Find the length of side x.
1 answer:
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Answer:
3.189 seconds
Step-by-step explanation:
You want f(t) = 0, so ...
0 = -16t^2 +13.4t +120
0 = t^2 -0.8375t -7.5 . . . . divide by -16
0 = (t^2 -0.8375t +0.41875^2) -7.5 -0.41875^2 . . . . complete the square*
0 = (t -0.41875)^2 -7.6753515625 . . . . write as a square
√7.6753515625 = t -0.41875 . . . . . . . . add 7.67... and take positive root
t = 0.41875 +√7.6753515625 ≈ 3.189192 . . . . add 0.41875
It will take the rock about 3.189 seconds to hit the ground.
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* We complete the square by adding the square of half the coefficient of the linear term (= (-0.8375/2)^2) inside parentheses and subtracting the same amount outside parentheses. This gives a form inside parentheses that is ...
(t^2 -2at +a^2) = (t -a)^2
Completing the square is complicated a little bit by a leading coefficient that is not 1. That is why we divided by -16 first.
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<em>Comment on the question</em>
We note that the rock "falls" from the 120 foot high balcony by first traveling upward at a rate of 13.4 feet per second. We also note that the height function is written f(x), but uses t as the variable. That is, it should be f(t) = ...
Question 16
Given that two golfers completed one round of golf.
It is stated that the first golfer had a score of +6 and the second golfer had a score of -3.
- Let suppose 'x' be the number of shots the first golfer took.
It is clear that the first golfer is 6 over par, while the second golfer is under 3.
Thus, the equation becomes:
adding -3 to both sides
simplify
Thus, the second golfer has taken 9 more shorts.
Question 17
When we talk about credit, it means:
Credit = +
When we talk about debt, it means:
Debit = -
Thus,
Credit = +84
Debt = -29
Balance = 84 + (-29)
= 84 - 29
= 55
Thus, the balance is: 55