F = k x
<span>15 = k *10 </span>
<span>k = 1.5 </span>
<span>check: </span>
<span>24 = 1.5 x </span>
<span>x = 16 sureenough </span>
<span>so 1.5 oz/inch </span>
<span>= 1/1.5 inches/oz = 2/3 = 0.6666.... in/oz</span>
Step-by-step explanation:
let's simply do the multiplications and then compare with the original.
(x-m)² + n
right ?
or is it
let's go for the first.
x² - 2mx + m² + n = x² - 3x
-2mx + m² + n = -3x
fun there we see two things :
-2m = -3
m = 3/2
and
m² + n = 0
(3/2)² = -n
9/4 = -n
n = -9/4
so our transformed expression looks like
(x - 3/2)² - 9/4
We will use vertex form of the parabola:
Where (h,k) is the vertex of our parabola. We know that focus and directrix are located at the same distance from the vertex. That distance is a.
We can use this to build a system of equations to calculate a and k. We already know that h=-5, keep in mind that focus and vertex share the same x coordinate.
We just add these two equations together:
We plug this back into the first equation:
That's all the information we need to write down the equation:
None of the answers you provided are correct.
Answer:
The average rate of change of <em>g</em> from <em>x</em> = <em>a</em> to<em> x</em> = <em>a</em> + <em>h</em> is -3.
Step-by-step explanation:
We are given the function:
And we want to determine its average rate of change of the function for <em>x</em> = <em>a</em> and <em>x</em> = <em>a</em> + <em>h</em>.
To determine the average rate of change, we find the slope of the function between the two points. In other words:
Simplify:
In conclusion, the average rate of change of <em>g</em> from <em>x</em> = <em>a</em> to <em>x</em> = <em>a</em> + <em>h</em> is -3.
This is the expected result, as function <em>g</em> is linear, so its rate of change would be constant.