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alekssr [168]
3 years ago
6

Write four related fact. use pictures to show how the number sentences are related.

Mathematics
1 answer:
sleet_krkn [62]3 years ago
8 0
Division , timetable , adding , and subtracting
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2〖sen〗^2 x+3 senx+1=0
KonstantinChe [14]

2 sin²(<em>x</em>) + 3 sin(<em>x</em>) + 1 = 0

(2 sin(<em>x</em>) + 1) (sin(<em>x</em>) + 1) = 0

2 sin(<em>x</em>) + 1 = 0   OR   sin(<em>x</em>) + 1 = 0

sin(<em>x</em>) = -1/2   OR   sin(<em>x</em>) = -1

The first equation gives two solution sets,

<em>x</em> = sin⁻¹(-1/2) + 2<em>nπ</em> = -<em>π</em>/6 + 2<em>nπ</em>

<em>x</em> = <em>π</em> - sin⁻¹(-1/2) + 2<em>nπ</em> = 5<em>π</em>/6 + 2<em>nπ</em>

(where <em>n</em> is any integer), while the second equation gives

<em>x</em> = sin⁻¹(-1) + 2<em>nπ</em> = -<em>π</em>/2 + 2<em>nπ</em>

2 cot(<em>x</em>) sec(<em>x</em>) + 2 sec(<em>x</em>) + cot(<em>x</em>) + 1 = 0

2 sec(<em>x</em>) (cot(<em>x</em>) + 1) + cot(<em>x</em>) + 1 = 0

(2 sec(<em>x</em>) + 1) (cot(<em>x</em>) + 1) = 0

2 sec(<em>x</em>) + 1 = 0   OR   cot(<em>x</em>) + 1 = 0

sec(<em>x</em>) = -1/2   OR   cot(<em>x</em>) = -1

cos(<em>x</em>) = -2   OR   tan(<em>x</em>) = -1

The first equation has no (real) solutions, since -1 ≤ cos(<em>x</em>) ≤ 1 for all (real) <em>x</em>. The second equation gives

<em>x</em> = tan⁻¹(-1) + <em>nπ</em> = -<em>π</em>/4 + <em>nπ</em>

<em />

sin(<em>x</em>) cos²(<em>x</em>) = sin(<em>x</em>)

sin(<em>x</em>) cos²(<em>x</em>) - sin(<em>x</em>) = 0

sin(<em>x</em>) (cos²(<em>x</em>) - 1) = 0

sin(<em>x</em>) (-sin²(<em>x</em>)) = 0

sin³(<em>x</em>) = 0

sin(<em>x</em>) = 0

<em>x</em> = sin⁻¹(0) + 2<em>nπ</em> = 2<em>nπ</em>

<em />

2 cos²(<em>x</em>) + 2 sin(<em>x</em>) - 12 = 0

2 (1 - sin²(<em>x</em>)) + 2 sin(<em>x</em>) - 12 = 0

-2 sin²(<em>x</em>) + 2 sin(<em>x</em>) - 10 = 0

sin²(<em>x</em>) - sin(<em>x</em>) + 5 = 0

Using the quadratic formula, we get

sin(<em>x</em>) = (1 ± √(1 - 20)) / 2 = (1 ± √(-19)) / 2

but the square root contains a negative number, which means there is no real solution.

2 csc²(<em>x</em>) + cot²(<em>x</em>) - 3 = 0

2 (cot²(<em>x</em>) + 1) + cot²(<em>x</em>) - 3 = 0

3 cot²(<em>x</em>) - 1 = 0

cot²(<em>x</em>) = 1/3

tan²(<em>x</em>) = 3

tan(<em>x</em>) = ± √3

<em>x</em> = tan⁻¹(√3) + <em>nπ</em>  OR   <em>x</em> = tan⁻¹(-√3) + <em>nπ</em>

<em>x</em> = <em>π</em>/3 + <em>nπ</em>   OR   <em>x</em> = -<em>π</em>/3 + <em>nπ</em>

7 0
3 years ago
Solve the inequality. 1/2 + x + 1/6 is greater than or equal to 1.
Andrew [12]

1/2 + x + 1/6 > = 1

First add the 2 fractions:

1/2 + 1/6 = 2/3

Now you have:

2/3 + x > =1

Subtract 2/3 from both sides:

x >= 1 - 2/3

X > = 1/3

5 0
3 years ago
Solve 2x+2&gt;10 i need to know what this is?
mrs_skeptik [129]

Answer:

x>4

Step-by-step explanation:

2x + 2 > 10 \\ 2x > 10 - 2 \\ 2x > 8 \\ x > 4

Sorry if there is any mistakes

6 0
3 years ago
If line segment AB measures approximately 8.6 units and is considered the base of parallelogram ABCD, what is the approximate co
Anna007 [38]

Answer:

4.8

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
There are ten shirts in your closet, four blue, three green, and three red. You randomly select a different shirt each day. You
Law Incorporation [45]
It's a probability problem to find the odds of picking a green or red shirt out of the 10 shirts on Thursday, Friday and Saturday since you have randomly already know you have picked a blue shirt on the other days. Not sure if you have this as a multiple question problem as you didn't list any possible answers (A. 7/20, B. 5/47, C. 2/5, D. 4/125) to the question. A, B, C, D being like 7 chances out of 20, 5 chances out 47, 2 chances out of chances 5 or 4 chances out of 125 (example answers only).

Probability = Number favorable outcomes / total number of outcomes





7 0
3 years ago
Read 2 more answers
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