All categories

3 years ago

Find the variation constant and an equation of variation where y varies directly as x and y=16 when x=2

Mathematics

1 answer:

Jlenok [28]3 years ago

5 0

Answer:

variation constant = k = 8

equation of variation : y = 8x

Step-by-step explanation:

Any relationship of variation can be written as y = kx

where k is the variation constant.

_______________________________________

Let the equationof relation between y and x be y =kx here as well

given

y = 16 when x = 2

substituting this value in the equation y = kx

16 = k*2

=> k = 16/2 = 8

Thus,

variation constant = k = 8

equation of variation : y = 8x

You might be interested in

Please help!!!!!!!!!!!

boyakko [2]

Answer:

(7√6)/2

Step-by-step explanation:

The side ratios in these special triangles are ...

30°-60°-90° triangle: 1 : √3 : 2

45°-45°-90° triangle: 1 : 1 : √2

This tells you the length of the horizontal line is 7√3, and the value of x is ...

(7√3)/√2 = (7√6)/2

_____

<em>Additional comment</em>

Call the length of the horizontal line "y". Then the given ratios tell you ...

7 : y = 1 : √3 ⇒ y/7 = √3/1 ⇒ y = 7√3

and

x : y = 1 : √2 ⇒ x/y = 1/√2 ⇒ x = y/√2

When we rationalize the denominator, we get ...

x = (y√2)/2 = ((7√3)√2)/2 = (7√6)/2

4 0

2 years ago

Find the distance traveled by a particle with position (x, y as t varies in the given time interval. x = 3?sin2 t, y = 3?cos2 t,

ANTONII [103]

Assuming the particle's position is given by

$\begin{cases}x(t)=3-\sin2t\\y(t)=3-\cos2t\\0\le t\le4\end{cases}$

then the distance traveled over the interval is

$\displaystyle\int_{t=0}^{t=4}\sqrt{\left(\dfrac{\mathrm dx(t)}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dy(t)}{\mathrm dt}\right)^2}\,\mathrm dt$
$=\displaystyle\int_0^4\sqrt{(-2\cos2t)^2+(2\sin2t)^2}\,\mathrm dt$
$=\displaystyle\int_0^4\sqrt{4\cos^22t+4\sin^22t}\,\mathrm dt$
$=\displaystyle2\int_0^4\mathrm dt$
$=2(4-0)=8$

5 0

3 years ago

The area of a rectangle is 42 square inches and one side is 12 inches long find the perimeter of the rectangle show your work

uranmaximum [27]

So first of all we need to know that area is length times width
Area = L x W
since we know the area is 42 and the length is 12 lets plug those in
42 = 12 x W
now we dont know what W is yet but we can figure it out by dividing 42 by 12
42/12 = 3.5
So W = 3.5!
but its asking for the perimeter and we know that perimeter is all of the sides of the rectangle added up. Heres a picture

___3.5___
| |
| |
12 | | 12
| |
************
3.5

see now we just add those all up together:)

12 + 12 + 3.5 + 3.5 = 31!!
so our perimeter is 31 inches:)
have a good one
PICK ME BRAINLIEST!:D

5 0

3 years ago

What is an equation of the line that passes through the point (-4,3) and is

Tom [10]

Answer:

5x + 4y = - 8

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

4x - 5y = 20 ( subtract 4x from both sides )

- 5y = - 4x + 20 ( divide all terms by - 5 )