How much must be deposited today into the following account in order to have $ 65,000 in 8 years for a down payment on a house?
1 answer:
Answer:
Step-by-step explanation:
we know that
The compound interest formula is equal to
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
substitute in the formula above
Solve for P
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Answer(s):
Step-by-step explanation:
<em>OR</em>
You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of <em>sine</em>, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the centre photograph displays the trigonometric graph of in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the <u>horisontal shift formula</u> above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY <em>REALLY</em> ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the <em>sine</em> graph [centre photograph] is shifted
to the right, which means that in order to match the <em>cosine</em> graph [photograph on the left], we need to shift the graph BACKWARD
which means the C-term will be negative, and by perfourming your calculations, you will arrive at
So, the sine graph of the cosine graph, accourding to the horisontal shift, is
Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph WILL hit
from there to the y-intercept of
they are obviously
apart, telling you that the period of the graph is
Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the <em>midline</em>. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at
in which each crest is extended <em>twenty-nine units</em> beyond the midline, hence, your amplitude. Now, there is one more piese of information you should know -- the cosine graph in the photograph farthest to the right is the OPPOCITE of the cosine graph in the photograph farthest to the left, and the reason for this is because of the <em>negative</em> inserted in front of the amplitude value. Whenever you insert a negative in front of the amplitude value of <em>any</em> trigonometric equation, the whole graph reflects over the <em>midline</em>. Keep this in mind moving forward. Now, with all that being said, no matter how far the graph shifts vertically, the midline will ALWAYS follow.
I am delighted to assist you at any time.
Answer:
4x² +100x
Step-by-step explanation:
The total area of the garden plus the pine bark border is given by:
The area of the garden alone, without the border, is:
Subtracting the total area by the area of the garden gives us the area of the border:
The total area of the border is described by 4x² +100x.