Current amount in account
P=36948.61
Future value of this amount after n years at i=11% annual interest
F1=P(1+i)^n
=36948.61(1.11)^n
Future value of $3000 annual deposits after n years at i=11%
F2=A((1+i)^n-1)/i
=3000(1.11^n-1)/0.11
We'd like to have F1+F2=280000, so forming following equation:
F1+F2=280000
=>
36948.61(1.11)^n+3000(1.11^n-1)/0.11=280000
We can solve this by trial and error.
The rule of 72 tells us that money at 11% deposited will double in 72/11=6.5 years, approximately.
The initial amount of 36948.61 will become 4 times as much in 13 years, equal to approximately 147800 by then.
Meanwhile the 3000 a year for 13 years has a total of 39000. It will only grow about half as fast, namely doubling in about 13 years, or worth 78000.
Future value at 13 years = 147800+78000=225800.
That will take approximately 2 more years, or 225800*1.11^2=278000.
So our first guess is 15 years, and calculate the target amount
=36948.61(1.11)^15+3000(1.11^15-1)/0.11
=280000.01, right on.
So it takes 15.00 years to reach the goal of 280000 years.
Use this "1 mg = (1/1000000) kg = 10-6<span> kg = 0.000001 kg"</span>
The axis of symmetry can be found by finding the average of the zeros, a derivation from the conservation of energy :P, or by finding the point when the velocity is equal to zero.
df/dx=-6x+12 so df/dx, velocity, equals zero when:
-6x+12=0
6x=12
x=2 so the axis of symmetry is the vertical line x=2
....
average of zeros...
3x^2-12x+6=0
x^2-4x+2=0
x^2-4x=-2
x^2-4x+4=2
(x-2)^2=2
x-2=±√2
x=2±√2 so the average of the zeros is obviously 2.
....
conservation of energy
vf-vi=at When vf=0, this is the maximum value for f(x)...
-vi=at, vi=b and a(acceleration)=2a(from quadratic) and t=x
-b=2ax
x=-b/(2a) in this case
x=-12/(2(-3))
x=-12/-6
x=2
Answer:
Step-by-step explanation:
<u>Sum of internal angles of a regular polygon is:</u>
<u>We have here 5-sided polygon:</u>
- S = 180*(5 - 2) = 180°*3 = 540°
<u>Now sum the given angles measures and solve for x:</u>
- 3x + 1 + 2x + 15 + 3x - 10 + 3x - 8 + 5x - 2 = 540
- 16x - 4 = 540
- 16x = 544
- x = 544/16
- x = 34°
<u>Find the measure of angle R:</u>
- m∠R = 3x - 10 = 3*34 - 10 = 102 - 10 = 92
- m∠R = 92°
Answer:
224
Step-by-step explanation:
Substitute x = 4 and y = 2 into the expression and evaluate
7x²y = 7 × 4² × 2 = 7 × 16 × 2 = 7 × 32 = 224.
Hope this helped you!
