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3 years ago

Why is the product of a rational number and an irrational number Irrational?

Mathematics

2 answers:

Llana [10]3 years ago

5 0

Answer:

Because the product is always non-termination,non-repeating decimal.

Step-by-step explanation:

If we have $a$ is irrational; $b$ is rational such that $b \neq 0$ , then $a \cdot b$ is irrational.

A way to represent this is:

$a\in\mathbb{R}\setminus\mathbb{Q}, b\in\mathbb{Q},ab\in\mathbb{Q}\implies a\in\mathbb{Q}\implies\text{Contradiction}\therefore ab\not\in\mathbb{Q}.$

Note that we have a contradiction, because $a$ is not a rational number, as I stated in the beginning. Therefore, ab is irrational.

Marta_Voda [28]3 years ago

5 0

Answer: A

Step-by-step explanation:

Multiplying an irrational number by a rational number will always be an irrational number because irrational numbers do not repeat and terminate.

So for example multiplying pi by a rational like two you will have an irrational number because pi is an irrational number.

$\pi * 2$ = 6.28318530718 as you could see that is an irrational number because there is no repetition or termination.

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What is the approximate volume of a basketball with the circumference of 42ft ?

Semmy [17]

We know that

[volume of a sphere]=(4/3)*pi*r³

length of a circumference=42 ft
[length of a circumference]=2*pi*r-------> r=[length of a circumference]/(2*pi)
r=[42]/(2*pi)---------> r=6.6845 ft

[volume of a sphere]=(4/3)*pi*6.6845³-----------> 1251.11 ft³

the answer is 1251.11 ft³

4 0

3 years ago

At the fair, the ratio of males to females was 4:5. If there are 180 people at the fair, how mamy males are there?

Setler79 [48]

Answer:

80 males

Step-by-step explanation:

180 / 9 = 20

20 x 4 = 80

3 0

3 years ago

Read 2 more answers

can someone please solve this? I clicked on homework help and it wasn't much help. I'm trying to turn in as much missing assignm

MA_775_DIABLO [31]

Answer:

One proportion to solve is 8/18 = x/8
Exact answer as a fraction: x = 32/9
Approximate answer in decimal form: x = 3.556

In reality, the 5's go on forever, but we have to round off somewhere.

========================================================

Explanation:

Break up the triangles as your teacher recommends. See the diagram below as to what I mean.

The smaller triangle has A = 8 as the horizontal side, and B = x as the vertical side

The larger triangle has C = 10+8 = 18 as the horizontal aside, and D = 8 as the vertical side.

We can form the proportion A/C = B/D.

A/C connects the horizontal sides (small/large) while B/D has the vertical sides tied together. The order of division is the same small over large. You could do large over small, but make sure you keep both sides consistent.

-----------------

Let's solve for x

A/C = B/D

8/18 = x/8

8*8 = 18*x .... cross multiply

64 = 18x

18x = 64

x = 64/18 .... divide both sides by 18

x = 32/9 exactly in fraction form

x = 3.556 approximately in decimal form

-------------------

Another proportion you can solve is A/B = C/D and you should get the same x value. It's the same as A/C = B/D because the B and C swap places. There are many other approaches you could take using different proportions.

6 0

3 years ago

Read 2 more answers

Find the area under the standard normal curve to the left of

JulijaS [17]

A. z = 0.74
The z-score of 0.74 translates to a percentile of 0.77035. Hence, the area under the standard normal curve to the left of z-score 0.74 is ~0.77.

b. z = -2.16
This z-score translates to a percentile of 0.015386 which is also the numerical value of the area under the curve to the left of the z-score

c. z = 1.02
The percentile equivalent of the z-score above is 0.846. The area is also 0.846.

d. z = -0.15
The percentile equivalent and the area is equal to 0.44.

6 0

3 years ago

A survey of voters explored the relationship between the ages of voters and wether or not they support building skateboard ramps

Novosadov [1.4K]

Answer:

(a)12%

(b)20%

Step-by-step explanation:

(a)In the age group 58 and above: