Find the constant of variation, K,for y = -8 varies directly when x = 12.
Write an inverse variation to model the situation and answer the question. Two rectangular fields have the same area. One measures 75yd by 60yd. If the other has a length of 75yd, what is its width?
K= -2/3
-8/12=-2/3
Y=(-2/3)x
we know that y=kx, so use that with the known values of x and y:
-8 = k*12
k = -2/3
The area is Width*Length. So,
WL=k
That means you want W such that
75W = 75*60
W=60
Huh? If the length of both fields is the same, where's the difficulty? I suspect a typo
oops nvm, i read it wrong and didn't realize there were two questions
Oh, you got the "direct variation" question. Well, the constant of variation, K, can be found by using the formula y = Kx. So, let's plug in the given values: y = -8 and x = 12.
Now solve for K: -8 = K * 12.
To find K, we need to divide both sides by 12: K = -8/12.
And you know what? Simplifying this fraction, we get K = -2/3. So, the constant of variation is -2/3.
Now, let's talk about the "inverse variation" question. A rectangular field's area is given by A = length * width. If two fields have the same area, we can set up an inverse variation equation:
A = k / x, where A is the area and x is the width of the other field we're trying to find.
In the given case, the first field measures 75 yd by 60 yd, so its area is 75 * 60 = 4500 yd^2.
Now we can plug in the values into the inverse variation equation: 4500 = k / 75.
To find the width, x, we need to solve for k and then substitute it back in. So, let's start by multiplying both sides by 75: 4500 * 75 = k.
After doing the math, we get k = 337,500 yd^2.
Now, let's plug k back into the equation and solve for x (the width): 337,500 = x / 75.
Dividing both sides by 75, we get x = 337,500 / 75.
And after doing the division, we find that x = 4,500 yd.
So, the width of the second field is 4,500 yd.
Hope that helped, and remember, if farming doesn't work out, you can always join the circus!
To find the constant of variation, K, in the equation y = kx, you need to substitute the given values of x and y into the equation and solve for K.
Given that y = -8 when x = 12, you can plug these values into the equation:
-8 = k * 12
To find K, divide both sides of the equation by 12:
-8/12 = k
Simplifying the fraction, you get:
-2/3 = k
Therefore, the constant of variation, K, is -2/3.
Now, let's move on to the second question about inverse variation.
Inverse variation occurs when two variables are related by the equation y = k/x, where k is the constant of variation.
To model the situation with two rectangular fields, you know that the area of the fields is the same.
In the first field, the dimensions are 75 yards by 60 yards. Therefore, the area is:
Area1 = length * width = 75 yd * 60 yd = 4500 square yards.
In the second field, you know the length is 75 yards, and you need to find the width.
Let's denote the width of the second field as w. Therefore, the equation for the second field would be:
Area2 = length * width = 75 yd * w.
Since both fields have the same area, you can set up an equation:
Area1 = Area2
Substituting the values:
4500 = 75 * w
To find the width, divide both sides of the equation by 75:
4500/75 = w
Simplifying the division, you get:
60 = w
So, the width of the second field is 60 yards.
^^^
think they got a bit confused. variation is just y÷x, or in this case (-8)÷12=-2/3