Serena invests $2500 for 3 years and 6 months and earns $328.13. What was the rate of interest? Explain how you solved.
1 answer:
Answer:
4.38%
Step-by-step explanation:
<em>Assuming simple interest</em>, we start by writing the formula for simple interest.
Where
SI is the interest amount (328.13)
P is the principal amount (2500)
r is the rate of interest (what we need to find)
t is the time, in years (t = 3)
Since we want rate of interest, we re-arrange the formula to get r in terms of the other variables. Shown below:
Now we simply plug-in the information we know and find r:
To convert into percentage, we multiply by 100:
r = 0.0438 * 100 = 4.38%
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Answers:
(1 Question in written form): 7.2 inches.
(2 Question in the picture): Option (D) and
and
Explanations:
1. (Question in written form):
First you need to know the standard form of a parabola (considering it opens in +x direction and the vertex of the parabola is at origin), which is as follows:
Since the vertex of the parabola is at origin, h = 0 and k = 0. The above equation will now become:
---- (A)
Where p is the distance between the vertex and the focus of a parabola, which we need to find (or where the microphone should be placed).
As the vertex is assumed to be placed at the origin, the parabolic dish, which is 24 inches wide, will be split evenly on both sides of the y axis (as the opening of the parabola is in x-axis—stated above), giving the distance of 12 inches from each sides of y axis (12 inches + 12 inches = 24 inches). Since it (parabolic microphone) is 5 inches deep, the coordinates will become: (5, +12) and (5, -12).
Plug any of the points—(5,+12) or (5,-12)—in equation (A), you will get the following:
Hence, the correct answer is 7.2 inches.
2. (Question in the picture):
First we need to write the following equation in the standard form:
----- (B)
The standard form of parabola is:
----- (C)
Rearrange equation (B) and solve as follows:
You can write the above equation as follows:
----- (D)
Now compare equation (D) with (C), we will get:
Focus = (h+p, k) = (-3+(1/2), -1)
Now, to find x, use the following formula:
x = h - p
Hence, the correct option is (D) -> and