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.
Inclusive means within and the number n, while exclusive means within and without the number n
Answer:
y = x*(6 feet/1 fathom)
Step-by-step explanation:
We know the relation:
1 fathom = 6 feet.
We can write:
1 = (6 feet/1 fathom)
Now, remember that any number multiplied by 1 does not change.
Then suppose that we have a measure of 3 fathoms, then:
3 fathoms = (3 fathoms)*1
= (3 fathoms)*((6 feet/1 fathom)) = (3 fathoms/1 fathom)*(6feet)
= 3*(6 feet) = 18 feet.
So we changed the units by multiplying the original measure by (6 feet/1 fathom)
Then, if x is the depth of water in fathoms and y is the depth of the water in feet, we can write:
y = x*(6 feet/1 fathom)
The answer is obtuse triangle
1000÷350=2.85714286 thats the answer
