(1 point) (a) Find the point Q that is a distance 0.1 from the point P=(6,6) in the direction of v=⟨−1,1⟩. Give five decimal places in your answer. Q = ( , )

(b) Use P and Q to approximate the directional derivative of f(x, y)=√(x+3y) at P, in the direction of v.
fv ≈
(c) Give the exact value for the directional derivative you estimated in part (b).
fv =

following are the solution to the given points:

Step-by-step explanation:

In point a:

calculating unit vector:

the point Q is at a distance h from P(6,6) Here, h=0.1  

the value of Q= (5.92928 ,6.07071  )

In point b:

Calculating the directional derivative of at P in the direction of

In point C:

Computing the directional derivative using the partial derivatives of f.

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.

600,000,000,000, or 6e14

step-by-step explanation: