Answer:
The correct answer is D
Step-by-step explanation:
The range of the function is all real numbers greater than or equal to 0.
33.68
27.4
x
--------
922.832
Let daniel's age = d and let jessica's age = j
let your current age = x and your wife's current age = y
x = 5d (given in question)
∴ x - 5d = 0
x + 21 = 2(d+21) (given in question)
∴ x + 21 = 2d + 42
∴ x - 2d = 21
We can solve these two rearranged equations simultaneously by multiplying the first equation by -1 and adding them. This gives us the following:
3d = 21
∴ d = 7
This means that daniel is currently 7 and (if we substitute d = 7 into one of the equations) you are 35. We use a similar method for your wife's and jessica's current ages.
y = 7j (given in question)
∴ y - 7j = 0
y + 8 = 3(j + 8)
∴y + 8 = 3j + 24
∴ y - 3j = 16
If we use a similar method of elimination we get this:
4j = 16
∴ j = 4
Hence, from this we can concur that daniel is 7 and jessica is 4.
F(x) is continuous for all x.
Pick a point and show that f(x) is either negative or positive. Pick another point and show that f(x) is negative, if positive, or positive, if negative.
At x = 30, f(30) - 1000 = 900 + 10sin(30) - 1000 ≤ 0
Now, show at another point f(x) - 1000 is positive, and hence, there would be root between 30 and such point.
Let's pick 40.
At x = 40, f(40) - 1000 = 1600 + 10sin(40) - 1000 ≥ 0
Since f(x) - 1000 is continuous, there lies a root between 30 and 40, and hence, 30 ≤ c ≤ 40
