Answer:
$7153.03
Step-by-step explanation:
To find the total amount after 3 years, we can use the formula for compound tax:
P = Po * (1+r/n)^(t*n)
where P is the final value, Po is the inicial value, r is the rate, t is the amount of time and n depends on how the tax is compounded (in this case, it is semi-annually, so n = 2)
For our problem, we have that Po = 5000, r = 12.3% = 0.123, t = 3 years and n = 2, then we can calculate P:
P = 5000 * (1 + 0.123/2)^(3*2)
P = 5000 * (1 + 0.0615)^6
P = $7153.029
Rounding to the nearest cent, we have P = $7153.03
The answer is C. The scale factor of the smaller triangle to the larger triangle is 18:54, or 1:3. The ratio of their areas is the scale factor squared, 1:9. If the larger triangle had an area of 567, the smaller triangle is 1/9th of that. 567 divided by 9 is 63.
Answer:
The tree break at 5 m height above ground
Step-by-step explanation:
At x m height the tree break, the upper part 18-x m fell
(18 - x)² - x² = 12²
324 - 36x + x² - x² = 144
36x = 324 - 144 = 180
x = 5
<span>To use Law of Cosines, you need to know an angle and two sides.
The simplest case is if you know two sides (a and b) and the included angle (C)
c² = a² + b² − 2ab cos(C)
cos(A) = (b² + c² − a²) / (2bc)
cos(B) = (a² + c² − b²) / (2ac)
You can also use Law of Cosines if you know 2 sides (b and c), and non-included angle (C). We use first equation above, solving for a. Since the equation is a quadratic (with respect to unknown variable a), it is simpler to use Law of Sines in this case.
You can also use Law of Cosines if you know the 3 sides (a,b,c)
cos(A) = (b² + c² − a²) / (2bc)
cos(B) = (a² + c² − b²) / (2ac)
cos(C) = (a² + b² − c²) / (2ab)</span>
I would say irrational. Hope this helps!
