1. Let a and b be coefficients such that
Combining the fractions on the right gives
so that
2. a. The given ODE is separable as
Using the result of part (1), integrating both sides gives
Given that y = 1 when x = 1, we find
so the particular solution to the ODE is
We can solve this explicitly for y :
2. b. When x = 9, we get
Answer:
Refer to the explanation.
Step-by-step explanation:
Let's take each one at a time.
1.
To solve for the complement, we simply subtract our markup rate by 100%.
100% - 30% = 70%
Now to solve for the selling price, we use the formula
Selling Price = $123.91
2.
We do the same process with the first number.
100% - 40% = 60%
SellingPrice = $366.67
3.
The same as the first two.
100% - 20% = 80%
SellingPrice = $111.88
4.
Now to solve for the markup rate, we use the formula:
In this case we first need to find the markup. The markup is the difference between the selling price and the cost.
Selling Price = $235.28
Cost = $199.99
Markup = $235.28 - $199.99
Markup = $35.29
Now the we know our markup, we can then solve for the markup rate using the formula.
MarkupRate = 0.1499 x 100 = 14.99% or 15%
5.
Now for the last one, we need to find for the cost. Let's use the selling price formula to find for the cost.
Selling Price = $30.77
Complement = 65% or 0.65
This will then give us.
We multiple both sides of the equation by 0.65 to leave our cost alone.
30.77 x 0.65 = Cost
Cost = $20