All categories

3 years ago

Suppose segment PQ has one endpoint at P (0,0). If T (6,3) is a point 3/10 of the way from P to Q, find the coordinates of Q.

Mathematics

1 answer:

mixer [17]3 years ago

3 0

Answer:

Q(20,10)

Step-by-step explanation:

If point T (6,3) is a point 3/10 of the way from P(0,0) to Q(x,y), then

$\overrightarrow {PT}=\dfrac{3}{10}\overrightarrow {PQ}.$

Find the coordinates of the vectors $\overrightarrow {PT},\ \overrightarrow {PQ}:$

$\overrightarrow {PT}=(6-0,3-0)=(6,3);\\ \\\overrightarrow {PQ}=(x-0,y-0)=(x,y).$

Thus,

$(6,3)=\dfrac{3}{10}(x,y),\\ \\(x,y)=\dfrac{10}{3}(6,3)=(20,10).$

You might be interested in

How do u benchmark 8/11/12 and 2/11/20

Viefleur [7K]

6 39/40!!!!!!!!!!!!!

8 0

2 years ago

Let φ(x, y) = arctan (y/x) .

Alexandra [31]

Answer:

a) $\large F(x,y)=(-\frac{y}{x^2+y^2},\frac{x}{x^2+y^2})$

b) $\large \mathbb{R}^2-\{(0,0)\}$

c) the points of the form (x, -x) for x≠0

Step-by-step explanation:

If φ(x, y) = arctan (y/x), the vector field F = ∇φ would be

$\large F(x,y)=(\frac{\partial \phi}{\partial x},\frac{\partial \phi}{\partial y})$

On one hand we have,

$\large \frac{\partial \phi}{\partial x}=\frac{\partial arctan(y/x)}{\partial x}=\frac{-y/x^2}{1+(y/x)^2}=-\frac{y/x^2}{1+y^2/x^2}=\\\\=-\frac{y/x^2}{(x^2+y^2)/x^2}=-\frac{y}{x^2+y^2}$

On the other hand,

$\large \frac{\partial \phi}{\partial y}=\frac{\partial arctan(y/x)}{\partial y}=\frac{1/x}{1+(y/x)^2}=\frac{1/x}{1+y^2/x^2}=\\\\=\frac{1/x}{(x^2+y^2)/x^2}=\frac{x}{x^2+y^2}$

$\large F(x,y)=(-\frac{y}{x^2+y^2},\frac{x}{x^2+y^2})$

The domain of definition of F is

$\large \mathbb{R}^2-\{(0,0)\}$

i.e., all the plane X-Y except the (0,0)

Here we want to find all the points such that

$\large (-\frac{y}{x^2+y^2},\frac{x}{x^2+y^2})=(k,k)$

where k is a real number other than 0.

But this means

$\large -\frac{y}{x^2+y^2}=\frac{x}{x^2+y^2}\Rightarrow y=-x$

So, all the points in the line y = -x except (0,0) are parallel to the vector field F, that is, the points (x, -x) with x≠ 0

8 0

2 years ago

Which of the following it's true about f(x) and g(x)

horsena [70]

Answer:

its c

Step-by-step explanation:

6 0

2 years ago

Jacksons family drove 496 in 8 hour what is the unit rate

stich3 [128]

62unit/hour is the answer
distance/time

5 0

3 years ago

The length of a rectangle is 6 feet more than three times the width of the

Nesterboy [21]

Answer:

<h2>width = 6 feet</h2>

Step-by-step explanation:

let l be the length of the rectangle

let w be the width of the rectangle

The statement

The length of a rectangle is 6 feet more than three times the width of the

rectangle is written as

l = 6 + 3w

From the question

l = 24 feet

Substitute the value into the above formula and solve for the width

That's

24 = 6 + 3w

3w = 24 - 6

3w = 18

Divide both sides by 3

w = 6

Therefore

<h3>width = 6 feet</h3>

Hope this helps you

3 0

3 years ago