Mathematics College

Solve the equation for exact solutions over the interval [0, 2π).

Answers

Answer 1

Answer:

[tex]\displaystyle x=\left\{0, \frac{2\pi}{3}, \frac{4\pi}{3}\right\}[/tex]

Step-by-step explanation:

We want to solve the equation:

[tex]-2\cos^2(x)=-\cos(x)-1[/tex]

Over the interval [0, 2π).

First, notice that this is in quadratic form. So, to make things simpler, we can let u = cos(x). Substitute:

[tex]-2u^2=-u-1[/tex]

Rearrange:

[tex]2u^2-u-1=0[/tex]

Factor:

[tex](2u+1)(u-1)=0[/tex]

Zero Product Property:

[tex]2u+1=0\text{ or } u-1=0[/tex]

Solve for each case:

[tex]\displaystyle u=-\frac{1}{2}\text{ or } u=1[/tex]

Back-substitute:

[tex]\displaystyle \cos(x)=-\frac{1}{2}\text{ or } \cos(x)=1[/tex]

Using the unit circle:

[tex]\displaystyle x=\left\{0, \frac{2\pi}{3}, \frac{4\pi}{3}\right\}[/tex]

Related Questions

HELP me with this work please

Answers

Answer:

135in^3

Step-by-step explanation:

Enter the values for the highlighted variables to
complete the steps to find the sum:
az
b =
3x 9
+
2x - 6 6 - 2x
CE
d =
3 x
9
+
2x-6 al 2x-6)
3x b.
+
2x-6 2x - 6
3х – с
2x-6
d{x - e)
f(x-3)
= 9
e =
f=
III
g=
DONE

Answers

Answer:

a = - 1

b = - 9

c = 9

d = 3

e = 3

f = 2

g = 3/2

Step-by-step explanation:

For a;

6 - 2x = - (2x - 6)

For b;

-1 * 9 = - 9

For x ;

3x + (-9) = 3x - 9

3x - 9 = d(x - e)

Factorizing :

3(x - 3)

d = 3 ; e = 3

2x - 6 = f(x - 3)

Factorize :

2x - 6 = 2(x - 3)

3(x - 3) / 2(x - 3)

g = 3/2

How many modes are on this list: 61, 60, 42, 43, 46, 61, 48, 57, 46, 52?
2
1
0
3

Answers

Answer:

There are 2 modes.

Step-by-step explanation:

Modes are the numbers we see most. There can be more than one mode or none at all.

Write a system of linear equations for the graph below.

Answers

Answer:

-3/-2

Step-by-step explanation:

because (x,y) the x coordinate is -3 and the y coordinate is -2

Two less than the product of five and a number x.

Answers

Answer:

5x - 2

Step-by-step explanation:

I am a line that intersects a circle at 2 points WHAT AM I?

Answers

if it’s a riddle i have no idea. if it’s a math question related to the rules of circles it would be a secant line.

PLEASE HELPI DON’T UNDERSTAND

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X= -3 this solution is extraneous

X= 5 this solution is valid

PLEASE I NEED HELP

SSS
AAS
NOT CONGRUENT
SAS
ASA

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SAS IS YOUR ANSWER!

HOPE THISE HELPS

If p is inversely proportional to the square of q, and pis 24 when q is 11,
determine p when q is equal to 2.

Answers

Answer:

726

Step-by-step explanation:

Here p = k / q², and 24 = k / 121, or k = 2904

Then p = 2904 / q²

If q = 2, p = 2904 /4 = 726

Answer:

p = 12 × 11²

Step-by-step explanation:

By question,

=> p ∝ 1/q²

=> p = k/q²

When p is 24 and q is 11

=> 24 = k/11²

=> k = 24 * 11²

When q is 2 ,

=> p = k/q²

=> p = 24*11²/2

=> p = 12 × 11²

Help meeeeeeeeeeeeeeeeeeee

Answers

Answer:

Dependent

Step-by-step explanation:

When the probability is AND, it is dependent. You *have* to get the A outcome for A and B to be valid.

ILL MARK U BRAINLESS IF YOU HELP ME PLEASE!!!!!

Answers

The one that is at the bottom :) have a nice day!

A bus is traveling at a constant speed. If the bus travels 15 miles in 1/3
of an hour,
how many miles will the bus travel in one hour?
evious
NO
HC
US

Answers

Answer:

Step-by-step explanation:

5 mph

x=21 is a solution to the inequality26≤ 2 + x
true or false

Answers

False! The solution should be x>24

Answer:

False

Step-by-step explanation:

Isolate by the x from one side of the equation.

First, you have to switch sides.

[tex]\sf{2+x\geq 26}[/tex]

Then, subtract by the 2 from both sides.

