Answer:
Account 1 yields greater return.
Step-by-step explanation:
Lets solve for the first formula:
First, change 6.5% into a decimal:
6.5% -> 
-> 0.065
Now, plug in the values for Account 1:
<u>Now solve for Account 2:</u>
Change 6% into a decimal:
6% -> 
-> 0.06
Now plug in the values:
Account 1 yields better money after 10 years.
The area of a regular hexagon with an apothem 18.5 inches long and a side 21 inches is 1, 165. 5 In²
<h3>
How to calculate the area of a regular hexagon</h3>
The formula is given thus;
Area of hexagon = (1/2) × a × P
where a = the length of the apothem
P = perimeter of the hexagon
Given a = 18. 5 inches
Note that Perimeter, p = 6a with 'a' as side
p = 6 × 21 = 126 inches
Substitute values into the formula
Area, A = 1 ÷2 × 18. 5 × 126 = 1 ÷2 × 2331 = 1, 165. 5 In²
Thus, the area of the regular hexagon is 1, 165. 5 In²
Learn more about the area of a hexagon here:
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The answer is. $1500.
Let x represent the amount invested at 5%, then is the amount invested at 8%, and is the amount invested at 6%. Since the total return is $1270:
let money invested at 5%= x
money invested at 6%
= 20000- (X+X-1500)
21500-2x
Total interest for 1 year.
x×5/100+ (x-1500)×8/100+(21500-2x)×6/100 = 1270
5x/100+8(x-1500)/100+(21500-2x)6/100=1270
5x+8x-12000+129000-12x = 127000
x+117000 = 127000
x = 10000
money invested at 8%
=21500-2×10000
= 1500.
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vi is going in the positive direction (up). (That's my choice). a (acceleration) is going in the minus direction (down). The directions could be reversed.
Givens
vi = 160 ft/s
vf = 0 (the rocket stops at the maximum height.)
a = - 9.81 m/s
t = ????
Remark
YOu have 4 parameters between the givens and what you want to solve. Only 1 equation will relate those 4. Always always list your givens with these problems so you can pick the right equation.
Equation
a = (vf - vi)/t
Solve
- 32 = (0 - 160)/t Multiply both sides by t
-32 * t = - 160 Divide by -32
t = - 160/-32
t = 5
You will also need to solve for the height to answer part B
t = 5
vi = 160 m/s
a = - 32
d = ???
d = vi*t + 1/2 a t^2
d = 160*5 + 1/2 * - 32 * 5^2
d = 800 - 400
d = 400 feet
Part B
You are at the maximum height. vi is 0 this time because you are starting to descend.
vi = 0
a = 32 m/s^2
d = 400 feet
t = ??
formula
d = vi*t + 1/2 a t^2
400 = 0 + 1/2 * 32 * t^2
400 = 16 * t^2
400/16 = t^2
t^2 = 25
t = 5 sec
The free fall takes the same amount of time to come down as it did to go up. Sort of an amazing result.
