If w is partly constant and partly varies directly as x and w=9 when x=4 w=27 when x= 16 find
An equation connection x and w
And (b) the value of w when x =8
K=1.5,C=3 ,when x=8 w=15
w=kx+c
9=k4+c
27=k*16+c
subtract eq 1 from eq 2
18=12k solve for k
then solve for c in either equation
To find the equation connecting x and w, we can use the information that w is part constant and part varies directly as x. Let's break this down into two parts: the constant part and the direct variation part.
1) Constant part:
From the given information, when x = 4, w = 9. This tells us that when x is 4, the value of w without the direct variation component is 9. Let's call this constant value "c".
So, the constant part of the equation is c = 9.
2) Direct variation part:
From the given information, when x = 4, w = 9, and when x = 16, w = 27. This tells us that as x increases from 4 to 16, w increases from 9 to 27.
To find the direct variation part, we can use the formula for direct variation: w = kx, where k is the constant of variation.
Using the data from x = 4, w = 9, we can find the value of k:
9 = k * 4
k = 9/4 = 2.25
Therefore, the equation connecting x and w is:
w = 2.25x + c
Now, let's find the value of w when x = 8.
Using the equation w = 2.25x + c, we substitute x = 8:
w = 2.25(8) + c
To find the value of c, we need another data point. However, the given information does not provide any value for w when x = 8.
Hence, we cannot find the value of w when x = 8 without additional data.
To find an equation connecting x and w, we know that w is partly constant and partly varies directly as x.
Let's break this down:
- The "partly constant" part means that there's a constant value, let's call it k.
- The "varies directly" part means that w can be expressed as a multiple of x.
So, we can write the equation as:
w = kx
To find the value of k, we can substitute the given values of w and x from the first set of data points (w=9 when x=4):
9 = k * 4
Dividing both sides by 4, we get:
k = 9 / 4
Now we have the value of k, we can substitute it back into the equation:
w = (9/4) * x
Now, let's find the value of w when x = 8.
Substituting x = 8 into the equation, we have:
w = (9/4) * 8
Simplifying, we get:
w = 18
Therefore, the value of w when x = 8 is 18.