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2 years ago

PLEASE HELP AND SHOW WORK!!

Mathematics

1 answer:

Nastasia [14]2 years ago

7 0

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:

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He vertices of square pqrs are p -4,0 q 4,3 r 7,-5 and s -1,-18.Show that the diagonals of square pqrs are congruent perpendicul

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Answer:

Step-by-step explanation:

The vertices of the square given are P(-4, 0), Q(4, 3), R(7, -5) and, S(-1, -18)

For this diagonal to be right angle the slope of the diagonal must be m1=-1/m2

So let find the slope of diagonal 1

The two points are P and R

P(-4, 0), R(7, -5)

Slope is given as

m1=∆y/∆x

m1=(y2-y1)/(x2-x1)

m1=-5-0/7--4

m1=-5/7+4

m1=-5/11

Slope of the second diagonal

Which is Q and S

Q(4, 3), S(-1, -18)

m2=∆y/∆x

m2=(y2-y1)/(x2-x1)

m2=(-18-3)/(-1-4)

m2=-21/-5

m2=21/5

So, slope of diagonal 1 is not equal to slope two

This shows that the diagonal of the square are not diagonal.

But the diagonal of a square should be perpendicular, this shows that this is not a square, let prove that with distance between two points

Given two points

(x1,y1) and (x2,y2)

Distance between the two points is

D=√(y2-y1)²+(x2-x1)²

For line PQ

P(-4, 0), Q(4, 3)

PQ=√(3-0)²+(4--4)²

PQ=√(3)²+(4+4)²

PQ=√9+8²

PQ=√9+64

PQ=√73

Also let fine RS

R(7, -5) and, S(-1, -18)

RS=√(-18--5)+(-1-7)

RS=√(-18+5)²+(-1-7)²

RS=√(-13)²+(-8)²

RS=√169+64

RS=√233

Since RS is not equal to PQ then this is not a square, a square is suppose to have equal sides

But I suspect one of the vertices is wrong, vertices S it should have been (-1,-8) and not (-1,-18)

So using S(-1,-8)

Let apply this to the slope

Q(4, 3), S(-1, -8)

m2=∆y/∆x

m2=(y2-y1)/(x2-x1)

m2=(-8-3)/(-1-4)

m2=-11/-5

m2=11/5

Now,

Let find the negative reciprocal of m2

Reciprocal of m2 is 5/11

Then negative of it is -5/11

Which is equal to m1

Then, the square diagonal is perpendicular

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