Answer:
Maximum rate change |f| = √65
Direction = ( 1, 8 ) / √65
i.e Maximum rate change is √65 and it occurs in a direction of ( 1, 8 )
Step-by-step explanation:
Given that;
f(x, y) = 4y √x, (4, 1)
{ x=4 and y=1 }
Maximum rate of change occurs with the gradient vector;
f = [ df/dx, df/dy ] = [ 2y/√x, 4√x ]
we substitute in our value of x and y
f = 2(1)/√4, 4√4
f = 2/√4, 4√4
f = ( 1, 8 )
Maximum rate change |f| = | ( 1, 8 ) | = √( 1² + 8² ) = √(1 + 64)
Maximum rate change |f| = √65
Direction = f / |f|
we substitute
Direction = ( 1, 8 ) / √65
i.e Maximum rate change is √65 and it occurs in a direction of ( 1, 8 )
Answer:
The answer is between 5/12 and 12/5
Step-by-step explanation:
Depending on where the angle is facing
Answer:
1/2 x 7/1 = 3 1/2 pieces of toast
Step-by-step explanation:
Hello here is a solution :
Answer:
k = 5
n = 10
p = 0.5
Step-by-step explanation:
Let X be a discrete random variable. The binomial probability formula is used to calculate the probability of obtaining k-successes in "n" independent trials for an experiment with probability of success p and probability of failure q.
The binomial formula is the following:
Where:
k = number of successes
n = number of trials
p = probability of success
q = probability of failure.
So, for the given problem
k = 5 Because you want to get the probability of getting 5 "heads"
n = 10 Because the experiment is repeated 10 times
p = 0.5 Because the probability of obtaining a "heads" when flipping a coin is 50%
q = 0.5