Trigonometry Question:
Find all solutions on the interval [0,2π)
12sin^2(x)+cos(x)-6=0
Answers
Recall the Pythagorean identity,
\(\sin^2(x) + \cos^2(x) = 1\)
Use it to rewrite the equation in terms of cos only.
\(12 (1 - \cos^2(x)) + \cos(x) - 6 = 0\)
\(-12 \cos^2(x) + \cos(x) + 6 = 0\)
Factorize the left side.
\(-(3\cos(x) + 2) (4\cos(x) - 3) = 0\)
Solve the two cases for \(\cos(x)\).
\(3 \cos(x) + 2 = 0 \text{ or } 4\cos(x) - 3 = 0\)
\(\cos(x) = -\dfrac23 \text{ or } \cos(x) = \dfrac34\)
From the first equation, we get one family of solutions:
\(\cos(x) = -\dfrac23\)
\(x = \cos^{-1}\left(-\dfrac23\right) + 2n\pi \text{ or } x = -\cos^{-1}\left(-\dfrac23\right) + 2n\pi\)
From the second equation, we get another family:
\(\cos(x) = \dfrac34\)
\(x = \cos^{-1}\left(\dfrac34\right) + 2n\pi \text{ or } x = -\cos^{-1}\left(\dfrac34\right) + 2n\pi\)
where \(n\) is an integer.
We get solutions in the given domain for
\(n = 0 \implies \boxed{x = \cos^{-1}\left(-\dfrac23\right)} \text{ or } \boxed{x = \cos^{-1}\left(\dfrac34\right)}\)
\(n=1 \implies \boxed{x = 2\pi - \cos^{-1}\left(-\dfrac23\right)} \text{ or } \boxed{x = 2\pi - \cos^{-1}\left(\dfrac34\right)}\)
Related Questions
100 POINTS!!!!!!!!!!! ( I NEED FAST ANSWERS ) Which of the following functions model the data given in the table below?
х
2
3
4
5
6 y
-5
-7
-9
-11
-13
Answers
Answer:
I thinkkk its Option 2
Step-by-step explanation:
Answer:
Option 2
Step-by-step explanation:
The line is linear and the y-intercept hits at -1 so option 2 is correct.
correct answer gets brainliest
Answers
Answer:
The awnser is B
Step-by-step explanation:
Have a great day! :D
help asap help asap for brainlist
part A and Part B
Answers
Answer:
part A:
32.10
part B:
156 miles
Step-by-step explanation:
Which word is associated with multiplication when computing probabilities? Choose the correct answer below Disjoint O And O Not
Answers
When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.
According to me , independent is the word which is associated with multiplication when computing probabilities . Because when the events are independent then we multiply the probabilities .
According to the multiplication rule of probability, the probability of occurrence of both the events A and B is equal to the product of the probability of B occurring and the conditional probability that event A occurring given that event B occurs.
The probability of the union of two events is equal to the sum of individual probabilities. The union of two set contains all the elements of previous sets. The union is denoted by ∪. The equation for the students earnings will be expressed as P(A∪B). The occurrence of event A changes the probability of B then the events are dependent. If the probability of two events happening together is zero then the events are mutually exclusive.
Therefore,
When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.
To learn more about Probability visit :
brainly.com/question/13490624
#SPJ4
all i need to know is what x and y is, so could someone help me pls n thx!!
Answers
Step-by-step explanation:
x and y are variables the represent a number
Write 3.242424 as a mixed number
Answers
this number can be written as 3+0.242424
Dr. Silva's gas tank holds up to 16 7 /8 gallons of gas. It took 11.55 gallons of gas to fill her tank.
How many gallons of gas did Dr. Silva have in her tank before she filled it?
Enter your answer as a decimal or as a mixed number in simplest form in the box.
Answers
Dr. Silva have 5.325 gallons of gas in her tank before she filled it.
What is the Subtraction operation?Subtraction is a mathematical operation that deducts the right-hand operand from the left-hand operand.
The gas tank holds up to 16 7 /8 gallons of gas. It took 11.55 gallons of gas to fill her tank.
To determine the number of gallons of gas did Dr. Silva have in her tank before she filled it :
⇒ The maximum capacity of the tank - Currently filled tank
⇒ 16 7 /8 - 11.55
Convert the mixed number into a decimal,
⇒ 16.875 - 11.55
Apply the subtraction operation,
⇒ 5.325
Therefore, Dr. Silva have 5.325 gallons of gas in her tank before she filled it.
