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Sophie [7]
2 years ago
5

If theta is a positive acute angles find theta when 2 sin^2 theta + 3 cos theta =3​

Mathematics
1 answer:
MArishka [77]2 years ago
6 0

Answer:

Theta = 0, 60 degrees.

Step-by-step explanation:

2 sin^2 theta + 3 cos theta = 3​

Using the identity sin ^2 theta = 1 - cos^2 theta :

2(1 - cos^2 theta) + 3 cos theta  = 3

2 - 2cos^2 theta) + 3 cos theta  = 3

2 cos^2 theta - 3 cos theta   + 3 - 2 = 0

2 cos^2 theta - 3 cos theta   + 1 = 0

(2 cos theta - 1)(cos theta - 1) = 0

cos theta = 1/2 , cos theta = 1

Theta = 60 degrees or theta = 0

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Step-by-step explanation:

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Answer:

81.8%

Step-by-step explanation:

Mean = \mu = 40

Standard deviation = \sigma = 5

Now we are supposed to find out what percent of the numbers fall between 35 and 50

z = \frac{x-\mu}{\sigma}

Substitute the values

z = \frac{x-40}{5}

Now for P(35<x<50)

Substitute x = 35

z = \frac{35-40}{5}

z =-1

Substitute x = 50

z = \frac{50-40}{5}

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So, P(-1<z<2)

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=0.8185

= 0.818 \times 100

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Hence  81.8% percent of the numbers fall between 35 and 50

7 0
3 years ago
Prove the multiple of two consecutive integers is positive
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Answer:

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Step-by-step explanation:

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irina1246 [14]

Answer:

<h3>          The mean is 3.74</h3>

Step-by-step explanation:

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