Answer:
^
Step-by-step explanation:
Answer:
The work done is 202.50Nm
Step-by-step explanation:
Given
Required
The work done
First, we calculate the spring constant (k)
So:
The work done using Hooke's law is:
This gives:
Rewrite as:
Integrate
This gives:
Convert to Nm
Fractions are useful for constant of proportionality, ratios, and just simplifying decimals. Ratios are good for recipes
Answer:
1. C(m) = 24.95 + 0.05m
2. $34.95
3. 250 miles
Step-by-step explanation:
1. Let's say C(m) is a function that determines the Cost in $ for every mile you drive. Since for any rental, no matter if you drive or not, you have to pay an upfront cost of rental, r, there is a constant you need to add ($24.95 in this case.)
2. Use your equation from part 1 to get C(200) = 24.95 + 0.05(200), this equalts 34.95 dollars.
3. Here, you want to find m (distance). It is given that C(m) = 37.45 (this is the total cost from equation (1). Subtract 24.95 from C(m) to isolate the 0.05(m) part. Thus, 0.05(m) = 37.45 - 24.95 = 12.5. Here, simply divide 12.5 by 0.05 to obtain m, which is 250 miles.
The first term in our arithmetic sequence = 13
The common difference of our arithmetic sequence = 17 - 13 = 4
The formula for finding an equation for any arithmetic sequence is a(n) = A + B(n - 1)
A = the first term
B = the common difference.
Let's plug our numbers in.
a(n) = 13 + 4(n - 1)
Let's check to make sure we're correct.
a(1) = 13 + 4(1 - 1) = 13 + 4(0) = 13 + 0 = 13
a(2) = 13 + 4(2 - 1) = 13 + 4(1) = 13 + 4 = 17
That verifies that our formula is correct.
In conclusion,
a(n) = 13 + 4(n - 1)