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(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 pla

natima [27]

Answer:

following are the solution to the given points:

Step-by-step explanation:

In point a:

$\vec{v} = -\vec{1 i} +\vec{1j}\\\\|\vec{v}| = \sqrt{-1^2+1^2}$

$=\sqrt{1+1}\\\\=\sqrt{2}$

calculating unit vector:

$\frac{\vec{v}}{|\vec{v}|} = \frac{-1i+1j}{\sqrt{2}}$

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

$a=-6+O.1 \times \frac{-1}{\sqrt{2}}\\\\= 5.92928 \\\\b= 6+O.1 \times \frac{-1}{\sqrt{2}} \\\\= 6.07071$

the value of Q= (5.92928 ,6.07071 )

In point b:

Calculating the directional derivative of $f (x, y) = \sqrt{x+3y}$ at P in the direction of $\vec{v}$

$f_{PQ} (P) =\fracx{f(Q)-f(P)}{h}\\\\$

$=\frac{f(5.92928 ,6.07071)-f(6,6)}{0.1}\\\\=\frac{\sqrt{(5.92928+ 3 \times 6.07071)}-\sqrt{(6+ 3\times 6)}}{0.1}\\\\= \frac{0.197651557}{0.1}\\\\= 1.97651557$

$\vec{v} = 1.97651557$

In point C:

Computing the directional derivative using the partial derivatives of f.

$f_x(x,y)= \frac{1}{2 \sqrt{x+3y}}\\\\ f_x (6,6)= \frac{1}{2 \sqrt{22}}\\\\f_x(x,y)= \frac{1}{\sqrt{x+3y}}\\\\ f_x (6,6)= \frac{1}{\sqrt{22}}\\\\f_{(PQ)}(P)= (f_x \vec{i} + f_y \vec{j}) \cdot \frac{\vec{v}}{|\vec{v}|}\\\\= (\frac{1}{2 \sqrt{22}}\vec{i} + \frac{1}{\sqrt{22}} \vec{j}) \cdot \frac{-1}{\sqrt{2}}\vec{i} + \frac{1}{\sqrt{2}} \vec{j}$

4 0

3 years ago

If someone is going 24.85 mi/h how far will they have gone in 4 hours?

Leokris [45]

You would have to do 24.85 x 4 because the 24.85 is per hour and if someone is going for 4 hours, this is what we would have to work out. So it would equal: 99.40 miles per hour. :)

6 0

3 years ago

Read 2 more answers

A student performed the following steps to find the solution to the equation

rusak2 [61]

Answer:

D

Step-by-step explanation:

step 2 : x + 3 = 0 and x - 5 = 0 ← correct

step 3

x = 3 and x = - 5 ← error made here with signs, correct statement should be

x + 3 = 0 ⇒ x = - 3

x - 5 = 0 ⇒ x = 5

3 0

1 year ago

Please it's urgent I really need answers

WITCHER [35]

(c)

We notice that they already have common denominators, therefore we can just add the numerators up.

(x+y+x-y)/2xy=

2x/2xy

Dividing both top and bottom by 2x, we get

-Hunter

5 0

2 years ago

Read 2 more answers

5.5(x+6 1/2)-(x+9 1/3)-(19-x)

anastassius [24]

The simplified form of the expression [5.5(x+6 1/2)-(x+9 1/3)-(19-x)] is 11x/2 + 89/12

<h3>What is the simplified form of the expression</h3>

Given the expression;

5.5(x+6 1/2) - (x+9 1/3) - (19-x)

First, we convert 6 1/2, 9 1/3 and 5.5 to an improper fraction

6 1/2 = 13/2, 9 1/3 = 28/3 and 5.5 = 11/2

So, we have

(11/2)( x + 13/2 ) - ( x + 28/3 ) - ( 19 - x )

Next, we remove the parentheses

11x/2 + 143/4 - x - 28/3 - 19 + x

11x/2 + 143/4 - 28/3 - 19

11x/2 + 317/12 - 19

11x/2 + 89/12

Therefore, the simplified form of the expression [5.5(x+6 1/2)-(x+9 1/3)-(19-x)] is 11x/2 + 89/12.

Learn more about fractions here: brainly.com/question/28039882

#SPJ1

3 0

1 year ago