Answer:
Step-by-step explanation:
Given the system of equations y=30x+10 y=and 5x²−25, since both functions are written in terms of a varaible y, we will equate the two functions to gether and firt alculate the value of x as shown;
30x+10 = 5x²−25,
Equating the expression to zero;
5x²−25-30x-10 = 0
5x²−30x-25-10 = 0
5x²−30x-35 = 0
Dividing through by 5;
x²−6x+7 = 0,
On factoring;
x = -b±√b²-4ac/2a
a = 1, b = -6 and c = 7
x = 6±√(-6)²-4(1)(7)/2(1)
x = 6±√36-28/2
x = 6±√8/2
x = 6±2√2/2
x = 3±√2
x = 3+√2 or 3-√2
Substituting x = 3+√2 into y = 30x+10
y = 30(3+√2 ) + 10
y = 10(3(3+√2)+1)
y = 10(9+1+3√2)
y = 10(10+3√2)
What is the product of (2p + 7)(3p2 + 4p – 3)?
6p3 + 29p2 – 34p + 21
6p3 + 29p2 – 22p + 21
6p3 + 29p2 + 22p – 21
6p3 + 29p2 + 34p – 21'
Answer: 6p^3+29p^2+22p-21
(9-6)+12 what’s is the answer?
Answer:
15
Step-by-step explanation:
Answer: 15
Step-by-step explanation: (9-6) + 12
(3) + 12
15
What is the angle of rotation from figure A to figure A’? Assume that the center of rotation is the origin. A. 180° clockwise B. 90° counterclockwise C. 180° counterclockwise D. 270° counterclockwise
Answer:
B.90°counterclockwise
Answer: B
Step-by-step explanation:
A. If you rotate a figure in the first quadrant 180 degrees clockwise it will end up in the third quadrant so the answer can't be A.
B. If you rotate a figure in the first quadrant 90 degrees counterclockwise it will end up in the second quadrant because you will rotate it backwards and as you could see A prime is in the second quadrant.
C.If you rotate a figure in the first quadrant 180 counterclockwise it will end up in the third quadrant. SO the answer can't be it C.
D.If your rotate a figure in the first quadrant 270 counterclockwise it will end up in the fourth quadrant. So the answer can't be D.
What numeral is in the 100th decimal place in the decimal representation of $\frac{6}{7}$?
Answer:
5
Step-by-step explanation:
[tex]\frac{6}{7}=0.857142857142857142857142...[/tex]
Or 0.857142 with "857142" recurring.
The hundredths place is the second decimal place of a number. In this case, it would be 5.
The function graphed is reflected across the x-axis to create a new function. Which is true about the domain and range of each function? Both the domain and range change. Both the range and domain stay the same. The domain stays the same, but the range changes. The range stays the same, but the domain changes.
Answer:
Domain stays the same while the range changes
Step-by-step explanation:
While reflecting cross x-axis, the x coordinates remains the same while the y-coordinate changes to its opposite.
=> x- coordinate = Domain
=> y-coordinate = Range
The domain stays the same, but the range changes. is true about the domain and range of each function. Option C is correct.
What is the domain and range of a function?Domain is the set of values for which the given function is defined.Range is the set of all values which the given function can output.
When reflecting across the x-axis, the x coordinates remain constant, but the y coordinate changes to its inverse.
The Domain represent as x-coordinate and the range as y-coordinate
The domain stays the same, but the range changes. is true about the domain and range of each function. Option C is correct.
Hence, option C is correct.
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The highway fuel economy of a 2016 Lexus RX 350 FWD 6-cylinder 3.5-L automatic 5-speed using premium fuel is a normally distributed random variable with a mean of μ = 26.50 mpg and a standard deviation of σ = 3.25 mpg.
Required:
a. What is the standard error of X and the mean from a random sample of 25 fill-ups by one driver?
b. Within what interval would you expect the sample mean to fall, with 98 percent probability?
