Answer:
F(x)=
+7cosh(x)+C
Step-by-step explanation:
The function is f(x)=3ˣ+7sinh(x), so we can define it as f(x)=g(x)+h(x) where g(x)=3ˣ and h(x)=7sinh(x).
Now we have to find the most general antiderivative of the function this means that we have to calculate 
wich is the same as 
The sum rule in integration states that the integral of a sum of two functions is equal to the sum of their integrals. Then,
= 
1- 
this is because of the rule for integration of exponencial functions, this rule is:
, in this case a=3
2-
, number seven is a constant (it doesn´t depend of "x") so it "gets out" of the integral.
The result then is:
F(x)=
The letter C is added because the integrations is undefined.
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Remark
The two trains are travelling towards each other. That means that their total distance = 912 km. Neither one has gone that distance by itself. The effect this has on the question is that you add the two rates multiplied by time.
Givens
r1 = x
r2 = x + 12
t = 3 hours
d = 912 km
Equation
d = r * t
r1 * t + r2 * t = 912
Solution
3x + 3*(x + 12) = 912 Remove the brackets
3x + 3x + 36 = 912 Combine like terms
6x + 36 = 912 Subtract 36 from both sides
<u> -36 -36</u>
6x = 876 Divide both sides by 6
6x/6 = 876/6
x = 146 km/h
Answer
Slow train = 146 km/hr
Fast train = 146 + 12 = 158 km/hr
