What is the equation for each reflected graph of f(x)=x^2-4? Reflect across the x-axis, reflect across the y-axis.
A function assigns the values. The equation for each reflected graph of f(x)=x²-4 can be written as shown below.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
A.) Reflect across the y-axis, to find the equation replace x with -x,
f(-x) = (-x)² - 4
= x² - 4
No, Change because the function is symmetrical about the y-axis
B.) Reflect across the x-axis, to find the equation replace y with -y,
y = f(x) = y
-y = -f(x)
= -(x² - 4)
= -x² + 4
Hence, The equation for the reflection of the function can be done as shown below.
Learn more about Function here:
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How many times will 1/4 go into 6 7/10?
Answer: 93 and 4/5
Step-by-step explanation:
6 7/10 divided by 1/14
= 67/10 divided by 1/14
= 67/10 x 14/1
= 67/5 x 7/1
= 469/5
121 divided by 3 987 divided by 9 675 divided by 5 432 divided by 7
Answer: Hi!
121 ÷ 3 = 40.3
987 ÷ 9 = 109.7
675 ÷ 5 = 135
432 ÷ 7 = 61.7
Hope this helps you!
Answer:
40 1/3
109 2/3
135
61.7
Step-by-step explanation:
Hey there!
Well lets divide all given expressions,
121 ÷ 3 = 40 1/3
987 ÷ 9 = 109 2/3
675 ÷ 5 = 135
432 ÷ 7 = 61.7 rounded to the nearest tenth
Hope this helps :)
What is the area surface of the triangular prism? A. 448cm B.608cm C.704cm or D.640cm
Answer:
608 squared centimeters.
Step-by-step explanation:
To find the surface area of the net of the triangular prism, we can find the area of each individual shape and add them up.
For the net, we have 3 rectangles and 2 (congruent) triangles.
The left rectangle has a length of 16 and a width of 10. Thus, it's area is A=16(10)=160 squared centimeters.
The middle rectangle has a length of 16 and a width of 12. Thus, it's area is A=16(12)=192 squared centimeters.
The right rectangle has a length of 16 and a width of 10. Thus, it's area is identical to the left rectangle. It's area is 160 squared centimeters.
Now, for the two triangles, it's important to note they are the congruent since they belong to one triangular prism. Thus, we only need to figure out the area of one and then multiply by 2 to get the area of both of them.
One triangle has a base length of 12 and a height of 8. In other words, its area is (1/2)(12)(8)=48. Two of them will be 48(2) or 96.
Now, let's add all the areas together to find the surface area of the triangular prism. Thus, the area is:
96+160+160+192=608 squared centimeters.
Answer:
608 cm^2
Step-by-step explanation:
Find the area of the large rectangle
length is 10+12+10 = 32 and width is 16
A = 32*16 =512 cm^2
Then we have 2 triangle
The area of 1 is
A = 1/2 bh where b = 12 and h = 8
A = 1/2 ( 12 *8)
= 1/2 (96)
But we have 2 triangles
2 * 1/2 (96)
96 cm^2
Add the area of the large rectangle and the two triangles
512+96 =608 cm^2
In the exercise, X is a binomial variable with n = 5 and p = 0.2. Compute the given probability. Check your answer using technology. HINT [See Example 2.] (Round your answer to five decimal places.) P(X = 3)
Answer:
0.0512
Step-by-step explanation:
We are told in the question that X isa Binomial variable. Hence we solve this question, using the formula for Binomial probability.
The formula for Binomial Probability = P(x) = (n!/(n - x) x!) × p^x × q ^n - x
In the above question,
x = 3
n = 5
p = probability for success = 0.2
q = probability for failures = 1 - 0.2 = 0.8
P(x) = (n!/(n - x) x!) × p^x × q ^n - x
P(3) = (5!/(5 - 3) 3!) × 0.2^3 × 0.8^5-3
P(3) =( 5!/2! × 3!) × 0.2³ × 0.8²
P(3) = 10 × 0.008 × 0.64
P(3) = 0.0512
The prime factorization of 25 is
TRIGONOMETRY NEED HELP ASAP
Answer:
x = 3.6 cmStep-by-step explanation:
Since the figure above is a right angled triangle we can use trigonometric ratios to find x
To find x we use tan
tan∅ = opposite/ adjacent
From the question
x is the opposite
10 is the adjacent
Substitute the values into the above formula and solve for x
That's
[tex] \tan(20) = \frac{x}{10} [/tex]
x = 10 tan 20
x = 3.63970
We have the final answer as
x = 3.6 cm to the nearest tenthHope this helps you
Brianna started a business making customized dog beds. She can make one bed every two hours. Wesley had a similar business, but used a different method. He can make two beds every threehours. They decided to combine their business ventures and received their first order for 49 beds from a local shop. How many hours will be required to fill the order?