Learn more about Subtraction operations here:
brainly.com/question/25834626
#SPJ1
M&M plain candies have a normally distributed weight with a mean of 0.8565 g and a standard
deviation of 0.0518 g. If 465 M&M plain candies are randomly selected, find the probability that
their mean weight is at least 0.8535 g each.
Answers
Answer:
0.89417
Step-by-step explanation:
Using the relation to obtain the Zscore :
Z = (x - mean) ÷ standard deviation / sqrt(n)
x = 0.8535
Mean = 0.8565
Standard deviation = 0.0518
Sample size, n = 465
P(x ≤ 0.8535) = (0.8535 - 0.8565) ÷ 0.0518/sqrt(465)
P(x ≥ 0.8535) = - 0.003 / 0.0024021
P(x ≥ 0.8535) = - 1.249
P(Z ≥ - 1.249) = 0.89417
And here’s the second pic for the Brainly
Answers
Answer:
3a³ -20a² +16a -24
Step-by-step explanation:
4.Unlike the other problems shown here, this one requires you combine like terms.
= a(3a² -2a +4) -6(3a² -2a +4)
= 3a³ -2a² +4a -18a² +12a -24
= 3a³ -20a² +16a -24
Regina wrote an integer The opposite of her integer is -18
Answers
Answer: C
Step-by-step explanation: The opposite of a positive integer (18) is -18
Which also means its value is 18
Hope this helps!
Write a System of Equations to solve the following problem:
The school that Maria goes to is selling tickets to the annual talent show. On the first day of ticket sales the school sold 1 senior citizen ticket and 12 student tickets for a total of $51. The school took in $93 on the second day by selling 5 senior citizen tickets and 6 student tickets. What is the price each of one senior citizen ticket and one student ticket?
Cost of Senior Citizen Ticket: $
Cost of Student Ticket: $
Answers
Answer:
Cost of Senior Citizen Ticket: $15
Cost of Student Ticket: $3
Step-by-step explanation:
Let the price of a senior citizen ticket be s.
Let the price of a student ticket be t.
Day 1:
s + 12t = 51
Day 2:
5s + 6t = 93
The system of equations is:
s + 12t = 51
5s + 6t = 93
Let's use the substitution method to solve it. Solve the first equation for s.
s = 51 - 12t
Now substitute s in the second equation with 51 - 12t.
5s + 6t = 93
5(51 - 12t) + 6t = 93
255 - 60t + 6t = 93
Subtract 255 from both sides. Combine -60t and 6t.
-54t = -162
Divide both sides by -54.
t = 3
Now substitute 3 for t in the equation
s = 51 - 12t
s = 51 - 12(3)
s = 51 - 36
s = 15
Answer:
Cost of Senior Citizen Ticket: $15
Cost of Student Ticket: $3
(will mark brainlist) Which of the following expressions is equivalent to 2x +37
○ 6(2)
8(2)*
2*
6
2*
8
Answers
Answer:
B) \(8(2)^{x}\)
Step-by-step explanation:
Using the Product Property of Exponents, we know that two exponents with the same base can have their exponents added together.
Step 1 - Convert 8 to an exponent with a base of 2:
\(8 = 2^{3}\)
Step 2 - Use the Product Property of Exponents:
\(2^{3} *2^{x}\)
\(2^{x+3}\)
Hope this helps and have a great day! :)
find Y thanks don’t be guessing cuz girl
Answers
Answer:
3 inches
Step-by-step explanation:
It's like 2 inches, but a little bigger.
Hope this helps and is correct.
Btw it's my birthday.
15.
Marco is making blueberry muffins. The ratio between flour and blueberries for the recipe being used is shown in the table below.
Cups of Cups of
Flour Blueberries
1-2
24
A.Ocup
2
8
How many cups of blueberries will Marco need if he has 2 cups of flour to use?
B.
cup
D
1
2
3
4
1
c. 11 cups
6 cups
Answers
The magic ratio for muffins in 2:2:1:1.
What is the appropriate liquid-to-flour ratio while baking muffins?The magic muffin ratio is 2:2:1:1. This equates to 2 parts flour, 2 parts liquid, 1 part fat, and 1 part eggs. The most crucial aspect is to remember to utilize the same unit of weight for each component!
Rinse frozen blueberries many times in cold water until the water turns lighter in color to prevent your batter and baked items from developing a purple-blue tint. Then, blot them dry with a paper towel and gently fold them into the batter. The goal of this procedure is to maintain fast breads light and delicate by limiting the quantity of gluten produced during the mixing process. To do this, the dry components are mixed in a one bowl, the wet ingredients are combined in a separate bowl, and then the two mixtures are combined together.
