a spring is 3 in. long with no weight suspended from it. For each ounce of weight, the spring stretches 0.2 in. Unitl it reaches its maximum lenght of 9 in. How much weight must be added for the spring to reach its maximum length? algebra
x=30
Well, well, well! It sounds like we've got a springy situation here! Let's do some spring-loaded calculations, shall we?
We know that for each ounce of weight added, the spring stretches 0.2 in. The difference between the original length of the spring (3 in.) and its maximum length (9 in.) is 9 - 3 = 6 in.
To find out how much weight must be added for the spring to reach its maximum length, we can divide this difference by the amount the spring stretches per ounce of weight.
So, 6 in. divided by 0.2 in. per ounce gives us a whopping weight of 30 ounces!
In other words, you'll need to add a weight of 30 ounces to extend the spring to its maximum length. Just watch out for those flying objects once you let go of the spring – you're in for a spring-loaded surprise! Happy stretching!
To find out how much weight must be added for the spring to reach its maximum length, we can set up an equation:
Let 'w' be the weight that needs to be added.
Given:
Length of the spring with no weight (L0) = 3 in.
Stretches per ounce of weight (S) = 0.2 in/oz
Maximum length of the spring (Lmax) = 9 in.
The length of the spring when weight 'w' is added is given by:
Length (L) = L0 + S * w
Therefore, we can write the equation:
L = 3 + 0.2w
We want the spring to reach its maximum length when L = Lmax.
So we have:
9 = 3 + 0.2w
To solve for 'w', we can subtract 3 from both sides of the equation:
9 - 3 = 3 - 3 + 0.2w
6 = 0.2w
Then, divide both sides by 0.2:
6 / 0.2 = (0.2w) / 0.2
30 = w
Therefore, 30 ounces of weight must be added for the spring to reach its maximum length.
To determine how much weight must be added to the spring to reach its maximum length, we need to use the given information about the spring's behavior.
Let's assume that x represents the weight we need to find in ounces.
According to the problem, for every ounce of weight added, the spring stretches 0.2 inches.
So, if x represents the weight in ounces, the total stretching of the spring can be expressed as 0.2x inches.
Since the spring's original length is 3 inches and it reaches a maximum length of 9 inches, the total stretching of the spring can also be expressed as 9 - 3 = 6 inches.
Now we can set up an equation:
0.2x = 6
To solve for x, divide both sides of the equation by 0.2:
x = 6 / 0.2
x = 30
Therefore, in order for the spring to reach its maximum length of 9 inches, we need to add 30 ounces of weight to it.
If x is the # ounces attached, then you need
3 + 0.2x = 9