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artcher [175]
3 years ago
15

2sin²(x)-5cos(x)+1=0

Mathematics
1 answer:
Margarita [4]3 years ago
7 0
Remember the basic trig identity

<u />\sin^2 x + \cos^2 x = 1

We can move the cosine term to the right side to get

\sin^2 x = 1 - \cos^2 x

We can then replace \sin^2 x in the original equation and basically factor the resulting equation like a quadratic:

2(1 - \cos^2 x) - 5 \cos x + 1 = 0
(2 - 2 \cos^2 x) - 5 \cos x + 1 = 0
{-2} \cos^2 x - 5 \cos x  + 3 = 0
2 \cos^2 x + 5 \cos x - 3 = 0
(2 \cos x - 1)(\cos x + 3) = 0&#10;&#10;

Then, we can see that \cos x either equals \frac{1}{2} or -3. But since the range of cosine is only from [-1, 1], cosine can't equal -3 at all! So, you just have to solve for x when \cos x =  \frac{1}{2}, which is when

x = \{ \frac{\pi}{3}, \frac{5\pi}{3} \} + 2 \pi k | k \in \mathbb{Z}
(The last part of the solution says that k can be any integer.)

If you only want solutions in the range [0, 2\pi), then your answer is just

x = \frac{\pi}{3}, \frac{5\pi}{3}









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Round off 2371 +1625 to the nearest hundred​
riadik2000 [5.3K]

Answer:

2000 + 2000 = 4000

Step-by-step explanation:

2371 is rounded to 2000

1625 is rounded to 2000

2000 + 2000 = 4000

Hope this helps!

6 0
3 years ago
Read 2 more answers
HELP ME PLEASE!
leva [86]
The answer is choice A

The sample space is basically the set of all possible outcomes. Each outcome is a pair of results from drawing a card coupled with spinning a spinner. 

Table A represents all of the possible outcomes properly. The card results are along the column on the left side. The spinner results along the row up at the top. Each cell is an intersection of the left and top result. For example, row1,column3 has "red,purple" to indicate you got "red" on the spinner and "purple" on the card. Each cell in table A is correctly labeled.

The other tables (B, C, D) are improperly labeled in at least one cell. 
* Table B has "blue, green" in the top row" middle cell when it should be "blue, purple"

* Table C has "green, green" in the upper left corner when it should be "green, purple"

* Table D has "blue, blue" in the bottom middle cell when it should be "blue, green". Saying "blue,blue" is impossible as there isn't a blue card.

The three items mentioned above help us eliminate choices B through D.
7 0
3 years ago
Read 2 more answers
The simple interest earned on a deposit of 4000 at 5% for 120 days
Ymorist [56]

Answer:A = $4,066.00

Step-by-step explanation:

Calculation:

First, converting R percent to r a decimal

r = R/100 = 5%/100 = 0.05 per year.

Putting time into years for simplicity,

120 days / 360 days/year = 0.33 years.

Solving our equation:

A = 4000(1 + (0.05 × 0.33)) = 4066

A = $4,066.00

The total amount accrued, principal plus interest, from simple interest on a principal of $4,000.00 at a rate of 5% per year for 0.33 years (120 days) is $4,066.00.

* Hopefully this helps:) Mark me the brainlliest:)!!

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5 0
3 years ago
Affonso has 14 fewer dimes than nickels. He has 21 dimes. Use the five-step problem-solving plan. How many nickels does Affonso
Helga [31]
HEY THERE!!

FIRST STEP :- Affonso has 14 fewer dimes than nickels.

SECOND STEP:- Nickels has 21 dimes.

so Affonso has nickels:-
21 - 14 = 7

Hope it helps you.
5 0
3 years ago
Select all equations that are equivalent to x² + 6x = 16.
ohaa [14]

Answer:

C and F

Step-by-step explanation:

2×2+6×2=16

×=2

C ) 2×2+6×2+9=25 ×=2

F) (2+3)2=25 ×=2

6 0
2 years ago
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