 9 x Over 9 x minus 7 EndFractiong(x)=9x9x−7(a) Find
(fplus+g)(x).
(fplus+g)(x)equals=nothing
(Simplify your answer.)What is the domain of
fplus+g?
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.The domain is
StartSet x vertical line nothing EndSetx .
(Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)
B.The domain is
StartSet x vertical line x is any real number EndSet{x x is any real number}.
(b) Find
left parenthesis f minus g right parenthesis left parenthesis x right parenthesis(f−g)(x).
left parenthesis f minus g right parenthesis left parenthesis x right parenthesis(f−g)(x)equals=nothing
(Simplify your answer.)What is the domain of
f minus gf−g?
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.The domain is
StartSet x vertical line nothing EndSetx .
(Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)
B.The domain is
StartSet x vertical line x is any real number EndSet{x x is any real number}.
(c) Find
(ftimes•g)(x).
(ftimes•g)(x)equals=nothing
(Simplify your answer.)What is the domain of
ftimes•g?
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.The domain is
StartSet x vertical line nothing EndSetx .
(Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)
B.The domain is
StartSet x vertical line x is any real number EndSet{x x is any real number}.
(d) Find
left parenthesis StartFraction f Over g EndFraction right parenthesis left parenthesis x right parenthesisfg(x).
left parenthesis StartFraction f Over g EndFraction right parenthesis left parenthesis x right parenthesisfg(x)equals=nothing
(Simplify your answer.)What is the domain of
StartFraction f Over g EndFractionfg?
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.The domain is
StartSet x vertical line nothing EndSetx .
(Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)
B.The domain is
StartSet x vertical line x is any real number EndSet{x x is any real number}.
(e) Find
(fplus+g)(44).
(fplus+g)(44)equals=nothing
(Type an integer or a simplified fraction.)(f) Find
(fminus−g)(33).
(fminus−g)(33)equals=nothing
(Type an integer or a simplified fraction.)(g) Find
(ftimes•g)(22).
(ftimes•g)(22)equals=nothing
(Type an integer or a simplified fraction.)(h) Find
left parenthesis StartFraction f Over g EndFraction right parenthesis left parenthesis 2 right parenthesisfg(2).
left parenthesis StartFraction f Over g EndFraction right parenthesis left parenthesis 2 right parenthesisfg(2)equals=nothing
(Type an integer or a simplified fraction.)
In: Advanced Math
A firm faces the demand schedule as ? = 660 − 3?
and the total cost schedule as
?? = 6?^3 − 72?^2 + 240? + 25. Please answer the followings:
a. Does the above cost function satisfy the parametric restrictions
we derived in the class?
b. What is the maximum profit the firm can make? Confirm your
results with second order
conditions as well.
In: Advanced Math
Use the Laplace transform to solve the given system of differential equations. dx/dt + 3x + dy/dt = 1 dx/dt − x + dy/dt − y = e^t x(0) = 0, y(0) = 0
In: Advanced Math
let a be a non zero constant and consider: y''+(1/t)y'=a
a. show that 1 and ln(t) are linear independent solutions of the corresponding homogenous equation
b. using variation of parameters find the particular solution to the non homogenous equation
c. express the solution to the non homogenous equation in terms of a. and b.
d.since y itself does not appear in the equation, the substitution w=y' can be used to reduce the equation to a linear 1st order equation. use this substitution to solve for w directly using a 1st order technique and verify that the two techniques produce the same answer
In: Advanced Math
Prove the following Theorems:
1. A finite union of compact sets is compact.
2. Any intersection of compact set is compact.
3. A closed subset of a compact set is compact.
4. Every finite set in IRn is compact.
In: Advanced Math
Given 2y' + 1.5y = 5x, y(0) = 3.3,
What is the value of y(3) using Ralston's method and a step size of h=1.5
Keep 4 decimal places
In: Advanced Math
Solve the LP problem using graphical method. Determine the optimal values of the decision variables and compute the objective function.
Maximize Z = 2A + 10B
Subject to
10A + 4B ≥ 40
A + 6B ≥ 24
A + 2B ≤ 14
A, B ≥ 0
with soln pls thank you!
In: Advanced Math
what are 5 college mathematics jeopardy
questions
what are 5 college anatomy jeopardy questions
In: Advanced Math
D22: When given any data set:
A.) How do we determine the type of model to use? (Linear, quadratic, exponential, logarithmic)?
B.) When fitting an exponential model to data, what is important to know about the input values?
C.) Provide an example to illustrate this idea.
In: Advanced Math
In: Advanced Math