Answer:
a) 0.65 mpg
b) Between 24.99 mpg and 28.01 mpg.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation, which is also called standard error, [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 26.50, \sigma = 3.25, n = 25, s = \frac{3.25}{\sqrt{25}} = 0.65[/tex]
a. What is the standard error of X and the mean from a random sample of 25 fill-ups by one driver?
s = 0.65 mpg
b. Within what interval would you expect the sample mean to fall, with 98 percent probability?
From the: 50 - (98/2) = 1st percentile
To the: 50 + (98/2) = 99th percentile
1st percentile:
X when Z has a pvalue of 0.01. So X when Z = -2.327.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-2.327 = \frac{X - 26.50}{0.65}[/tex]
[tex]X - 26.50 = -2.327*0.65[/tex]
[tex]X = 24.99[/tex]
99th percentile:
X when Z has a pvalue of 0.99. So X when Z = 2.327.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]2.327 = \frac{X - 26.50}{0.65}[/tex]
[tex]X - 26.50 = 2.327*0.65[/tex]
[tex]X = 28.01[/tex]
Between 24.99 mpg and 28.01 mpg.
Choose the correct simplification of the expression (7x - 3)
(4x2 – 3x - 6). (1 point)
Answer:
Step-by-step explanation:
hello,
I assume that you want to develop the expression
[tex](7x-3)(4x^2-3x-6)=7x(4x^2-3x-6)-3(4x^2-3x-6)\\= 28x^3-21x^2-42x-12x^2+9x+18\\\\=28x^3-33x^2-33x+18[/tex]
hope this helps
If (x) = 3x - 5 and g(x) = x + 3, find (f - g)(x).
O A. 8 - 2x
O B. 2x-2
O c. 2x-8
O D. 4x-2
Answer:
C
Step-by-step explanation:
(f-g)(x)=(3x-5)-(x+3) = 3x-5-x-3 = 2x-8
Answer:
2x -8
Step-by-step explanation:
f (x) = 3x - 5
g(x) = x + 3,
(f - g)(x) = 3x - 5 - ( x+3)
Distribute the minus sign
= 3x-5 -x-3
Combine like terms
= 2x -8
When dividing polynomials using factorization, cancelling identical factors in the denominator and the numerator will give the _______. a.remainder b.divisor c.dividend d.quotient
Answer:
The answer is not "REMAINDER" it's "Quotient"
Step-by-step explanation:
Cancelling identical factors in the numerator and the denominator will give the quotient.
When dividing polynomials using factorization, cancelling identical factors in the denominator and the numerator will give the remainder.
What is a polynomial?A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.
Given that when dividing polynomials using factorization, cancelling identical factors in the denominator and the numerator will give the remainder.
A quotient in mathematics is the amount created by dividing two numbers. The term "quotient" is used frequently in mathematics and is also known as the integer portion of a division, a fraction, or a ratio.
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After adding up all your expenses for the month you spent $465.36. your total budget for the month is$529.What percentage are under budget?(Round to the nearest whole percentage).Do not include symbol
Answer:
12%.
Step-by-step explanation:
It is given that, after adding up all your expenses for the month you spent $465.36. your total budget for the month is $529.
Total budget = $529
Total expenditure = $465.36
Under budget = $529 - $465.36 = $63.64
We need to find the percentage of under budget.
[tex]\%=\dfrac{\text{Under budget}}{\text{Total budget}}\times 100[/tex]
[tex]\%=\dfrac{63.64}{529}\times 100[/tex]
[tex]\%=0.12030\times 100[/tex]
[tex]\%=12.030\%[/tex]
[tex]\%\approx 12\%[/tex]
Therefore, the required percentage is 12%.
Help me please I dont understand
Answer:
42°
Step-by-step explanation:
This is right triangle and sum of 2 angles is 90°:
y+48°=90°
so y= 90°- 48°= 42°
A low calorie dinner has 480 calories in an 9 ounce serving. What is the unit rate in simplest form?
