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PtichkaEL [24]
3 years ago
9

Given: sin(18m-12)=cos(7m+2), find the value of m.

Mathematics
1 answer:
V125BC [204]3 years ago
3 0

Answer:

m = -2/7 + π/14 + (π n_1)/7 for n_1 element Z

or m = 2/3 - (π n_2)/18 for n_2 element Z

Step-by-step explanation:

Solve for m:

-cos(7 m + 2) sin(12 - 18 m) = 0

Multiply both sides by -1:

cos(7 m + 2) sin(12 - 18 m) = 0

Split into two equations:

cos(7 m + 2) = 0 or sin(12 - 18 m) = 0

Take the inverse cosine of both sides:

7 m + 2 = π n_1 + π/2 for n_1 element Z

or sin(12 - 18 m) = 0

Subtract 2 from both sides:

7 m = -2 + π/2 + π n_1 for n_1 element Z

or sin(12 - 18 m) = 0

Divide both sides by 7:

m = -2/7 + π/14 + (π n_1)/7 for n_1 element Z

or sin(12 - 18 m) = 0

Take the inverse sine of both sides:

m = -2/7 + π/14 + (π n_1)/7 for n_1 element Z

or 12 - 18 m = π n_2 for n_2 element Z

Subtract 12 from both sides:

m = -2/7 + π/14 + (π n_1)/7 for n_1 element Z

or -18 m = π n_2 - 12 for n_2 element Z

Divide both sides by -18:

Answer: m = -2/7 + π/14 + (π n_1)/7 for n_1 element Z

or m = 2/3 - (π n_2)/18 for n_2 element Z

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Answer:

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Step-by-step explanation: You have to combine like terms first:

-3.8x -5.9x                 =223.1

-9.7x                          = 223.1

Then divide om each side of the equation by -9.7.

-9.7x/-9.7                   = 223.1/-9.7

x                               =- 23

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3 years ago
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ANSWER

\cos(150 \degree)  =    -  \frac{ \sqrt{3} }{2}

EXPLANATION

We want to find the exact value of cos(150°).

150° makes an angle of 30° with the positive direction of the x-axis and it is also in the second quadrant.

The cosine ratio is negative in the second quadrant.

Using the unit circle,

\cos(150 \degree)  =  - \cos(30 \degree) =   -  \frac{ \sqrt{3} }{2}

8 0
3 years ago
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True or false: if a figure is a hexagon, then it is a regular polygon
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2 years ago
Show that each of these conditional statements is a tautology by using truth tables. a) [¬p ∧ (p ∨ q)] → q b) [(p → q) ∧ (q → r)
nlexa [21]

Step-by-step explanation:

To show that a statement is a tautology using truth table - is to show that all the entries in the expression are truths T.

We can do this by taking each statement, expression by expression. For example, to show that

[~p ∧ (p ∨ q)] → q

is a tautology, knowing we have 3 columns, we have 2^3 = 8 rows. We start by putting putting truth values for p, q, and r respectively

Next, we find ~p, then find (p ∨ q), then find ~p ∧ (p ∨ q), before finally arriving at the required [~p ∧ (p ∨ q)] → q

TERMINOLOGIES AND SYMBOLS

- T means Truth

- F means False

- ~p means negation of p.

~p is F if p is T, and vice versa

- ∧ means conjunction.

p ∧ q is T only if p is T and q is T.

- ∨ means disjunction.

p ∨ q is T if either p or q is T.

- → is for conditional 'if then'

p → q is T if both p and q are T, or both p and q are F, or p is F and q is T, otherwise, it is F.

THE STEP BY STEP WORKINGS FOR THE STATEMENTS GIVEN ARE IN THE ATTACHMENT.

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Answer:

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1.

4/9,4/3,4,12,36

Multiply each term by 3 to get the next term. There is a common ratio between terms, so it geometric.

2.

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Add 1 to each term to get the next term. Since there is a common difference between terms, it is an arithmetic sequence.

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