Answer:
1 A= pi 21^2
2 C=pi 21
3 A= pi 10.5^2
4 C= 2pi 10.5
Step-by-step explanation:
Answer:
21 roads
Step-by-step explanation:
If each two cities are connected by a direct road, to find the number of roads we just need to solve a combination of 7 choose 2, that is, we need to find all pairs of two cities among the 7 cities:
Combination of 7 choose 2 = 7! / (5! * 2!) = 7*6/2 = 21
So there is a total of 21 roads on the island.
The question regards composite functions. A composite function is a function composed of more than one function. Sorry for saying the word function so many times there, it's just what it is...
The phrase f(g(x)) means 'perform g on an input x, then perform f on the result'. You can then see that there are many options for f(x) and g(x) here, in fact an infinite number of one were to be ridiculous about it.
However a sensible choice might be g(x) = x^2, and f(x) = 2/x + 9. Checking:
g(x) = x^2
f(g(x)) = 2/(x^2) + 9
That is the first question dealt with. Next up is Q2. It is relatively simple to show that these functions are inverses. If you start with a value x, apply a function and then apply the function's inverse, you should return to the same starting value x. To take a common example, within a certain domain, sin^-1(sin(x)) = x.
f(g(x)) = (sqrt(3+x))^2 - 3 = 3 + x - 3 = x
g(f(x)) = sqrt(x^2 - 3 + 3) = sqrt(x^2) = x
A final note is that this is only true for a certain domain, that is x <= 0. This is because y = x^2 is a many-to-one function, so unrestricted it does not have an inverse. Take the example to illustrate this:
If x = -2, f(x) = (-2)^2 - 3 = 4 - 3 = 1
Then g(f(x)) =sqrt(1 + 3) = sqrt(4) = 2 (principal value).
However the question isn't testing knowledge of that.
I hope this helps you :)
15376
/ I
961 16
/ I / I
31 31 4 4
31 × 4 = 124
The square root of 15376 is 124
6 in the number 6.45 is the ones digit.
6 in the number 62 is the tens digit.
