ANSWER
1. k=13
2. x=-10
EXPLANATION
The given function is
To find f(x+5), plug in (x+5) wherever you see x.
This implies that:
Expand:
Simplify to obtain
We now compare with,
This implies that:
To find the smallest zero of f(x+5), we equate the function to zero and solve for x.
The smallest zero is -10.
7 1/2 happy early thanksgiving :)
1. We use the recursive formula to make the table of values:
f(1) = 35
f(2) = f(1) + f(2-1) = f(1) + f(1) = 35 + 35 = 70
f(3) = f(1) + f(3-1) = f(1) + f(2) = 35 + 70 = 105
f(4) = f(1) + f(4-1) = f(1) + f(3) = 35 + 105 = 140
f(5) = f(1) + f(5-1) = f(1) + f(4) = 35 + 140 = 175
2. We observe that the pattern is that for each increase of n by 1, the value of f(n) increases by 35. The explicit equation would be that f(n) = 35n. This fits with the description that Bill saves up $35 each week, thus meaning that he adds $35 to the previous week's value.
3. Therefore, the value of f(40) = 35*40 = 1400. This is easier than having to calculate each value from f(1) up to f(39) individually. The answer of 1400 means that Bill will have saved up $1400 after 40 weeks.
4. For the sequence of 5, 6, 8, 11, 15, 20, 26, 33, 41...
The first-order differences between each pair of terms is: 1, 2, 3, 4, 5, 6, 7, 8...since these differences form a linear equation, this sequence can be expressed as a quadratic equation. Since quadratics are functions (they do not have repeating values of the x-coordinate), therefore, this sequence can also be considered a function.
Answer:
Ok, suppose you want to create a battery that fits exactly in the hole that is already created for an electric device, like a cellphone for example.
If the battery is slightly bigger, it will not enter the socket, and the battery will be a loss in time and resources.
If the battery is slightly smaller, it will move when it is in the socket, so the cell phone will shut down randomly when you move it, then this battery is also a loss in time and resources.
So you need to measure exactly the socket in order to make a battery that fits exactly inside of it with very good precision.
This example can be extended for any electronic piece that you need to fit in a given space (for example in microtechnology, the precision of the measures is must be extreme because working with those things is really expensive and you can not mess up with the dimensions of the pieces)
