Given that P = (2, 9) and Q = (4, 14), find the component form and magnitude of vector PQ.

1 answer:

6 0

We are asked to determine the lengths of the line segment drawn with these points as endpoints. The equation of the distance between points is,
d = sqrt ((y2 - y1)² + (x2 - x1)²)
Substituting the coordinates of the points,
d = sqrt ((14 - 9)² + (4 - 2)²)
The numerical value for d is approximately 5.39.

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Suppose f(x, y) is a differentiable function of x and y and let g(r, s) = f (2rs, 8s − 2r). Use

worty [1.4K]

By the chain rule,

$\dfrac{\partial g}{\partial r} = \dfrac{\partial f}{\partial r} \\\\ ~~~~~ = \dfrac{\partial f}{\partial x} \dfrac{\partial x}{\partial r} + \dfrac{\partial f}{\partial y} \dfrac{\partial y}{\partial r} \\\\ ~~~~~ = 2 s \dfrac{\partial f}{\partial x} - 2 \dfrac{\partial f}{\partial y}$

where $x(r,s)=2rs$ and $y(r,s)=8s-2r$ .

If $r=2$ and $s=1$ , then

$x = 2\cdot2\cdot1 = 4$

$y=8\cdot1-2\cdot2 = 4$

so that

$g_r(2,1) = 2\cdot1 f_x(4,4) - 2 f_y(4,4) = 2\cdot2-2\cdot3 = \boxed{-2}$

5 0

1 year ago

2x-1=3/4x+9<br> Help Me Brainilist to whoever explains the best

alexdok [17]

Answer:

x=8

Step-by-step explanation:

normally it would be 2x-1= $\frac{3}{4}$ x+9 so now we have to combine the x into one fraction which will be 2x-1= $\frac{3x}{4}$ +9 now for my way i will be taking the -1 to the other side and when that happens its going to become positive so now the answer will be 2x= $\frac{3x}{4}$ +10 ok so now we have to have the x's to the same side so i have to drag the fraction to the other side and making it positive which will conclude into 1.25x=10 and now 10 divided by 1.25 is 8 so the answer is x=8 (sorry for the ok nows) hope this helped