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3 years ago

Find the primary solution of cosθ=−0.3 ⁡

Mathematics

1 answer:

Agata [3.3K]3 years ago

4 0

The solution of cos θ = −0.3 is θ = 107.45760312 degrees

<em><u>Solution:</u></em>

Given that we have to find the primary solution of $cos \theta = -0.3$

To solve this equation, you must find the unknown (theta)

$cos \theta = -0.3$

Use the inverse of cosine (Arccos) to find the angle measurement (in degrees) of theta

$\theta = arccos (-0.3)$

We know that arccos (-0.3) = 107.45760312 degrees

[ If you reference a unit circle or use a calculator ]

$\theta = 107.45760312^{\circ}$

Therefore solution of cos θ = −0.3 is θ = 107.45760312 degrees

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Find the common fraction equivalent to 0.12

jonny [76]

The answer is: " $\frac{4}{33}$ "  .
______________________________
Given: 0.1212121212..... repeating ; write that value as a fraction;
______________________________________________________
In other words; we are given: "0.1212121212..... repeating infinitely" ;

→ that is to say; "0.12 ... ; {the "12" decimal portion repeats infinitely} ;
_______________________________________________________
→ We write this value, as a fraction, as: "12/99" ;
__________________________________________
→Explanation:
__________________________________________

Note: "0.99999999...... repeating infinitely; = "1" .
_________________________________________
→Since:

Let us say that we have:

"x = 0.999999 ; repeating infinitely;

In order words, let us say we have: "x = 0.9.... ; the "9" decimal repeats infinitely;
_____________________________________________________
Then "10x" ; (that is: "10" multlipled by "x"; or "10*x" or "10x" ); is equal to:

"10" * (0.999999.....) = 9.99999999...... (the "9" decimal repeats infinitely);

in other words: 10x = 9.99999999....

Divide each side by "10" ;

to get "x = 0.9999999....." ; the decimal "9" repeats indefinitely...." ;

But if you have: "10x = 10" ; divide each side of the equation by "10" ;
you get: "x = 1" .
____________________
Also, if "x = 0.9999...(repeating infinitely);

then: 10x = 9.99999.
_______________________________________________
10x = 9.999999999999999......
−   x = 0.999999999999999.......
_____________________________________
9x = 9.00000000000000000000.....

→ 9x = 9 ;

Divide each side of the equation; to get;

9x /9 = 9/ 9 ; to get: x = 1 ; and we have: x = 0.9999.... ; so
x= 0.99999.... = 1 ;
__________________________________________________
So, if the numbers "12" is repeating, we divie "12" by "99" ;
that is; we divide "12" by "two 9's" ; since "12" is a "TWO-digit number"; a "two-digit number" is being repeated infinitely.
________________________________________
So; 0.12121212.....(the "12" is the decimal that repeats infinitely);

= 12/99 ; which can be simplified;

Divide each side (both the numerator AND the denominator); by "3" ;
_________________________________________
" 12/99 " = "(12÷3) / (99÷3) = 4/33 " .
_________________________________________
The answer is: $\frac{4}{33}$   .
_________________________________________

8 0

3 years ago

Read 2 more answers

If the measure of angle JKP is 3r + 12 and the measure of angle PKN is 4r - 2, what is the measure of angle JKN

il63 [147K]

Answer should be 108 would you mind sending a visual so I can be sure

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2 years ago

Give an example of two numbers that are both 6-digit numbers, but the greater number is determined by the hundreds place

SashulF [63]

The order of the numbers for a 6-digit number from left to right is as follows:
hundred thousands, ten thousands, thousands, hundreds, tens and then units

We want two numbers were the greater number is determined by its hundreds place, these two numbers can be:
165,827 and 165,229
The hundreds in the first is 8 while the hundreds in the second is 2. Therefore, the first number is larger.

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3 years ago

Mary must choose a new password where the first and last choices are possibly repeated lowercase letters; the second and third

Salsk061 [2.6K]

The number of ways she can choose a password is 3986236800

<h3>In how many ways can she choose a password?</h3>

The given parameters and the possible selection of characters are:

First and last choices are possibly repeated lowercase letters;

There are 26 lower characters.

Since the characters can be repeated, then we have

First = 26

Last = 26

The second and third positions must be distinct uppercase letters

There are 26 upper characters.

Since the characters are distinct, then we have

Second = 26

Third = 25

The fourth position must be a # , $, or & symbol;

So, we have

Fourth = 3

The next four positions are distinct nonzero digits.

There are 9 nonzero digits.

Since the digits are distinct, then we have

Next = 9, 8, 7, 6

The number of ways she can choose a password is

Ways = First * Second * Third * Fourth * Next * Last

So, we have

Ways = 26 * 26 * 25 * 3 * 9 * 8 * 7 * 6 * 26

Evaluate the product

Ways = 3986236800

Hence, the number of ways she can choose a password is 3986236800