Complete the paragraph proof. Given: and are right angles Line segment A B is-congruent-to line segment B C Line segment B C is-
2 answers:
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Answer:
Pipe 1 alone fills a tank in 10 min
Pipe 2 alone fills the tank in 20 min
If both are turned on together, how long will it take to fill the tank???
Pipe 1 fills at the RATE of 1/10th tank per min
Pipe 2 fills at the RATE of 1/20th tank per min
Pipe 1 + Pipe 2 fills at the rate of 1/10+1/20 or 3/20th tank per min
Let x= time to fill the tank
(3/20)(x)=1 Where 1 denotes a full tank (Multiply both sides by 20)
3x=20
x=6 2/3 min----------both working together
NOW YOUR PROBLEM
Let x= amount of time for smaller pipe to fill the tank
Then (x-5)=amount of time for larger pipe to fill the tank
NOW HERE'S WHERE THE RECIPROCAL COMES IN:
The smaller pipe fills the tank at the RATE of 1/x cu units per min
The larger tank fills the tank at the RATE of 1/(x-5) cu units per min
Together, they fill the tank at the rate of 1/x+(1/(x-5)) cu units per min
But now we are told that together the fill the tank in 11 1/9 minutes. so our equation to solve is:
(1/x+(1/(x-5))(11 1/9)=1 where 1 denotes a full tank. In fact, in each of the above reciprocals, the 1 denotes a full tank.
So, dividing both sides by 11 1/9, we get:
1/x+(1/(x-5)=1/(11 1/9)-------------- which is your equation
I assume that you have no problems solviing this eq.
Hope this helps----ptaylor
Step-by-step explanation:
Answer:
x= -11/4 is a maximum.
Step-by-step explanation:
Remember that a function has its critical points where the derivative equal zero. Therefore we need to compute the derivative of this function and find the points where the derivative is zero. Using the chain rule and the product rule we get that
And then we get that if then
. So it has a critical point at
.
Now, if the second derivative evaluated at that point is less than 0 then the point is a maximum and if is greater than zero the point is a minimum.
Since
x= -11/4 is a maximum.