The manager of a money-market fund has invested $4.2 million in certificates of deposit that pay interest at the rate of 5.4% pe
1 answer:
Answer:
549192.188 $
Step-by-step explanation:
Compounded interest is calculated each year based on the starting amount of that year.
To calculate compounded interest the following formula is used
where
A = Amount at the end of the year
P = 4,200,000 (Principal amount at the start)
r = 0.054 (rate of interest, i.e. 5.4%)
n = 4 (compounding frequency in an year, i.e. quarterly)
t = 5 (number of years)
The solution will thus be
A = 549192.188
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Answer:
The coordinates of the point on a circle with radius 4 at an angle of radians are x = -2 and y = 3.464.
Step-by-step explanation:
This problem ask us to determine the rectangular coordinates from polar coordinates. The polar coordinates of the point in rectangular form is expressed by the following expression:
Where and
are the radius of the circle and the angle of inclination of the point with respect to horizontal, measured in radians. If
and
, the coordinates of the point are:
The coordinates of the point on a circle with radius 4 at an angle of radians are x = -2 and y = 3.464.
Answer:
Step-by-step explanation:
If our interval is between 0 and 90 degrees, that means that our angles are first quadrant angles. Since the formulas for the half angles of sin and cos consider both the positive and negative roots, knowing that we are in QI leaves us using only the principle, or positive, root.
Also, if we know that the sin of angle is 3/4, we can set up a right triangle in QI and find the missing side of that triangle using Pythagorean's Theorem. Sin of an angle is the ratio opposite side/hypotenuse. That means that, according to Pythagorean's Theorem,
and
and
Now for the forula for the sin of a half-angle:
Referring to the right triangle we created and found the missing side for, we see that the cosine of that same triangle is
Filling in the formula then:
Get a common denominator on the upper fraction:
Bring up the 2 as 1/2 to multiply and get:
When you do the exact same thing to find the cos of the half angle, you are using a + sign instead of a - sign under the radical. That gives you as your exact value: