Answer:
C
Step-by-step explanation:
In general for arithmetic sequences, recursive formulas are of the form
aₙ = aₙ₋₁ + d,
and the explicit formula (like tₙ in your problem), are of the form
aₙ = a₁ + (n - 1)d,
where d is the common difference. So converting between the two of these isn't so bad. In this case, your problem wants you to have an idea of what t₁ is (well, every answer says it's -5, so there you are) and what tₙ₊₁ is. Using the formulas above and your given tₙ = -5 + (n - 1)78, we can see that the common difference is 78, so no matter what we get ourselves into, the constant being added on at the end should be 78. That automatically throws out answer choice D.
But to narrow it down between the rest of them, you want to use the general form for the recursive formula and substitute (n + 1) for every instance of n. This will let you find tₙ₊₁ to match the requirements of your answer choices. So
tₙ₊₁ = t₍ₙ₊₁₎₋₁ + d ... Simplify the subscript
tₙ₊₁ = tₙ + d
Therefore, your formula for tₙ₊₁ = tₙ + 78, which is answer choice C.
Answer:
$16,640
Step-by-step explanation:
Tim's total annual wage expense is ...
($8.00 /h)(40 h/wk)(52 wk/yr) = $8×40×52 /yr = $16,640 per year
Answer:
its just a black screeeeen
Step-by-step explanation:
Answer:
108 bottles
Step-by-step explanation:
the total is 4.536 oz of vitamin pills
each bottle can accomodate 0.042 oz of vitamin pills
to know the quantity of each bottle
we calculate
0.042 oz of vitamin pills = 1 bottle
4.536 oz of vitamin pills = (4.536 x 1)/0.042=108
so therefore 4.536 oz of vitamin pills will accomodate 108 bottles
The diver will hit the water when the height is zero, so we will want to set our height function equal to zero
0 = -4t^2 + 11t + 3
we will then factor to find out value of t that make the function equal to zero
0 = (-4t - 1 ) ( t - 3 )
This means our function equals zero when t = -1/4 s and t = 3 seconds
Since time cannot be negative, our final solution is t = 3 seconds