Answer: 53.333333, 53 1/3
Step-by-step explanation:
The unit rate in this question means how many calories for one ounce. Thus, you can simply divide 480 by 9 to get 53.3333333
Answer:
53.33 caloriesStep-by-step explanation:
Calories in a low calorie dinner = 480 calories
Serving at one time = 9 ounce
then,
Unit rate = Amount of calories in one serving
So,
Amount of calorie in 9 serving = 480
Amount of calorie in 1 serving = 480/9
In simple form : 160/3
= 53.33 calories
Hope this helps...
Good luck on your assignment..
I NEED HELP PLEASE THANKS!
Answer: A) 0.5
Step-by-step explanation:
The denominator should be in the form 1 + e sin θ
Currently the denominator is: 2 + 1 sin θ
Divide the denominator by 2 to get: 1 + 0.5 sin θ
Thus, e = 0.5
The number of people who voted in the most recent local election was up from the last local election by about 24%. Therefore the number of people who voted in this election was how many times the number who voted in the last election
Answer:
The number of people who voted in this election was 1.24 times the number who voted in the last election
Step-by-step explanation:
The multiplier for a increase of a% is 1 + a/100.
The multiplier for a decrease of b% is 1 - b/100.
In this question:
Up by about 24%, so we want the multiplier for a increase of 24%.
So
1 + (24/100) = 1 + 0.24 = 1.24
The number of people who voted in this election was 1.24 times the number who voted in the last election
Use the following data to compute a 98% upper confidence bound for μ1 − μ2:
m = 41
x = 42,700
s1 = 2030
n = 41
y = 36,275
s2 = 1360.
Answer:
[tex] (42700- 36275) -2.374 \sqrt{\frac{2030^2}{41} +\frac{1360^2}{41}}= 5519.071[/tex]
[tex] (42700- 36275) +2.374 \sqrt{\frac{2030^2}{41} +\frac{1360^2}{41}}=7330.929[/tex]
Step-by-step explanation:
For this case we have the following info given:
[tex]n_1 = 41 , \bar X_1 =42700 , s_1 = 2030[/tex]
[tex]n_2 = 41 , \bar X_2 =36375 , s_2 = 1360[/tex]
And for this case we want a 98% confidence interval. The significance would be:
[tex] \alpha= 1-0.98=0.02[/tex]
The degrees of freedom are:
[tex] df = n_1 +n_2 -2= 41+41 -2= 80[/tex]
And the critical value for this case is:
[tex] t_{\alpha/2}= 2.374[/tex]
And the confidence interval would be given by:
[tex](\bar X_1 -\bar X_2) \pm t_{\alpha/2} \sqrt{\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}[/tex]
And replacing we got:
[tex] (42700- 36275) -2.374 \sqrt{\frac{2030^2}{41} +\frac{1360^2}{41}}= 5519.071[/tex]
[tex] (42700- 36275) +2.374 \sqrt{\frac{2030^2}{41} +\frac{1360^2}{41}}=7330.929[/tex]
Assume that cans are filled so that the actual amounts have a mean of 17.00 ounces. A random sample of 36 cans has a mean amount of 17.79 ounces. The distribution of sample means of size 36 is normal with an assumed mean of 17.00 ounces and a standard deviation of 0.08 ounce.
Required:
How many standard deviations is the sample mean from the mean of the distribution of sample?
Answer:
The sample mean is 9.875 standard deviations from the mean of the distribution of sample
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation s, the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{s}[/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 pvalue, we get the probability that the value of the measure is greater than X.
In this question:
[tex]X = 17.79, \mu = 17, s = 0.08[/tex]
How many standard deviations is the sample mean from the mean of the distribution of sample?
