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Alekssandra [29.7K]
2 years ago
14

Trigonometric equations 4sin^2(theta) + 4 = 5

Mathematics
1 answer:
Drupady [299]2 years ago
5 0

Answer:

Θ = (π/6) + πn

Θ = (5π/6) + πn

Step-by-step explanation:

4sin²Θ + 4 = 5

            -4    -4

4sin²Θ = 1

÷4         ÷4

sin²Θ = (1/4)

√sin²Θ = √(1/4)

sinΘ = (1/2), (-1/2)

-------------------------

Θ = arcsin (1/2)

Θ = (π/6)

to find the quadrant subtract π

Θ = π - (π/6)

Θ = (5π/6)

Find the period

2π / |b|

b = 1

2π/1 = 2π

The sin Θ function is 2π, so values will repeat 2π in both directions.

Θ = (π/6) + 2πn (n is the variable)

Θ = (5π/6) + 2πn

-------------------------------------------------------------------------------------------------------

sin Θ = (-1/2)

Θ = arcsin (-1/2)

Θ = (-π/6)

To find the second function add π

Θ = 2π + (π/6) + π

Θ = (7π/6)

Find the period

2π/|b|

2π/1

2π

(-π/6) + 2π

2π       6         π

----- ×  ----- -  -----

1           6        6

Θ = (11π/6) will repeat every 2π in both directions

-------------------------------------------------------------------------------------------------------

Θ = (π/6) + 2πn

Θ = (5π/6) + 2πn

Θ = (7π/6) + 2πn

Θ = (11π/6) + 2πn

(π/6) + π = (7π/6)

(5π/6) + π = (11π/6)

Θ = (π/6) + πn

Θ = (5π/6) + πn

----------------------------------------------------------------------------------------------------------

I hope this helps!

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Remember, to the find the volume, you have to do length*width*height.

So it would be 7/4 * 3/2 * 1/2

To answer this, multiply all the numerators together, and multiply all the denominator together.

This would be:

21/16



So the answer is 21/16 cm^3 or 1.3125 cm^3.


Hope this helps. If you have any questions, place it in the comment section below.


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3 years ago
4(3x + 2) =16x + 7 -4x + 1
GrogVix [38]

Answer:

All real numbers are solutions.

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

4(3x+2)=16x+7−4x+1

(4)(3x)+(4)(2)=16x+7+−4x+1(Distribute)

12x+8=16x+7+−4x+1

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12x+8=12x+8

12x+8=12x+8

Step 2: Subtract 12x from both sides.

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Use the cumulative normal distribution table to find the z-scores thqt bound the middle of 68% of theje area under the stanrard
padilas [110]

Answer:

Z scores between -0.995 and 0.995 bound the middle 68% of the area under the stanrard normal curve

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

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16th percentile:

X when Z has a pvalue of 0.16. So X when Z = -0.995

84th percentile:

X when Z has a pvalue of 0.84. So X when Z = 0.995.

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