All categories

3 years ago

What are all the exact solutions of 2 sin^2 x- sin x = 0

2 answers:

8 0

2sin^2 x - sinx = 0
add sinx to both sides

2sin^2 x = sinx
divide bot sides by sinx

2sinx = 1
divide both sides by 2

sinx = 1/2
inverse trig function

x = π/6
** but the sine function is harmonic and hits 1/2 every 2π from π/6

So the answer is..
x = π/6 + 2nπ

where n is an integer

alexandr1967 [171]3 years ago

7 0

Factor:

2sin^2x-sinx = 0

sinx(2sinx - 1) = 0

Therefore the solutions are when:

sin x = 0
And
sinx = 1/2

So sinx = 0
is true when x = 0 and pi and all the angles coterminal with these points. Thus, the answer is x = pi*n, (where n is some integer)

sinx = 1/2
is true when x = pi/6 and 5pi/6 and the angles coterminal with these points.
Thus, the answer is x = pi/6 + 2pi*n (where n is some integer)
and x = 5pi/6 + 2pi*n (where n is some integer)

You might be interested in

What is the inverse of this function?<br> [Will give Brainliest]

ira [324]

Answer:

the inverse of a function is the exact opposite

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

A random sample of 20 recent weddings in a country yielded a mean wedding cost of $ 26,388.67. Assume that recent wedding costs

Makovka662 [10]

Answer:

a) 95% confidence interval for the meancost, μ, of all recent weddings in this country = (22,550.95, 30,226.40)

.The 95% confidence interval is from $22,550.95 to $30,226.40.

b) For the interpretation of the result, option D is correct.

We can be 95% confident that the mean cost, μ, of all recent weddings in this country is somewhere within the confidence interval.

c) Option B is correct.

The population mean may or may not lie in this interval, but we can be 95% confident that it does.

Step-by-step explanation:

Sample size = 20

Sample Mean = $26,388.67

Sample Standard deviation = $8200

Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample mean) ± (Margin of error)

Sample Mean = 26,388.67

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the mean)

Critical value will be obtained using the t-distribution. This is because there is no information provided for the population mean and standard deviation.

To find the critical value from the t-tables, we first find the degree of freedom and the significance level.

Degree of freedom = df = n - 1 = 20 - 1 = 19.

Significance level for 95% confidence interval

(100% - 95%)/2 = 2.5% = 0.025

t (0.025, 19) = 2.086 (from the t-tables)

Standard error of the mean = σₓ = (σ/√n)

σ = standard deviation of the sample = 8200

n = sample size = 20

σₓ = (8200/√20) = 1833.6

99% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]

CI = 26,388.67 ± (2.093 × 1833.6)

CI = 26,388.67 ± 3,837.7248

99% CI = (22,550.9452, 30,226.3948)

99% Confidence interval = (22,550.95, 30,226.40)

a) 95% confidence interval for the meancost, μ, of all recent weddings in this country = (22,550.95, 30,226.40)

.The 95% confidence interval is from $22,550.95 to $30,226.40.

b) The interpretation of the confidence interval obtained, just as explained above is that we can be 95% confident that the mean cost, μ,of all recent weddings in this country is somewhere within the confidence interval

c) A further explanation would be that the population mean may or may not lie in this interval, but we can be 95% confident that it does.

Hope this Helps!!!

4 0

2 years ago

Read and analyze the following then solve. <br>ASAP ASAP ASAP ASAP ASAP ASAP ASAP

Vaselesa [24]

☾☆☾☆☾☆☾☆☾☆☾☆☾☆☾☆☾☆☾☆☾☆☾

<h3>JOH-EUN OHUEYO!!</h3>

(GOOD AFTERNOON)

➢

$\frac{3}{6} \times \frac{1}{2} = \frac{1}{4}$

➢

$\frac{5}{7} \times \frac{3}{8} = \frac{15}{32}$

➢

$\frac{4}{8} \times \frac{1}{4} = \frac{1}{8}$

➢

$2 \frac{1}{2} \times 3 \frac{2}{5} = 8 \frac{1}{2}$

➢

$\frac{8}{14} \times \frac{1}{2} = \frac{2}{7}$

➢

$\frac{3}{4} \div \frac{1}{4} = 3$

➢

$1 \frac{2}{3} \div 2 \frac{3}{5} = \frac{25}{39}$

➢

$\frac{3}{9} \div \frac{2}{3} = \frac{1}{2}$

➢

$1 \frac{3}{7} \div 2 \frac{1}{6} = \frac{60}{91}$

➢

$2 \frac{4}{5} \div \frac{3}{10} = 9 \frac{1}{3}$

☾☆☾☆☾☆☾☆☾☆☾☆☾☆☾☆☾☆☾☆☾☆☾

3 0

2 years ago

Read 2 more answers

Andrea is told that the means of two groups in a study were statistically significant. She knows the means and standard deviatio

salantis [7]

Answer:

Cohen's D

Step-by-step explanation:

Cohen's D is a statistic that measures effect size. It shows standardised difference between 2 means.

Effect size is defined as how large the effect of a something is or its magnitude.

Cohen's D works effectively when the sample is >50 (that is for large samples). However a correction factor can be used to make results from small samples more accurate

The formular for Cohen's D is:

D = (mean1 - mean2) ÷ (√({standard deviation1}^2 + {standard deviation 2}^2)/2)

This is the most appropriate method in the given scenario

5 0

2 years ago

Solve for k:<br><br> k + 6 > -20

FrozenT [24]

Answer:

k > -26

Step-by-step explanation:

To isolate the k, you subtract 6 from both sides to get k < -26.

4 0

3 years ago

Read 2 more answers