Answer:
The directional derivative of f at A in the direction of
AD is 7.
Step-by-step explanation:
Step 1:
Directional of a function f in direction of the unit vector
is denoted by
,
.
Now the given points are
,
Step 2:
The vectors are given as
AB = (10-8, 9-9),the direction is
AC=(8-8,10-9), the direction is

AC=(11-8,13-9), the direction is

Step 3:
The given directional derivative of f at A
is 9,

The given directional derivative of f at A
is 2,

The given directional derivative of f at A
is



The directional derivative of f at A in the direction of
is 7.
Answer:
x = 3 is extraneous
Step-by-step explanation:
Given
= x - 5 ( square both sides to clear the radical )
4x - 8 = (x - 5)² ← expand using FOIL
4x - 8 = x² - 10x + 25 ( subtract 4x - 8 from both sides )
0 = x² - 14x + 33 ← in standard form
0 = (x - 11)(x - 3) ← in factored form
Equate each factor to zero and solve for x
x - 11 = 0 ⇒ x = 11
x - 3 = 0 ⇒ x = 3
As a check
Substitute these values into the equation and if both sides are equal then they are solutions
x = 11
left side =
=
= 6
right side = 11 - 5 = 6
Thus x = 11 is a solution
x = 3
left side =
=
= 2
right side = 3 - 5 = - 2 ≠ 2
Thus x = 3 is an extraneous solution
Answer:
x = 9
Step-by-step explanation:
The big triangle is similar to smaller one so we can use the side lengths' proportion to find x:
7/4 = (x-3)+8/8
7/4 = (x+5)/8 cross multiply expressions
56 = 4x + 20 subtract 20 from both sides
36 = 4x divide both sides by 4
9 = x
Answer:
C) a = 6 D) m = 5
Step-by-step explanation:
C) 3a + 11 = 7a - 13
4a = 24
a = 6
D) 2m + m - 8 = 7
3m = 15
m = 5