[tex]\sf{2+x-2\geq 26-2}[/tex]

Solve.

Subtract.

[tex]26-2=24[/tex]

[tex]\large\boxed{x\geq 24}[/tex]

The answer should be false.

Each year, a large warehouse uses thousands of fluorescent light bulbs that burn 24 hours per day until they burn out and are replaced. The lifetime of the bulbs is a normally distributed random variable with mean equal to 600 hours and standard deviation of 12 hours. The supplier of the light bulbs and the manager agree that any bulb whose lifetime is among the lowest 1% of all possible lifetimes will be replaced at no charge. What is the maximum lifetime a bulb can have (hrs) and still be among the lowest 1% of all lifetimes

Answers

Answer:

The maximum lifetime a bulb can have and still be among the lowest 1% of all lifetimes is 572 hours.

Step-by-step explanation:

Normal Probability Distribution:

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

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

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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.

The lifetime of the bulbs is a normally distributed random variable with mean equal to 600 hours and standard deviation of 12 hours.

This means that [tex]\mu = 600, \sigma = 12[/tex]

What is the maximum lifetime a bulb can have (hrs) and still be among the lowest 1% of all lifetimes?

This is the 1st percentile of lifetimes, which is X when Z has a pvalue of 0.01, that is, X when Z = -2.327.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-2.327 = \frac{X - 600}{12}[/tex]

[tex]X - 600 = -2.327*12[/tex]

[tex]X = 572[/tex]

The maximum lifetime a bulb can have and still be among the lowest 1% of all lifetimes is 572 hours.

Animal house rescue is holding a fundraiser raffle. they sell 2,980 tickets for $1 each for a prize telescope valued at $425. what is the expected gain or loss to a participant purchasing ten tickets
A)$4,240.00 gain
B)$8.57 loss
C)$0.86 loss
D)$12.85 gain

Answers

Answer: The answer is C, hope I helped :)

Step-by-step explanation:

A purchase of 10 tickets is at an expected loss of $0.857 to the person.

Option B) $8.57 loss is the right choice.

What do we mean by Expected Gain or Loss?

The expected gain or loss is a weighted average of the probability of the different gains or losses and the gains or losses.

How do we solve the given question?

We are asked to calculate the expected gain or loss for a participant who purchases 10 tickets for a raffle costing $1 each, with a prize of a telescope valued at $425. We are told that a total of 2980 tickets have been sold.

First, we calculate the expected gain or loss on 1 ticket,

= 425*(1/2980) + (-1)(1)

= 0.1426174496 - 1

= -0.857382550.

∴ A purchase of 1 ticket is at an expected loss of $0.857

Now, we multiply this by 10 to get the expected gain or loss for the person with 10 tickets.

= -0.857382550*10 = -8.57382550

∴ A purchase of 10 tickets is at an expected loss of $0.857 to the person. Option B) $8.57 loss is the right option.

Learn more about Expected Gain or Loss at

https://brainly.com/question/24175866

#SPJ2

What is the measure of ZGVI/?

Answers

Answer:

answer is A

Step-by-step explanation:

180-140=40

can anyone solve this rq, it’s due tonight?

Answers

Answer:

The slope represents the change/rise is the yearly imcome based on age. The y-intercept is the amount that they make when they first get a job.

Step-by-step explanation:

Grayson bought a rectangular waste basket that is 3 1/2 feet long, 3/4 foot wide, and 1 foot high.

Answers

Answer:

cool and whats the question

Step-by-step explanation:

a coffee shop sells coffee beans by the pound. A container hold 16 kilograms of coffee beans. For every 1 kilogram, there are approximately 2.2 pounds

Answers

Answer:

23.6

Step-by-step explanation:

Answer: 23.6

Step-by-step explanation:

what are the measures of 7 and 2 ? Explain please

Answers

Answer:

angle 2 is 99

angle 7 is 81

Step-by-step explanation:

Angle 2 and the angle we are given are congruent because they are vertical.

Angle 7 and the angle we are given form a line, so they add up to 180.

180-99 = 81

“Write the equation of the line that passes through the points (0,7) and (-2,7). Put
your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.”

Answers

Answer:

y = 7

Step-by-step explanation:

Let the equation of the line is,

y = mx + b

Here, m = Slope of the line

b = y-intercept

Line passes through two points (0, 7) and (-2, 7)

Therefore, slope of the line will be,

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m = [tex]\frac{7-7}{0+2}[/tex]

m = 0

If the slope of a line is 0 then the graph of the line will be parallel to x-axis.

