Answer:
7 years
Step-by-step explanation:
The depreciation rate of 12% using the declining balance method means the car is worth 12% less at the end of the year than it was worth at the beginning. That is, each year the value is multiplied by (1 -12%) = 0.88. So, after n years, the value has been multiplied by 0.88^n.
We want to find n such that ...
7600 = 18600·0.88^n
7600/18600 = 0.88^n
log(76/186) = n·log(0.88)
log(76/186)/log(0.88) = n ≈ 7.00
It will take 7 years for the value of the car to decline to $7600.
_____
<em>Comment on declining balance depreciation</em>
Often, you will see declining balance depreciation specified in terms of an acceleration factor (often 150% or 200% ("double declining balance")) and a useful life. As with any depreciation, what is depreciated is the difference between the initial value and the salvage value. The percentage rate quoted above is essentially calculated as ...
(acceleration factor)/(useful life) = depreciation rate per year
One way to get a 12% depreciation rate is using an acceleration factor of 150% and a useful life of 12.5 years (with a salvage value of 0).
If these triangles are congruent, then side RS is congruent to side TV and that means that y = 4 - x. If y = 4-x, we can sub that into the next equation where side RV = side ST and 1 = 4x - y. If y = 4-x, we sub in accordingly to get 1 =4x - (4 - x). That simplifies to 1 = 4x - 4 + x which is, combining like terms, 5 = 5x. That means that x = 1. If x = 1, and y = 4 - x, then y = 4 - 1 and y = 3. There you go!
9514 1404 393
Answer:
C) 65°
Step-by-step explanation:
The relevant trig relation is ...
Cos = Adjacent/Hypotenuse
cos(?) = 25/59
? = arccos(25/59) ≈ 64.93°
The indicated angle is about 65°.
_____
You can see that the figure is drawn approximately to scale and that the angle is more than 45°. (The unmarked leg is longer than the given leg.) The only answer choice that is more than 45° is the one shown above.