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{17.79 - 17}{0.08}[/tex]
[tex]Z = 9.875[/tex]
The sample mean is 9.875 standard deviations from the mean of the distribution of sample
[tex] 3 {x}^{2} - 15x = 15[/tex]
[tex]3x^2-15x= 15\\\\x^2 -5x = 5\\\\x^2-5x-5=0\\\\\Delta = 25+20\\\\\Delta = 45\\\\\\x = \dfrac{5\pm \sqrt{\Delta}}{2}\\\\\\x = \dfrac{5\pm \sqrt{45}}{2}\\\\\\x = \dfrac{5\pm 3\sqrt{5}}{2}\\\\\\[/tex]
Please answer this correctly
Answer:
1/2
Step-by-step explanation:
The numbers 3 or odd are 1, 3, 5, and 7.
4 numbers out of 8.
4/8 = 1/2
P(3 or odd) = 1/2
A car is driving at 100 kilometers per hour. How far, in meters, does it travel in 3 seconds?
Answer:
The car travels 83 1/3 meters in 3 seconds.
Step-by-step explanation:
Speed of car = 100 KM/ hour
1 km= 1000m
1 hour = 3600 seconds
Lets find speed of car in Meters/second
speed of car in m/sec = 100*1000 m/3600 second
here we have taken 1000 for km and 3600 for hour
speed of car in m/sec = 100*1000 m/3600 second = 500/18 m/second
speed of car in m/sec = 250/9 m per sec
We know that
distance = speed*time
speed = 250/9 m per sec
time =3 second
distance = 250/9 * 3 meters = 250/3 meters = 83 1/3 meters.
Thus, car travels 83 1/3 meters in 3 seconds.
Matías and José want to distribute 4.5 kilograms of lemons in 3/4 kilogram bags. How many bags will they be able to complete?
Answer:
6 bags
Step-by-step explanation:
3/4 = .75
4.5/.75 = 6 =
6 BAGS
A bag contains 17 counters all of different colours. Colin chooses one counter and gives it to Obi, and another counter and gives it to Zeema. In how many ways can Colin do this?
Answer:
Colin can do this is 272 ways.
Step-by-step explanation:
The first counter goes to Obi and the second to Zeema, so the order is important. This means that we use the permutations formula to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this question:
Two counters from a set of 17. So
[tex]P_{(17,2)} = \frac{17!}{(17-2)!} = 272[/tex]
Colin can do this is 272 ways.
798/8×41 rounded to one significant figure
Answer:
2.5
Step-by-step explanation:
the other persons answer is wrong
The number after rounding to the one significant figure is 4000.
What is significant figure?
The term significant figures refers to the number of important single digits (0 through 9 inclusive) in the coefficient of an expression in scientific notation
What is round off?Rounding off means a number is made simpler by keeping its value intact but closer to the next number
According to the given question we have an expression.
[tex]\frac{798}{8} (41)[/tex]
When we evaluate this expression we get
[tex]\frac{798}{8} (41)[/tex]
[tex]=99.75(41)[/tex]
[tex]= 4089.75[/tex]
Here, the first significant figure is 4 and the second one is 0 which is less than 5.
Hence, the number after rounding to the one significant figure is 4000.
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A teacher based in California calculated a particular date in the calendar and named it Square Root Day. Try and find out why the day was named so. Can you find more such days? When was last square root day and when is next square root day
Answer:
may 5 the is squareroot day and it is when the day and the month has the first two digits in the date are the square root of the last two digits. examples 2nd February,2004 3rd March 2009 and the last time we had one was April 4th 2016. The next square root day is May 5th 2025
I NEED HELP PLEASE, THANKS! :)
Take a look at the attachment below. It proves that the inverse of matrix P does exists, as option c,
Hope that helps!
