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MAXImum [283]
2 years ago
8

Use the results of exercises 18 and 19 to prove that given any two rational numbers r and s with r , s, there is another rationa

l number between r and s. An important consequence is that there are infinitely many rational numbers in between any two distinct rational numbers.
Mathematics
1 answer:
777dan777 [17]2 years ago
5 0

Answer:

Step-by-step explanation:

Let r and s be two rational numbers

Without loss of generality assume that r<s, because one number has to be necessarily less than the other otherwise two would be equal.

Then find mid value of r and s as

\frac{r+s}{2} =t

So we have atleast one rational number between r and s. Note that t is rational because it is sum of two rational numbers r/2 and s/2

Now using r and t we find one rational number say u between r and t.  

Again with r and u we find another rational number between them

This process can be repeated infinitely

Thus we conclude there are infinitely many rational numbers in between any two distinct rational numbers.

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PLEASE HELP!!!<br>Simplify the expression and show your work<br><br>sqrt110x^17y^12
leonid [27]

Answer:

Step-by-step explanation:

10y2 - 17y + 12 = y + 16

10y2 - 17y + 12 - 16 = y

10y2 - 17y - 4 = y

10y2 -17y - y -4 = 0

10y2 -16y - 4 = 0

Now put formula

x = -b +- (square root) b2 - 4ac

                 2a

a = 10 b= -16 c= -4

y = -(-16) +- (square root) -16 - 4 (10) (-4)

                             2(10)

y = 16 +- (square root) -16 - 400

                                20

y = 16 +- (square root) -416

                         20

y = 16 +- 20.396

              20

Now this +- is the plus minus thingy in which two answers come

The first we will do is +

16 + 20.396                                         16 - 20.396

  20                                                             20

= 1.8198                                                           = -0.2198

6 0
3 years ago
If one redskin and 4 golden roughs cost $1.65, whereas 2 redskins and 3 golden roughs cost $1.55, how much does each type or swe
Bas_tet [7]

Answer:

Redskins cost $0.25 and golden roughs cost $0.35.

Step-by-step explanation:

Let r be the cost of a redskin and g the cost of golden roughs. So we have the system of equations:

r + 4g = 1.65

2r + 3g = 1.55

Multiply the first equation by -2:

-2r - 8g = -3.30

Adding this to the second equation:

-5g = -1.75

g = 0.35.

Now substitute this into the first equation:

r + 4*0.35 = 1.65

r  = 1.65 - 1.40

r = 0.25.

5 0
3 years ago
Sean and his family are picking strawberries at a pick-your-own fruit farm. The rectangular strawberry field has an area of 210,
nasty-shy [4]

Answer:

512 ft is the length of the field

Step-by-step explanation:

Firstly, we need to know the area of the field. We have confirmed this to be rectangular. Since it’s a rectangular field, the area of the field can be obtained by multiplying the length of the field by the breadth or width of the field.

Mathematically A = L * W

In the question, A = 210,944 ft^2

L= ? and W = 412ft

In essence, we are trying to calculate the value for the length of the field

L = A/W

L = (210,944)/412 = 512ft

8 0
3 years ago
Help pls! I can't figure it out
katrin2010 [14]
Answer:

It’s 72
Hope this helps!
5 0
2 years ago
A glass containing water is in the shape of a right circular cylinder with a radius of 3
Lubov Fominskaja [6]

Answer:

Step-by-step explanation:

The equation for a cylinder is the radius of the circle times pi squared, multiplied by the height. 3 squared is 9, times pi is 9(pi). If we multiply this by the height, the answer is 90(pi) centimeters in volume.

5 0
3 years ago
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