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Consider the curve given by x^2+4y^2 = 7 + 3xy
a) Show that there is a point P with x-coordinate 3 at which the line tangent to the curve at P is horizontal. Find the y-coordinate of P.
b) Find the value of d^2*y/d*x^2 at the point P found in part a).
Suppose A & B are Hermitian matrices and AB=BA, show that A and B are simultaneously diagonalizable, ie, there exists an unitary matrix C so that both C*AC adn C*BC are diagonal.
The probability that a teenage driver will speed is 0.8; for a twenty-something driver, the probability of speeding is 0.5; for a mature driver
A bag contains 5 yellow marbles, 16 green marbles, and 2 red marbles. What is the chance of drawing a yellow marble? If a yellow marble is drawn the first time and then a second marble is drawn without replacement
Calculate the percentage of students who score between 550 and 650.
Solve equations and systems of equations in two variables, formulate real-world problems in terms of linear equations and solve these systems by several commonly applied methods.
Estimate rate of changes.
Relation between Cyclic Group and Abelian Group. If G is a finite group whose order is a prime number p, then G is a cyclic group. Or, Every group of prime order is cyclic. Or, Every group of prime order is abelian.
The solution to Linear transformations, A linear transformation L: V -- W is said to be one-to-one if L(v1) = L(v2) implies that v1=v2. Show that L is one-to-one if and only if ker(L) = {0v}.
One month ago the ratio of nurses to doctors on a hospital staff was 3:5. Since that time two additional nurses joined the staff, no nurses left & the number of doctors remained the same. Find the ratio of nurses to doctors.
Estimating the value of a function using 3rd Taylor polynomial and use our error guarantee to give a Plus- or-minus error to your estimate
Eva created a coffee blend for her restaurant by mixing Kenya and French Roast coffee beans. The Kenya beans cost $15 per pound and the French Roast costs $8 per pound. She bought a total of 10 pounds of coffee for a total of $97.50.
Which two variables have the strongest strength of relationship?
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