Answer: C
Step-by-step explanation:
Given a b
c d
Multiply the reciprocal of the determinant by d -b
-c a
Determinant = ad - bc = 2(-3) - 4(1)
= -6 - 4
= -10
[tex]-\dfrac{1}{10}\left[\begin{array}{cc}-3&-4\\-1&2\end{array}\right] \\\\\\\\=\left[\begin{array}{cc}\dfrac{-3}{-10}&\dfrac{-4}{-10}\\\\\dfrac{-1}{-10}&\dfrac{2}{-10}\end{array}\right]\\\\\\\\=\left[\begin{array}{cc}\dfrac{3}{10}&\dfrac{2}{5}\\\\\dfrac{1}{10}&-\dfrac{1}{5}\end{array}\right][/tex]
Identify the slope and y-intercept of the line whose equation is given. Write the y-intercept as an ordered pair s=3/4 t+ 2
Answer:
b
Step-by-step explanation:
The slope is 3/4 and the y-intercept is y(0,2)
The slope is what we multiply by the variable ( here t) and the y-intercept is the number we add
In a basketball shooting competition there are ten balls from 1-10. The number of points earned is based on the number on the ball (I.e shoots a 7 gets 7 points), if a person misses 2 shots what number is not possible
52
44
41
38
35
The answer is 41 because all of the them are in the 7 times table .so I deducted 2 from each one of them and 41 was not part
How can you find f(2) f(x) = - 3x ^ 2 - 7
Answer:
-19Step-by-step explanation:
Plug in 2 for x.
f(2) = -3(2)² - 7
f(2) = -3(4) - 7
f(2) = -12 - 7
f(2) = -19
PLEASE HELP ME FOR BRAINLIEST Reduce to simplest form. 6/3+(-1/6)
Answer: 1 5/6, or 11/6, or 1.83333333
Step-by-step explanation:
[tex]\frac{6}{3} + -\frac{1}{6}[/tex]
6/3 is 2.
Thus, the answer is 2 - 1/6 or 1 5/6
Answer:
11/6
Step-by-step explanation:
First, we need to find a common denominator for the 2 fractions.
A common denominator for 3 and 6 is 6.
Let’s get the fraction 6/3 to a denominator of 6.
Multiply by 2/2
6/3 * 2/2
(6*2) / (3*2)
12/6
Now the fractions have common denominators and can be added.
12/6 + (-1/6)
When adding negative fractions, you can simply subtract.
12/6 - 1/6
Subtract across the numerator and leave the denominator as is
11/6
This fraction can be written as: 2 1/6, 11/6, or 1.83333
Hawkins Manufacturing Company produces connecting rods for 4- and 6-cylinder auto-mobile engines using the same production line. The cost required to set up the production line to produce the 4-cylinder connecting rods is $2,000, and the cost required to set up the production line for the 6-cylinder connecting rods is $3,500. Manufacturing costs are $15 for each 4-cylinder connecting rod and $18 for each 6-cylinder connecting rod. There is no production on weekends, so on Friday the line is diassembled and cleaned. On Monday, the line must be set up to run whichever product will be produced that week. Once the line has been set up, the weekly production capacities are 6000 6-cylinder connecting rods and 8000 4-cylinder connecting rods. Letx4 5 the number of 4-cylinder connecting rods produced next week x6 5 the number of 6-cylinder connecting rods produced next week s4 5 1 if the production line is set up to produce the 4-cylinder connecting rods; 0 if otherwise s6 5 1 if the production line is set up to produce the 6-cylinder connecting rods; 0 if otherwise Using the decision variables x4 and s4, write a constraint that sets next week
Complete question:
