Select the correct answer.<br> Over which interval of the domain is function h decreasing?<br> 25?

(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

2 years ago

HELP ASAPJennifer and Chris completed some chores and split the earnings in the ratio 3:2. Jennifer earned $48.

elixir [45]

Let the total earnings be = x

Jennifer and Chris split the earnings in the ratio 3:2

Jennifer earned = $48

$\frac{3x}{5}=48$

$3x=240$

x=80

Hence total earnings are $80

(a) Chris earning is = $\frac{2x}{5}=\frac{2*80}{5}=32$

Hence, Chris earns $32

(b) Jennifer spends 30% of her earnings on a book.

So, price of the book = $\frac{30}{100}\times48$

Price of book = $14.40

(c) Jennifer also buys a magazine for = $5.40

So, total money Jennifer spent on book and magazine = 14.40+5.40=19.80

Money left with Jennifer = 48-19.80= $28.20

In fractions = $\frac{28.20}{48}$

or multiplying the numerator and denominator by 10, we get

$\frac{282}{480}$ = $\frac{47}{80}$

(d) Let the original price of the shirt = x

reduction percentage on x= 40%

Price paid after reduction = 16.80

$\frac{40x}{100}=16.80$

$40x=1680$

$x=42$

Hence, the original price of the shirt was $42.

8 0

3 years ago

Fixed expenses are expenses that do not change from month to month, and variable expenses are expenses that can fluctuate from m

notsponge [240]

Answer:

yes

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

The bills won 57.1% of their 140 games last year. How many did they win

antoniya [11.8K]

Answer:

79.94

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

Given cosx=12/13

TiliK225 [7]

1. You have the following information:

Sinx=5/13

Cosx=12/13

2. By definiton, you have:

Tanx=(Senx)/(Cosx)

3. When you susbtitute Senx=5/13 and Cosx=12/13 into Tanx=(Senx)/(Cosx), you obtain:

Tanx=(Senx)/(Cosx)
Tanx=(5/13)/(12/13)
Tanx=(5)(13)/(13)(12)
Tanx=65/156

4. Therefore, the answer is;

Tanx=65/156

7 0

2 years ago

Select the correct answer. Over which interval of the domain is function h decreasing? 25?