If d varies s and d =120 when s =30 find the formula connecting d and s
if d varies directly,
d = ks, so k = 4, and d = 4s
if d varies inversely,
ds = k, so k=3600, and ds=3600
Well, let's analyze the situation. We have d varying with s, and we know that when s is 30, d is 120.
To find the formula connecting d and s, let's use a little math humor. We can say that the relationship between d and s is "a bit of a stretch."
Now, let's solve it. Since we are given that d is 120 when s is 30, let's see what happens if we divide d by s: 120/30 = 4.
Ah, it seems there's a pattern here! For every increase in s, d is increased by a factor of 4. So, we can say that the formula connecting d and s is: d = 4s.
Remember, as a Clown Bot, my answers might be a bit silly, but hopefully they still help you!
To find the formula connecting d and s, we need to determine the relationship between the two variables. From the given information, we know that d varies with s, and when s = 30, d = 120.
We can suppose that the relationship between d and s is a direct proportion. This means that as s increases or decreases, d will also increase or decrease by the same factor.
Let's use the proportionality constant k to represent the relationship between d and s. Then, we can write the formula as:
d = k * s
To find the value of k, we can substitute the given values into the formula and solve for k:
120 = k * 30
Dividing both sides by 30:
k = 120/30
k = 4
Substituting the value of k back into the formula, we have:
d = 4s
So, the formula connecting d and s is d = 4s.
To find the formula connecting d and s, we need to determine the relationship between the two variables. From the given information, we know that d varies with s, and when s is 30, d is 120.
To find the formula, we start by identifying whether the relationship is linear or non-linear. In a linear relationship, the change in one variable is proportional to the change in another variable.
To check if the relationship is linear, we can divide the change in d by the change in s:
Change in d = 120 - 0 (when s = 0) = 120
Change in s = 30 - 0 (when s = 0) = 30
d/s = 120/30 = 4
Since the ratio of the change in d to the change in s is constant (4), we can conclude that the relationship between d and s is linear.
Now, we can construct the linear equation using the slope-intercept form:
y = mx + b
where y is the dependent variable (d), x is the independent variable (s), m is the slope (rate of change), and b is the y-intercept (the value of d when s is 0).
Using the given information, we can substitute the values into the equation:
d = ms + b
d = 4s + b
To find the value of b, substitute the known values of d and s:
120 = 4(30) + b
120 = 120 + b
b = 120 - 120
b = 0
Therefore, the formula connecting d and s is:
d = 4s + 0
Simplifying, the formula can be written as:
d = 4s