Hawkins Manufacturing Company produces connecting rods for 4- and 6-cylinder auto-mobile engines using the same production line. The cost required to set up the production line to produce the 4-cylinder connecting rods is $2,000, and the cost required to set up the production line for the 6-cylinder connecting rods is $3,500. Manufacturing costs are $15 for each 4-cylinder connecting rod and $18 for each 6-cylinder connecting rod. There is no production on weekends, so on Friday the line is diassembled and cleaned. On Monday, the line must be set up to run whichever product will be produced that week. Once the line has been set up, the weekly production capacities are 6000 6-cylinder connecting rods and 8000 4-cylinder connecting rods. Letx4 5 the number of 4-cylinder connecting rods produced next week x6 5 the number of 6-cylinder connecting rods produced next week s4 5 1 if the production line is set up to produce the 4-cylinder connecting rods; 0 if otherwise s6 5 1 if the production line is set up to produce the 6-cylinder connecting rods; 0 if otherwise
a) Using the decision variables x4 and s4, write a constraint that sets next week's maximum production of the 4-cylinder connecting rods to either 0 to 8000 units
b) Using the decision variables x6 and s6, write a constraint that sets next week's maximum production of the 4-cylinder connecting rods to either 0 to 6000 units
c) Write a constraint that requires that production be setup for exactly one of the two rods
d) Write the cost function to be minimized
Answer:
a) x₄ ≤ 8000s₄
b) x₆ ≤ 8000s₆
c) s₄ + s₆ = 1
d) MIN 15x₄ + 18x₆ + 2000s₄ + 3500s₆
Explanation:
a) The constraint that sets next week's maximum production of the 4-cylinder connecting rods to either 0 to 8000 units, is written as:
x₄ ≤ 8000s₄
b) The constraint that sets next week's maximum production of the 4-cylinder connecting rods to either 0 to 6000 units is written as:
x₆ ≤ 8000s₆
c) The constraint that requires that production be setup for exactly one of the two rods:
Since we have:
x₄ ≤ 8000s₄ ; x₆ ≤ 8000s₆
The constraint that requires that production be setup for exactly one of the two rods will be:
s₄ + s₆ = 1
d) Write the cost function to be minimized:
Since we are to find the cost function to be minimized, we take the function below:
MIN 15x₄ + 18x₆ + 2000s₄ + 3500s₆
Find all solutions of the equation in the interval , 02π. =4cosx+−sin2x4 Write your answer in radians in terms of π. If there is more than one solution, separate them with commas.
Answer:
The answer is "2nπ".
Step-by-step explanation:
Given:
[tex]4 \cos x= -\sin^2x+4.......(1)[/tex]
We know:
[tex]\Rightarrow \sin^2 x+\cos^2 x=1\\\\\Rightarrow \sin^2 x= 1 -\cos^2 x\\[/tex]
put the value of [tex]\sin^2 x[/tex] value in the above equation:
[tex]\Rightarrow 4 \cos x= - (1-\cos^2 x)+4\\\\\Rightarrow 4 \cos x= - 1+\cos^2 x+4\\\\\Rightarrow 4 \cos x= \cos^2 x+3\\\\\Rightarrow \cos^2 x-4 \cos x+3=0\\\\[/tex]
Let [tex]\cos x= A[/tex]
[tex]\Rightarrow A^2-4A+3=0 \\ \Rightarrow A^2-(3A+A)+3=0 \\\Rightarrow A^2-3A-A+3=0\\\Rightarrow A(A-3)-1(A-3)=0\\\Rightarrow (A-3)(A-1)=0 \\[/tex]
[tex]\Rightarrow A- 3=0 \ \ \ \ \ \ \ \ \ \ \ \Rightarrow A -1 =0 \\\\[/tex]
[tex]\Rightarrow A= 3\ \ \ \ \ \ \ \ \ \ \ \Rightarrow A =1 \\\\\Rightarrow \cos x = 3\ \ \ \ \ \ \ \Rightarrow \cos x =1\\\\\Rightarrow x = \cos^{-1} 3\ \ \ \ \ \ \ \Rightarrow \cos x =\cos 0\\\\\Rightarrow x = \cos^{-1} 3\ \ \ \ \ \ \ \Rightarrow x = 0\\\\[/tex]
The value of x is [tex]2n\pi\ \ \ _{where} \ \ \ \ \ \ \ n=1, 2, 3......[/tex]
[tex]\boxed{\bold{x=2 n \pi}}[/tex]