By substituting the value of slope in the equation,

Equation of the line will be,

y = 0(x) + b

y = b

Since, the given line passes through (0, 7),

Equation of the line will be,

y = 7

Suppose we have two independent, normally distributed, populations and we draw a random sample from each population. For population A, we drew a sample of 13 and found the mean to be 17 with a standard deviation of 4. For population B, we drew a sample of 12 with a mean of 19 and a standard deviation of 3. We want to determine if the treatments result in the same effect. Show all work.

Answers

Answer:

Since the calculated value of z= -1.421 does not lie in the critical region z >

- 1.96 the null hypothesis is accepted and it is concluded that the treatments result in the same effect.

Step-by-step explanation:

1) Let the null and alternate hypothesis be

H0: μa − μb = 0 the treatments result in the same effect

against the claim

Ha: μa − μb ≠ 0 the treatments do not result in the same effect

2) The significance level is set at 0.05

3) The critical region is z = ± 1.96

4) The test statistic

Z= x1`-x2`/ sqrt [( s1²/n1+ s2²/n2)]

Here

x1`= 17 s1= 4 n1= 13

x2`= 19 s2= 3 n2= 12

5) Calculations

Z= x1`-x2`/ sqrt [( s1²/n1+ s2²/n2)]

z= 17-19/sqrt [( 16/13+ 9/12)]

z= -2/1.40739

z= -1.421

6) Conclusion

Since the calculated value of z= -1.421 does not lie in the critical region z >

- 1.96 the null hypothesis is accepted and it is concluded that the treatments result in the same effect.

Help pls!Pls and ty!

Answers

Answer:

Step-by-step explanation:

Greg made the dart board shown. It is divided into equal sections. A dart is randomly thrown and lands on the board.
5
1
2
3
3
2
4
1
5
What is the probability that a dart will land on a section marked with the number 1?
O A 5%
B. 10%
O C. 20%
OD. 25%
O E SOS
SRESET
Gianna Faith Russell, ID#***93
Question #22
Growth: Math 6+ MD 2011
A 407
1:24 PM
5/10/2021
Type here to search
RI

Answers

Answer:

Step-by-step explanation:

x dvided 8 = 9
what is value of x

Answers

Answer:

Step-by-step explanation:

72/8 = 9

Answer:

x=72

Step-by-step explanation:

Step- by- step Explanation

The two dot plots below show the number of the miles run by 14 students at the beginning and end of the school year. complete the comparison of the medians for the two dot plots. If necessary, round to the nearest tenth.
The median at the start of the year was _____ miles, and the median at the end of the year was _____ miles. Please answer, it’s a quiz!

Answers

Answer:

Start of the year: 77 End of the year: 87

Step-by-step explanation:

1 dot equals the number represented below, so I multiplied up to the answers for both! (Hope you pass ur test :D)

PLEASE ANYONE HELP! DONT ANSWER IF UNSURE PLEASE

Answers

Answer:

length 5cm, width 4cm, door width 2/5cm or. 4cm, length 10 ft, width 7.5 ft

What is the slope of the line

Answers

Answer:

Step-by-step explanation:

The talk-time battery life of a group of cell phone is normally distributed with a mean
of 5 hours and a standard deviation of 15 minutes.
b) What percent of the phones have a battery life between 4.5 hours and 5.25
hours? (include 1 decimal place WITHOUT the % sign)

Answers

Answer:

Step-by-step explanation:

What is it help

Approximately 47.72% of phones have a battery life of between 4.5 and 5.25 hours.

What is standard deviation?

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

here, we have,

To determine the percentage of phones with a battery life between 4.5 hours and 5.25 hours, we need to find the area under the normal curve between those two points.

To do this, we can standardize the lower and upper limits of the range and use a table of the normal distribution to find the area.

The lower limit of the range, 4.5 hours, is 0.25 hours less than the mean of 5 hours. Since the standard deviation is 15 minutes, which is equal to 0.25 hours, the lower limit is 0.25 standard deviations below the mean.

The upper limit of the range, 5.25 hours, is 0.25 hours more than the mean of 5 hours. Since the standard deviation is 15 minutes, which is equal to 0.25 hours, the upper limit is 0.25 standard deviations above the mean.

The area under the normal curve between the lower and upper limits is therefore the area under the normal curve between -0.25 and 0.25 standard deviations.

Using a table of the normal distribution, we find that the area under the normal curve between -0.25 and 0.25 is approximately 0.4772.

Thus, about 47.72% of phones have a battery life between 4.5 hours and 5.25 hours.

Learn more about the standard deviation here:

brainly.com/question/14747159

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4. Solve the logarithmic equation for X:
log(x) -log(4) = 3

Answers

Answer:

X=7

Step-by-step explanation:

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Solve the equation for exact solutions over the interval​ [0, 2π​).

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Solve the equation for exact solutions over the interval [0, 2π).