Write the multiplication table for D8. Find the order of each element D8.
In: Advanced Math
please explain the multiplication rule as it applies to the Rules of Probability in at least 400 words
In: Advanced Math
Use a LaPlace transform to solve
d^2x/dt^2+dx/dt+dy/dt=0
d^2y/dt^2+dy/dt-4dy/dt=0
x(0)=1,x'(0)=0
y(0)=-1,y'(0)=5
In: Advanced Math
Q5. During peak hours, customers arrive at the cashier check-out queue in a local supermarket according to a Poisson process with an average rate of 120 customers per hour. There are four cashiers serving the check-out, and they provide identical service to customers. The time to service any customer by any of the cashier is exponentially distributed with a mean of 20 seconds. If all the cashiers are busy, customers join in a single queue on arrival.
(a) Compute the probability that an arriving customer have to
wait in the queue for an available cashier;
(b) Suppose the supermarket opens at 10am, and Peter arrives at the
cashier check-out at 10.02am. What assumptions are needed to
approximate the probability that Peter do not have to queue.
Pls explain with workings. Thxs
In: Advanced Math
1. Compute the product in the given ring.
a) (16)(12) in Z24
b) (-4)(11) in Z5
c) (2,4)(4,7) in Z5 x Z9
2. Describe all units in the given ring.
a) Z7
b) Z8
c) Z x Z x Q
In: Advanced Math
1. Consider the group Zp for a prime p with multiplication multiplication mod p). Show that (p − 1)2 = 1 (mod p)
2. Is the above true for any number (not necessarily prime)?
3. Show that the equation a 2 − 1 = 0, has only two solutions mod p.
4. Consider (p − 1)!. Show that (p − 1)! = −1 (mod p) Remark: Think about what are the values of inverses of 1, 2, . . . , p − 2.
In: Advanced Math
List ONLY positive relationships between two variables. (Please list as many as possible, the more the better.)
In: Advanced Math
Consider an ecological niche with three species A, B and C. Their dynamics are given by their population rates shown below
dA/dt=A+B-C … (2a)
dB/dt=-A+2B … (2b)
dC/dt=C-A-B … (2c)
Initially, the niche is in equilibrium with the population of C=30. Obtain the population densities of the rest of participants in the niche at its equilibrium. Starting from the point (A=8,B=4,C=10), obtain their individual populations over time t. What if the initial starting point is perturbed to (A=7,B=4,C=10)? Would the system emerge in the same way?
In: Advanced Math
1. Determine an inverse of a modulo m for a = 6 and m = 11. This is equivalent to answering the question “_______ is the unique inverse of 6 (mod 11) that is non-negative and < 11.” Show your work following the steps.
Hint: All of these inverses are congruent to each other mod 11.
Determine if the congruence 6x ≡ 11(mod 8) has a solution.
If there is a solution, identify a value for x. If there is no solution, explain why not.
In: Advanced Math
(a) Give a definition of a closed set.
(b) Show, directly from the definition, that a union of finitely many closed sets is closed.
(c) Give an example of a countable collection of closed intervals In such that ∪ n=1 to ∞ In is open (make sure to prove it).
In: Advanced Math
MATLAB question
The range of a projectile launched at velocity V and angle q
is R=2 V2 sin(q) cos(q)
What should the accuracy of the launch angle have be to keep the uncertainty of the range to within 5%.
In: Advanced Math
Find the positive root of the equation x^3-×-11 using
inspection method.
In: Advanced Math
1.- Prove that the set of irrational numbers is uncountable by using the Nested Intervals Property.
2.- Apply the definition of convergent sequence, Ratio Test or Squeeze Theorem to prove that a given sequence converges.
3.- Use the Divergence Criterion for Sub-sequences to prove that a given sequence does not converge.
Subject: Real Analysis
In: Advanced Math
Prove Euler's Formula for graph inductively.
In: Advanced Math
In: Advanced Math