Explanation:
In order to prove that affirmation, we define the function g over the interval [0, 1/2] with the formula 
If we evaluate g at the endpoints we have
g(0) = f(1/2)-f(0) = f(1/2) - f(1) (because f(0) = f(1))
g(1/2) = f(1) - f(1/2) = -g(0)
Since g(1/2) = -g(0), we have one chance out of three
- g(0) > 0 and g(1/2) < 0
- g(0) < 0 and g(1/2) > 0
- g(0) = g(1/2) = 0
We will prove that g has a zero on [0,1/2]. If g(0) = 0, then it is trivial. If g(0) ≠ 0, then we are in one of the first two cases, and therefore g(0) * g(1/2) < 0. Since f is continuous, so is g. Bolzano's Theorem assures that there exists c in (0,1/2) such that g(c) = 0. This proves that g has at least one zero on [0,1/2].
Let c be a 0 of g, then we have
Hence, f(c+1/2) = f(c) as we wanted.
The formula is V = (4/3) pi * r^3
r = 10 cm^3 = 1000 cm^3 That let's out D
V = (4/3) * 3.14 * 1000
V = (1.3333) * 3.14 * 1000
V = 1333 * 3.14
V = 4185 cm^3
A <<<< ==== answer
Utilice la división larga. olvidarse de los puntos decimales. para que sea más fácil llevar a cabo. A continuación, poner el punto decimal en el mismo lugar que el dividendo (el número se divide) primero cambie el número estamos dividiendo por un número entero en primer lugar, desplazando el punto de ambos números de decimal a la derecha for example:
6.85/.5=68.5/5
solve
13.7
Answer: 27 feet per second
Step-by-step explanation:
A submarine dives 378 in 14 seconds.
So to find the number of feet a submarine dives per second, divide 378 by 14.
So your answer is 27 feet per second.
The amount of money she have one year after she started the investment = 1000((1 + r/t)^nt - 1) / (r/t); where r = 3% = 0.03, t = 12 and n = 1 year.
Amount = 1000((1 + 0.03/12)^(1 x 12) - 1) / (0.03 / 12) = 1000((1 + 0.0025)^12 - 1) / (0.03 / 12) = 1000((1.0025)^12 - 1) / 0.0025 = 1000(1.0304 - 1) / 0.0025 = 12,166.38
Therefore, the amount she has in her bank account at the end of the year is $12,166.38
