Answer: the interest rate is 6%
Step-by-step explanation:
The formula for continuously compounded interest is
A = P x e (r x t)
Where
A represents the future value of the investment after t years.
P represents the present value or initial amount invested
r represents the interest rate
t represents the time in years for which the investment was made.
e is the mathematical constant approximated as 2.7183.
From the information given,
A = $4482
P = 1000
t = 25 years
Therefore,
4482 = 1000 x 2.7183^(r x 25)
4482/1000 = 2.7183^25r
4.482 = 2.7183^25r
Taking ln of both sides, it becomes
Ln 4.482 = 25rLn2.7183
1.5 = 25r
r = 1.5/25 = 0.06
r = 0.06 × 100 = 6%
“The breaking distance is directly proportional to the square of its speed”
Using your variables, this means: d = k•b^2
k here is some unknown (and for this question irrelevant) number.
Now if b (the speed) is increased by 200%, then your new speed is b+2b = 3b. The 2b is the 200% increase.
Throw 3b into the first equation we have the new d as:
d = k • (3b)^2
Simplifying this, you have d = k•9b or d=9kb
This means the new braking distance is 9 times the original braking distance.
Baily had 36 and Elena had 40
First, the angles of triangle MNP add up to 180º. Since angle M is 142º and angle P is 24º, angle N must be (180-24-142)º or 14º.
Now angle N is congruent to angle U.
2x - 50 = 14
2x = 64
x = 32
Segment NP is congruent to segment US, so 13 = 2x - y AND x=32.
13 = 62 - y
y = 49
