All categories

3 years ago

The sum of rational number and an irrational number

Mathematics

1 answer:

Angelina_Jolie [31]3 years ago

5 0

Answer:

The sum of a rational number and an irrational number is irrational." By definition, an irrational number in decimal form goes on forever without repeating (a non-repeating, non-terminating decimal). By definition, a rational number in decimal form either terminates or repeats.

Step-by-step explanation:

However, if the irrational parts of the numbers have a zero sum (cancel each other out), the sum will be rational. "The product of two irrational numbers is SOMETIMES irrational." Each time they assume the sum is rational; however, upon rearranging the terms of their equation, they get a contradiction (that an irrational number is equal to a rational number). Since the assumption that the sum of a rational and irrational number is rational leads to a contradiction, the sum must be irrational.

You might be interested in

. A hawk flying at a height of 60 feet spots a rabbit on the ground. If the hawk dives at a speed of 55 feet per second, how

Vladimir [108]

Answer:

The hawk reaches the rabbit at t=4.3 sec

Step-by-step explanation:

Let

h ----> is the height in feet

t ----> is the time in seconds

v ---> the initial velocity in feet pr second

s ----- is the starting height

we have

$h=-16t^{2} +vt+s$

when the hawk reaches the rabbit the value of h is equal to zero

we have

$v=55\ ft/sec$

$s=60\ ft$

substitute

$0=-16t^{2} +55t+60$

Solve the quadratic equation by graphing

The solution is t=4.3 sec

see the attached figure

8 0

3 years ago

How do you do this question?

tatyana61 [14]

Answer:

Step-by-step explanation:

The increments are 0.4, and the width of the interval is 10, so the number of increments (the number of times you need to use Euler's method) is:

10 / 0.4 = 25

8 0

2 years ago

Find the surface area of the figure. 22 m 12 m 5 m

prohojiy [21]

Answer:

12 m

Step-by-step explanation:

3 0

3 years ago

Find the common difference of the sequence shown 1/6,1/3,1/2,2/3,......

tekilochka [14]

Answer:

Common Difference(d) is

$d=\frac{1}{6}$

Step-by-step explanation:

Given sequence is :

$\frac{1}{6}, \frac{1}{3} ,\frac{1}{2} ,\frac{2}{3} .........$

If a sequence has a constant common difference throughout the sequence, then the sequence is called Arithmetic Progression.

Considering a sequence:

$a_1,a_2,a_3,a_4..........\\$

$a_2-a_1=a_3-a_2=a_4-a_3=a_n-a_n_-_1=d$

where 'd' is the common difference of the A.P.

Similarly, finding the common difference of the given sequence.

$\frac{1}{3} -\frac{1}{6}= \frac{1}{2}- \frac{1}{3}=\frac{2}{3} - \frac{1}{2}=d\\$

$d=\frac{1}{3}-\frac{1}{6}=\frac{(2)(1)-(1)(1)}{6}=\frac{1}{6}$

$d=\frac{1}{6}$

Common Difference(d) is

$d=\frac{1}{6}$

8 0

3 years ago

Read 2 more answers

Find the area of the region that lies under the parabola y=5x - x^2, where 1≤x≤4. I would definitely like to see some work :)

Elena L [17]

Answer:

16.5 square units

Step-by-step explanation:

You are expected to integrate the function between x=1 and x=4:

$\displaystyle\text{area}=\int_1^4{(5x-x^2)}\,dx=\left.\left(\dfrac{5}{2}x^2-\dfrac{1}{3}x^3\right)\right|_{x=1}^{x=4}\\\\=\dfrac{5(4^2-1^2)}{2}-\dfrac{4^3-1^3}{3}=37.5-21=\boxed{16.5}$

Additional comment

If you're aware that the area inside a (symmetrical) parabola is 2/3 of the area of the enclosing rectangle, you can compute the desired area as follows.

The parabolic curve is 4-1 = 3 units wide between x=1 and x=4. It extends upward 2.25 units from y=4 to y=6.25, so the enclosing rectangle is 3×2.25 = 6.75 square units. 2/3 of that area is (2/3)(6.75) = 4.5 square units.

This region sits on top of a rectangle 3 units wide and 4 units high, so the total area under the parabolic curve is ...

area = 4.5 +3×4 = 16.5 . . . square units

4 0

2 years ago