Which of the expressions (on the photo document I inserted) together represent all solutions to the following equation?

Mathematics

1 answer:

Ipatiy [6.2K]3 years ago

7 0

Answer:

x =15 + 30n

Step-by-step explanation:

8cos(12x)+4=-4

Subtract 4 from each side

8cos(12x)+4-4=-4-4

8cos(12x)=-8

Divide by 8

8/8cos(12x)=-8/8

cos(12x) = -1

Take the arccos on each side

arccos(cos(12x)) = arccos(-1)

12x = 180 degrees

But we can go around in a circle of 360 and get the same result

12 x = 180+360n where n is an integer

Divide each side by 12

x = 180/12 +360n/12

x =15 + 30n

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What much expression represents a rational number?

Pie

Answer:

$\displaystyle \frac{2}{7}+\sqrt{121}$

Step-by-step explanation:

<u>Rational Numbers</u>

A rational number is any number that can be expressed as a fraction

$\displaystyle \frac{a}{b}, \ b\neq 0$

for a and b any integer and b different from 0.

As a consequence, any number that cannot be expressed as a fraction or rational number is defined as an Irrational number.

Let's analyze each one of the given options

$\displaystyle \frac{5}{9}+\sqrt{18}$

The first part of the number is indeed a rational number, but the second part is a square root whose result cannot be expressed as a rational, thus the number is not rational

$\pi + \sqrt{16}$

The second part is an exact square root (resulting 4) but the first part is a known irrational number called pi. It's not possible to express pi as a fraction, thus the number is irrational

$\displaystyle \frac{2}{7}+\sqrt{121}$

The square root of 121 is 11. It makes the whole number a sum of a rational number plus an integer, thus the given number is rational

$\displaystyle \frac{3}{10}+\sqrt{11}$