Simplify to a single trig function with no denominator.csc^2 x -cot^2 x
1 answer:
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(a) I have attached the graph.
(b) The function g(x) is given by g(x) = f(2x + 2)/3. You can work this out algebraically. You can also work this out by using the graph of the function.
(c) We can obtain the graph of y = g(x) from the graph of y = f(x) through the following transformations:
* stretch horizontally by a factor of 2
* stretch vertically by a factor of 3
* shift downwards by 2 units
Answer:
<em>Steve should place $6,250 in the 5-year CD and $18,750 in the corporate bond</em>
Step-by-step explanation:
<u>System of Equations</u>
We need to find how Steve will distribute his investments between two possible options: one of them will pay 5% per annum and the other will pay 9% per annum. We know Steve has $25,000 to invest and wants to have an overall annual rate of return of 8%.
Let's call x to the amount Steve will invest in the CD paying 5% per annum and y to the amount he will invest in a corporate bond paying 9% per annum.
The total investment is $25,000 which leads to the first equation
If x dollars are invested at 5%, then the interest return is 0.05x. Similarly, y dollars at 9% return 0.09y. The overall return is 8% on the total investment, thus
Rearranging:
Simplifying
Multiplying by 100
Substituting in the first equation
And therefore
Steve should place $6,250 in the 5-year CD and $18,750 in the corporate bond