If the price of a gallon of gas increases from $3.20 to $3.68, what percent did it increase?
1 answer:
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Answer:
Check attachment for complete question
Step-by-step explanation:
Given that,
y=Coskt
We are looking for value of k, that satisfies 4y''=-25y
Let find y' and y''
y=Coskt
y'=-kSinkt
y''=-k²Coskt
Then, applying this 4y'"=-25y
4(-k²Coskt)=-25Coskt
-4k²Coskt=-25Coskt
Divide through by Coskt and we assume Coskt is not equal to zero
-4k²=-25
k²=-25/-4
k²=25/4
Then, k=√(25/4)
k= ± 5/2
b. Let assume we want to use this
y=ASinkt+BCoskt
Since k= ± 5/2
y=A•Sin(±5/2t)+ B •Cos(±5/2t)
y'=±5/2ACos(±5/2t)-±5/2BSin(±5/2t)
y''=-25/4ASin(±5/2t)-25/4BCos(±5/2t
Then, inserting this to our equation given to check if it a solution to y=ASinkt+BCoskt
4y''=-25y
For 4y''
4(-25/4ASin(±5/2t)-25/4BCos(±5/2t))
-25A•Sin(±5/2t)-25B•Cos(±5/2t).
Then,
-25y
-25(A•Sin(±5/2t)+ B •Cos(±5/2t))
-25A•Sin(±5/2t) - 25B •Cos(±5/2t)
Then, we notice that, 4y'' is equal to -25y, then we can say that y=Coskt is a solution to y=ASinkt+BCoskt
Felecia's husband will catch up to her 1 hour 30 minutes after leaving.
Step-by-step explanation:
Step 1; Felecia is traveling at 45 mph, her husband starts 20 minutes after her but travels at a speed of 55 mph. So first we need to calculate how much of a head start Felecia got.
Head start = × 45 miles an hour = 15 miles.
So Felecia got a head start of 15 miles.
Step 2; Since Felecia and her husband are traveling at different rates, we can determine how much distance there is between them. Since Felecia is traveling at 45 mph and her husband is traveling at 55 mph, their gap in between is closing at a rate of 55 - 45 = 10 miles every hour. So for every hour, the gap between them is closing by 10 miles.
Total gap initially = 15 miles.
The rate at which gap is being closed = 10 miles an hour.
Time to close the gap = 15 / 10 = 1.5 hours.