285 ml = 285 cm3
Assuming the bottle is cylindrical we have A*19 = 285 where A is the base area. So A = 285/19 = 15 cm2.
Capacity of bottle = A*h where h = 19 + 4 cm = 23 cm so Capacity of bottle = 15*23 cm3 = 345 cm3 = 345ml
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5% of $6000 is (5/100)*6000 = $300 so he borrowed $5700
18% p.a. of $5700 is (18/100)*5700 = $1026
If he pays this back each month he pays $1026/12 = $85.50 each month.
(25/45)*100 ≈ 55.6%
Good try gibsonj, but you should check your working. I get the following:
Start by multiplying all terms by 10 to get:
It gives 1x10-7 for me!
Gravitational potential energy is given by mass*g*height, where g is gravitational acceleration (9.81 m/s2 ). You can plug in the numbers!
If F1 and F2 are at the same angle then they must have the same magnitude to prevent any horizontal movement.
The vertical components of force require that 2F1*sin(48.5) = 9.8*2.8
or: F1 = 9.8*2.8/(2sin(48.5))
Can you take it from here?
The domain is x<0 and x>3
The region between 0 and 3 produces values of 3x^2 - 9x for which the logarithm isn't defined (for Real numbers).
This has already been answered at: http://web2.0calc.com/questions/an-automobile-is-depreciating-at-10-per-year-every-year-a-22-000-car-depreciating-at-this-rate-can-be-modeled-by-the-equation-v-t-22-000-0-90-t-what#r1
The term (5/2)^x is common to both terms as (5/2)^(x+3) can be written in the form (5/2)^x*(5/2)^3
So (5/2)^x + (5/2)^(x+3) → (5/2)^x*(1 + (5/2)^3) → (5/2)^x*(1 + 125/8) → (5/2)^x*(133/8)
So with A = 133/8 we have (5/2)^x + (5/2)^(x+3) = A*(5/2)^x
+33667 
