Answer:
<em>The domain of f is (-∞,4)</em>
Step-by-step explanation:
<u>Domain of a Function</u>
The domain of a function f is the set of all the values that the input variable can take so the function exists.
We are given the function

It's a rational function which denominator cannot be 0. In the denominator, there is a square root whose radicand cannot be negative, that is, 4-x must be positive or zero, but the previous restriction takes out 0 from the domain, thus:
4 - x > 0
Subtracting 4:
- x > -4
Multiplying by -1 and swapping the inequality sign:
x < 4
Thus the domain of f is (-∞,4)
Answer:
The time taken by Allan to complete the marathon 3.5 hours
Step-by-step explanation:
Given as :
The distance cover in marathon = d = 26.2 miles
∵ 1 mile = 1.609 km
So, d = 26.2 × 1.609 km
i.e d = 42.155 kilo meter
The average speed of Allan = s = 12 km per hour
Let the time taken by Allan to complete the marathon = t hours
Now, ∵ Time = 
Or, t = 
Or, t = 
or, t = 3.512 hours
So , The time taken by Allan to complete the marathon = t = 3.5 hours
Hence, The time taken by Allan to complete the marathon 3.5 hours Answer
Answer:
We can have two cases.
A quadratic function where the leading coefficient is larger than zero, in this case the arms of the graph will open up, and it will continue forever, so the maximum in this case is infinite.
A quadratic function where the leading coefficient is negative. In this case the arms of the graph will open down, then the maximum of the quadratic function coincides with the vertex of the function.
Where for a generic function:
y(x) = a*x^2 + b*x + c
The vertex is at:
x = -a/2b
and the maximum value is:
y(-a/2b)
Answer:
60
Step-by-step explanation:
You need the least common multiple of 5, 3, and 4.
5 = 5, 10, 15, 20, 25... 60
3= 3, 6, 9...60
4=4, 8, 12, ...60