Answer:
a) 
.
b) 
Step-by-step explanation:
Given a function 
, this function has the following gradient:
.
(a) find the gradient of f
We have that 
. So
.
.
(b) find the directional derivative of f at (2, 4, 0) in the direction of v = i + 3j − k.
The directional derivate is the scalar product between the gradient at (2,4,0) and the unit vector of v.
We have that:
.
The vector is 
To use v as an unitary vector, we divide each component of v by the norm of v.
So
Now, we can calculate the scalar product that is the directional derivative.
Answer:
First figure is a hexagon
second figure is a dodecagon
third figure is a decagon
Step-by-step explanation:
We can classify each figure by how many sides it has.
the first one had 6 sides. a six sided polygon is known as a hexagon
the second one has 12 sides. a 12 sided polygon is known as a dodecagon
the third one has 10 sides. a 10 sided polygon is known as a decagon
Consecutive numbers can be written as such:
n + (n + 1) = 73
Open the parentheses and simplify:
2n + 1 = 73
Subtract 1 from both sides:
2n = 72
Divide both sides by 2:
n = 36
The numbers are 36 and 37
Answer:
x + 15
Step-by-step explanation:
Since I don't know what this number is, I'm going to use the variable x to substitute for the value of the unknown number.
So it would just be x + 15 because addition is the operation of adding and the key words are usually more. Since one of the numbers is unknown, we can't get an answer like "100" because x is undefined.
Say x=100, then the number would be written as 115 in it's simplest form but you could also write it as 100+15. So I'm just using substitution.
answer:
1.94117647058
Step-by-step explanation:
33/50 her free throw % is 66% at the moment based on how many she missed you'd do 33 / by 17 you get 1.94117647058