Answer:
It will take them 42 hours
Step-by-step explanation:
Brianna rate = one bed for 2 hours
But for one hour = 0.5 bed per hour
Wesley rate = two bed for 3 hours
For one hour= 2/3 bed per hour
So their total rate for one hour
= 1/2 +2/3
= 7/6 bed per hour
If they received an order of 49 beds
It will take them x hours
Rate= bed/hour
7/6= 49/x
X= 49/(7/6)
X= 49 * 6/7
X= 7*6
X= 42 hours
What is the product? 4 • (–5)
Answer:
4×(-5)=-20
Step-by-step explanation:
Answer:
[tex]\huge \boxed{-20}[/tex]
Step-by-step explanation:
[tex]4*(-5)[/tex]
[tex]\Rightarrow 4* -5[/tex]
Multiplying.
[tex]\Rightarrow -20[/tex]
A man x years old which his son Is your years old. the sum of their age is twice the difference of their age. if the product of their age is 675. find the age of the man
Let's take as x and y the age of the man and of his son
We will do a system, so we can satisfy all the request:
1. sum of ages = 2 (difference)
2. product = 675
[tex]\left \{ {x + y = 2 (x-y)} \atop {x*y=675}} \right.[/tex]
semplify the first equation
x + y = 2x -2y
now let's choose one of the incognite (x) and we solve for it
x - 2x = - 2y - y
- x = - 3y
x = 3y
Let's substitute this solution in the second equation
[tex]\left \{ {x=3y} \atop {(3y)*y=675}} \right.[/tex]
note: x = 3y, so in the second equation x * y = 3y * y
Now let's solve the second equation
3y * y = 675
3y² = 675
y² = 675 / 3 =
y² = 225
y = 15
Son's age is 15
Man's age is 15 * 3 = 45 (See the first equation [x = 3y])
what of the following are true statements about the expression 4- (-4)
The data show systolic and diastolic blood pressure of certain people. Find the regression equation, letting the first variable be the independent (x) variable. Find the best predicted diastolic pressure for a person with a systolic reading of 118 . Use a significance level of 0.05.
Full Question:
The data show systolic and diastolic blood pressure of certain people. Find the regression equation, letting the first variable be the independent (x) variable. Find the best predicted diastolic pressure for a person with a systolic reading of 113. use a significance level of 0.05.
Systolic| 150 129 142 112 134 122 126 120
Diastolic| 88 96 106 80 98 63 95 64
a. What is the regression equation?
^y = __ + __x (Round to two decimal places as needed.)
b. What is the best predicted value?
^y is about __ (Round to one decimal place as needed.)
Answer:
A. yhat = a + bx = -10.64 + 0.75x
B. 74.0
Step-by-step explanation:
A. To find the regression equation here, we apply the formulas and then apply it to find the value of y given value of x:
calculate xbar and ybar which is the average of the variables:
Where n(number of values in x or y)=8
xbar = sum of x/n = 129.375
ybar = sum of y/n = 86.25
to calculate b
b= [Sum x^2 * Sum y - Sum x * Sum x*y] / [N*Sum x^2 - (Sum x)^2]
b = 0.74891
To calculate a
a = ybar - b * xbar = -10.64023
Regression equation:
y=mx+b= -10.64 + 0.75x
B. given x = 113,
y = -10.64023 + 0.74891 * 113
y= 74.0
What is the distance, rounded to the nearest tenth, between the points (0,5) and (8,0)?
Answer:
The answer is 9.4 unitsStep-by-step explanation:
The distance between two points can be found by using the formula
[tex]d = \sqrt{( {x1 - x2})^{2} + ({y1 - y2})^{2} } [/tex]where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(0,5) and (8,0)
So the distance between them is
[tex]d = \sqrt{ ({0 - 8})^{2} + ({5 - 0})^{2} } \\ d = \sqrt{ ({ - 8})^{2} + {5}^{2} } \\ d = \sqrt{64 + 25} \\ \\ d = \sqrt{89} [/tex]d = 9.4339811
We have the final answer as
d = 9.4 unitsHope this helps you
if you have 8 children and each child had at least Z=26 toys they get W=? more toys. How many do all the children have total
A plant is already 57cm talk and it will grow one centimeter every month the plant height h in centimeters after m months is given by the following function what is the plants height after 22 months
Answer:
the plant is 79 cm
Step-by-step explanation:
every month = 1 cm
months = 22 months
57 cm + 22 cm
= 79cm
An advertiser goes to a printer and is charged $37 for 80 copies of one flyer and $54 for 209 copies of another flyer. The printer
charges a foced setup cost plus a charge for every copy of single-page flyers. Find a function that describes the cost of a printing job, if 2 is the
number of copies made. C(x)
Answer: c(x) = y = $0.132*x + $27.16
Step-by-step explanation:
The chargers are a fixed price plus a charge for every copy, then we have a linear relationship.