To know more about muffins visit:
brainly.com/question/28950026
#SPJ1
Simplify the expression.
2x³y +7x³y-xy³
Answers
Answer:
xy*(2x^2 + 7x^2 - y^2)
Step-by-step explanation:
You can get xy out of the expression since all have xy
a.) State the decision rule. Select the correct choice below and fill in any answer boxes in your choice.(Round to four decimal places as needed.)Reject the null hypothesis if the calculated value of the test statistic, t, is less than the critical value ofnegative _______. Otherwise, do not reject
Answers
Reject the null hypothesis if the calculated value of the test statistic, t, is less than the critical value of negative t*. Otherwise, do not reject.
Please note that the critical value of t* depends on the significance level (alpha), degrees of freedom, and the specific hypothesis test being conducted. It is not provided in the given information and would need to be determined based on the specific context and requirements of the test.
what is critical value ?
A critical value is a specific value or threshold used in statistical hypothesis testing or confidence interval estimation. It is based on the chosen level of significance (alpha) and the distribution of the test statistic or the sampling distribution.
In hypothesis testing, critical values are used to determine whether to reject or fail to reject the null hypothesis. The test statistic is compared to the critical value to make a decision. If the test statistic falls in the critical region (beyond the critical value), the null hypothesis is rejected in favor of the alternative hypothesis.
To know more about negative visit:
brainly.com/question/29250011
#SPJ11
I need help please help out right quick
Answers
Answer:
I'm answering the same
Step-by-step explanation:
I'm answering the same
Answer:
Y = 22
Step-by-step explanation:
use diamond to split 6 and 2
group 6 and 16
take out 2 and 8
and add y and 16
Y = 22
In the expression 4/5 ÷ 3/4 is the same as..
Answers
Answer:
Multiplying by
\( \frac{4}{3} \)
Step-by-step explanation:
\( \frac{4}{5} \div \frac{3}{4} \)
\( = \frac{4}{5} \times \frac{4}{3} \)
Answer:
multiplying by 4/3
Step-by-step explanation:
"keep-change-flip"
1. "keep" the 4/5
2. change the division sign to multiplication sign
3. flip the fraction 3/4, to 4/3
Chastity ran a hypothesis test with an alpha level of .01 and her test statistic fell outside of the critical region. what should she do?
Answers
The critical region is determined based on the alpha level, which is the probability of making a Type I error (rejecting the null hypothesis when it is true). An alpha level of .01 means that there is a 1% chance of making a Type I error.
If Chastity ran a hypothesis test with an alpha level of .01 and her test statistic fell outside of the critical region, it means that the test statistic does not provide enough evidence to reject the null hypothesis.
In this case, Chastity should fail to reject the null hypothesis and accept it as the plausible explanation. This implies that there is not enough evidence to support the alternative hypothesis.
When a test statistic falls outside of the critical region, it indicates that the observed data is not extreme enough to reject the null hypothesis. The critical region is determined based on the alpha level, which is the probability of making a Type I error (rejecting the null hypothesis when it is true). An alpha level of .01 means that there is a 1% chance of making a Type I error.
In summary, when Chastity's test statistic falls outside of the critical region, she should fail to reject the null hypothesis and accept it as the plausible explanation. This means that there is not enough evidence to support the alternative hypothesis at the given alpha level of .01.
to learn more about null hypothesis.
https://brainly.com/question/30821298
#SPJ11
Find the average rate of change for the function
Answers
Answer:
average rate of change on [-1,3] = 11
Step-by-step explanation:
avg rate of change = \(\frac{f(b)-f(a)}{b-a}\)
\(\frac{f(3)-f(-1)}{3-(-1)}\)
1. find your y-values.
we are given the x values from the interval [-1,3]. Plug each into the equation to get the y-value of the coordinates.
\(f(-1)=4(-1)^2+3(-1)-4\\f(-1)=4(1)-3-4\\f(-1)=-3\\\)
coordinate: (–1,3)
\(f(3)=4(3)^2+3(3)-4\\f(3)=4(9)+9-4\\f(3)=36+9-4\\f(3)=41\)
coordinate: (3, 41)
2. plug into the slope formula
\(m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} } \\m=\frac{41-(-3)}{3-(-1)} \\m=\frac{41+3}{4} \\m=\frac{44}{4} \\m=11\)
Fatoumata has a deck that measures 7 feet by 12 feet. She wants to increase each
dimension by equal lengths so that its area is increased by 50%. By how much should she increase each dimension?
Answers
Based on common factors, Fatoumata can increase each dimension of the deck by 2 feet so that the deck's new area is increased by 50% to 126 ft².
