Answer:
<em>The rate of the boat is 75.17 km/h and the rate of the stream is 17.83 km/h</em>
Step-by-step explanation:
<u>System of Equations</u>
Let's call:
B = speed (rate) of the boat in still water
S = speed (rate) of the stream
The boat travels 172 km in 3 hours when going upstream, that is when the speed of the stream subtracts its own speed. The speed is the distance divided by the time, thus:
Multiplying by 3:
3B - 3S = 172 [1]
The boat travels 372 km in 4 hours downstream when the speed of the current adds to its own:
B + S = 93
Solving for B:
B = 93 - S [2]
Substituting in [1]
3(93 - S) - 3S = 172
Operating:
279 - 3S - 3S = 172
279 - 6S = 172
Subtracting 279:
- 6S = 172 - 279
- 6S = -107
Multiplying by -1 and solving for S:
From [2]:
Answer:
1845 years
Step-by-step explanation:
Decay of Carbon-14 is usually modeled by an exponential function. It x is the number of years since the original amount was brought into existence, then the fraction remaining (y) is modeled by ...
... y = (1/2)^(x/5730)
We want to find the value of x when y = 80% = 0.80. The equation is then ...
... 0.80 = 0.50^(x/5730)
Taking logarithms, we get
... log(0.80) = (x/5730)·log(0.50)
Multiplying by the inverse of the coefficient of x, we have
... x = 5730·log(0.80)/log(0.50) ≈ 1845 . . . . years
The property which states that multiplying a number by 1 does not change the number's value is the identity property. <span>Adding zero to a number does not change the number's value is the zero property, but some people do also call it the identity property of addition. Hope this helped!</span>
Answer:
244 inches squared
Step-by-step explanation:
basically just subtract the area of four rectangles by the total area of cardboard. so you would get 500-256=244
