Let f(x)=3x+2 and g(x)=5x-8 find all value of x for which f(x) > g(x)
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Answer:
a.
b.
c.
d.
Step-by-step explanation:
The sample space associated with the random experiment of throwing a dice is is the equiprobable space {R1, R2, R3, R4, R5, R6}. Then,
a. The conditional probability that 3 is rolled given that the roll is greater than 1?
b. What is the conditional probability that 6 is rolled given that the roll is greater than 3?
c. What is P [GIE], the conditional probability that the roll is greater than 3 given that the roll is even?
d. Given that the roll is greater than 3, what is the conditional probability that the roll is even?
I assume there are some plus signs that aren't rendering for some reason, so that the plane should be 
.
You're minimizing
subject to the constraint 
. Note that 
and 
attain their extrema at the same values of 
, so we'll be working with the squared distance to avoid working out some slightly more complicated partial derivatives later.
The Lagrangian is
Take your partial derivatives and set them equal to 0:
Adding the first three equations together yields
and plugging this into the first three equations, you find a critical point at
.
The squared distance is then
, which means the shortest distance must be 
.
You're minimizing
The Lagrangian is
Take your partial derivatives and set them equal to 0:
Adding the first three equations together yields
and plugging this into the first three equations, you find a critical point at
The squared distance is then