What are common factors?Common factors are the numbers that can divide another number evenly without a remainder.
In this situation, 9 and 14 can divide 126 equally and the product of 9 and 14 are 126.
The old dimensions of the deck:
Width = 7 feet
Length = 12 feet
Area = 84 ft² (7 x 12)
The expected new area of the deck:
Increase in the new area = 5%
Increased factor for the area = 1.5 (100% + 50%)
Area = 126 ft² (84 x 1.5)
The common factors of 126 include 9 and 14 and the product of 9 and 14 = 126.
Therefore, we can increase each length of the deck by 2 feet.
Check:
Width = 9 feet
Length = 14 feet
Area = 126 ft² (9 x 14)
Learn more about common factors at https://brainly.com/question/219464.
#SPJ1
Change 80% to a fraction in its lowest terms.
Answers
Answer:
4/5
Step-by-step explanation:
80%=80/100 then simplify it.
Answer:
4/5, have a nice day <3
Step-by-step explanation:
Write the complex conjugate of the complex number and multiply the complex number by its complex conjugate.
16+i√10
will give brainliest please help
Answers
Answer:
266
Step-by-step explanation:
Don't give more points. We work for a great deal less. Thank you for what you have given.
The complex conjugate of 16 + i√10
is
16 - i√10 Notice the only difference is the minus sign.
(16 + i√10)(16 - i√10)
First: 16 * 16 = 256
Outside: - 16 * i√10
Inside: 16*i√10
Last: i*√10 * -i*√10 = - i^2 (√10)^2
i^2 = -1
(√10)^2 = 10
Last: + 10
Notice the outside and inside terms cancel and the last term becomes + 10
The answer is 256 + 10 = 266
the ratio of the measures of the three angles in a triangle is 9:3:6.
find the measures of the largest angle.
Answers
Step-by-step explanation:
this is how you solve it :)
The sum of 6 and x
x + 4
6/x
X+ 6
6x
Answers
Answer:
x + 6
Step-by-step explanation:
Sum means to add the 2 terms , so
x + 6 ← represents the sum of 6 and x
Multiplying Polynomials
Find each product.
1) 6v(2v + 3) 2) 7(−5v − 8)
3) 2x(−2x − 3)
Answers
A polynomial is an equation made up of coefficients and in determinates that uses only the addition, subtraction, multiplication, and powers of positive-integer variables.
Multiplying Polynomials Find each product. 1) \(6v(2v + 3) 2) 7(-5v - 8)3) 2x(-2x -3)6v(2v + 3)\)
To distribute the 6v over the binomial 2v + 3, we multiply 6v by each term inside the parenthesis:
\(6v(2v) + 6v(3)\)
\(= 12v^2 + 18v7(-5v - 8)\)
To distribute the 7 over the binomial -5v - 8, we multiply 7 by each term inside the parenthesis:
\(7(-5v) + 7(-8)= -35v - 562x(-2x - 3)\)
To distribute the 2x over the binomial -2x - 3, we multiply 2x by each term inside the parenthesis:
\(2x(-2x) + 2x(-3)= -4x^2 - 6x\)
for such more question on Polynomials
https://brainly.com/question/4142886
#SPJ4
James can do a job in 1.5 hours. Jane can do the same job in 1 hour. How long will it take them to do the job if they work together?
(BTW 30 minutes is not the answer)
Answers
Answer:
36 mins
Step-by-step explanation:
90 mins , 60 mins
1/90 + 1/60. = 2/180 + 3 / 180 = 5/180
1/36
Determine whether this table represents a probability distribution.xP(x)00.0510.120.330.55Yes, it is a probability distributionNo, it is not a probability distribution
Answers
Recall that to determine if a table represents a probability distribution, the sum of the probabilities must add up to 1, and all the probabilities have to be positive numbers less or equal to 1.
Now, notice that:
\(0.05+0.1+0.3+0.55=1.\)From the table, we notice that all the given probabilities are positive numbers between 0 and 1. Therefore, we can conclude that the given table represents a probability distribution.
Answer:Yes, it is a probability distribution.
A customer returns an item to a toy store in Chicago. The customer’s receipt shows $1.66 tax was charged on a $25 item. What percent is the tax rate in Chicago?
Answers
Answer:
0.87 I think
Step-by-step explanation:
What are the solutions of x squared + 6 x minus 6 = 10?
x= -11 or x= 1
x= -11 or x= -1
x= -8 or x= -2
x= -8 or x= 2
Answers
x^2 +6x-6-10=0
x^2 +6x-16=0
(x-2) (x+8)=0
so, x= 2, x=-8