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2 years ago

What is the slope of the line

Mathematics

1 answer:

Makovka662 [10]2 years ago

4 0

Answer: 3/5

Step-by-step explanation

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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

Write the following expression in radical form

zlopas [31]

Answer:

See below

Step-by-step explanation:

Write the following expression in radical form

(8x)¹/² = $\sqrt{8x}$

Write the following expression in exponential form.

$\sqrt{19}$ = 19¹/²

8 0

3 years ago

Worth a lot of points

Dima020 [189]

6. Is 6MPH because 12M / 2H
8. Is 40Seconds because 120 / 3
10. Is 113.3 seconds

3 0

2 years ago

Yes or no ?????????????

lbvjy [14]

Answer:

yes

Step-by-step explanation:

I am pretty sure. sorry if I'm wrong

3 0

2 years ago

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Find the missing side. 6 is A^2 10 is B^2 what is the missing side

topjm [15]

Answer:

Step-by-step explanation:

This is a right triangle, which fits the Pythagorean Theorem, a^2 +b^2 = c^2. The variables a, b, and c all are sides of the triangle, while a and b are the two legs and c is the hypothenuse.

In this problem, we see that 6 and x are the legs and 10 is the hypothenuse. We put 6 as "a" and x as "b" (but it doesn't matter which is a and b) and 10 is c. Therefore, we have the equation:

6^2 + x^2 = 10^2

which further simplifies to:

36 + x^2 = 100

x^2 = 64

and so x would equal 8 (or -8, but it is impossible to have a side length of -8).

Therefore, the missing side is 8.

7 0

3 years ago

Read 2 more answers