A boat drops an anchor 17.5 feet to the bottom of a lake.If the anchor falls at a rate of .07 feet each second how long will it
1 answer:
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Answer:
See below.
Step-by-step explanation:
First, notice that this is a composition of functions. For instance, let's let and
. Then, the given equation is essentially
. Thus, we can use the chain rule.
Recall the chain rule: . So, let's find the derivative of each function:
We can use the Power Rule here:
Now:
Again, use the Power Rule and Sum Rule
Now, we can put them together:
Answer:
5.6 gallons.
Step-by-step explanation:
If we take x gallons of 25% grape juice then it will contain gallons of pure grape juice.
Again, if we take y gallons of 75% grape juice then it will contain gallons of pure grape juice.
If we mix them then the total volume will become x + y = 7 gallons ...... (1)
Again the mixture will become 35% juice.
So,
⇒ 0.25x + 0.75y = 0.35x + 0.35y
⇒0.1x = 0.4y
⇒x = 4y........ (2)
Now, solving equations (1) and (2) we get, 5y = 7, ⇒ y = 1.4 gallons
Hence, x = 4y = 5.6 gallons
Therefore, the 25% grape juice was mixed by 5.6 gallons. (Answer)