A linear relationship can be written as:
c(x) = y = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
In this case, c(x) = y represents the cost in dollars, x is the number of copies bought, and b is the fixed cost.
We know two points in this line:
(80, $37) and (209, $54)
Whit those two points we can find the slope:
a = ($54 - $37)/(209 - 80) = $17/129 = $0.132 per copy.
Then our equation is:
c(x) = y = $0.132*x + b
To find the value of b, we know that 80 copies cost $37, we can replace those values in the equation:
$37 = $0.132*80 + b
$37 = $9.84 + b
($37 - $9.84) = $27.16 = b.
Then the equation is:
c(x) = y = $0.132*x + $27.16
A piece of wire 23 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle.
Required:
a. How much wire must be used for the square in order to maximize the total area?
b. How much wire must be used for the square in order to minimize the total area?
Answer:
wire for square to maximize total area = 23 m
Wire to minimize total area = 2.019 m
Step-by-step explanation:
For the square, let's say the total length of the square is "y" m.
Thus, length of one side is = y/4
And area of the square = (y/4) = y²/16
Since the wire is 23 m, then total length of equilateral triangle is; 23 - y.
Thus, length of one side of equilateral triangle = (23 - y)/3
Using trigonometric ratio, we can find the height of the triangle and thus area.
Area of triangle = (√3)/4) × ((23 - y)/3)²
Area of triangle = (√3)/36)(23 - y)²
So, total area of square and triangle is;
A_total = (y²/16) + (√3)/36)(23 - y)²
Now, extremizing this function by derivatives, we have;
dA/dy = (y/8) - (√3)/18)(23 - y)
d²A/dy² = ⅛ + (√3)/18)
So, d²A/dy² > 0
Now,let's find the maximum or minimum of the function.
So, we equate dA/dy to zero.
Thus;
(y/8) - (√3)/18)(23 - y) = 0
y/8 = (√3)/18)(23 - y)
(y/8) + (√3)/18)y = 23((√3)/18)
Multiply through by 8 to give;
y + 0.0962y = 2.2132
1.0962y = 2.2132
y = 2.2132/1.0962
y = 2.019 m
2.019 will be a minimum because d²A/dy² > 0
The maximum will occur at a boundary of the allowed values. Thus, the absolute maximum is for y = 23.
Note that a square has more area than a triangle and as such it is normal for the square to get the largest area over the triangle and therefore we will have to use all of the wire to construct the square.
5x+2y=12
Solve for y
Answer:
y = 1
Step-by-step explanation:
5·x
x=2
5·2=10
10+2y
y=1
2·1=2
10+2=12
Answer:1
Step-by-step explanation:5(x)+2(y)=12
5 x 2 =10
2 x 1=2
10 + 2=12
Damien worked at a grocery store earning $9.00 an hour. He worked 30 hours a week and was paid every two weeks. He paid $62 in taxes and had a $50 savings account deduction.What was Damien's net income?
Answer: $428.00
Step-by-step explanation: First, we need to calculate the person’s total hours, (30 x 2 = 60 hours) then the money per hour (60 x 9) then take away the taxes and account deductions.
Solve for x, please help
Answer:
x = 18
Step-by-step explanation:
ΔABC ≅ ΔDEC
∠ B ≅ ∠E
40 = 2x + 4
-2x = 4 - 40
-2x = -36
2x = 36
x = 36/2
x = 18
the value of 3 in 546300 is how many times more than 3456
Answer:
10 times.
Step-by-step explanation:
We need to find that the value of 3 in 546300 is how many times more than 3456.
The place value of 3 in 546300 is 300 and the place value of 3 in 3456 is 3000.
Now dividing 3000 by 300 as follows :
[tex]\dfrac{3000}{300}=10[/tex]
It means that the value of 3 in 546300 is 10 times more than the value of 3 in 3456.
A basketball player scored 33 points during a game by shooting 1-point free throws, 2-point field goals, and 3-point field goals. The player scored 17 times. She scored 3 more 2-point field goals than 1-point free throws. The system of equations below represents the situation, where x is the number of 1-point free throws, y is the number of 2-point field goals, and z is the number of 3-point field goals. x + y + z = 17 x + 2y + 3z = 33 y – x = 3
Answer:
The number of 1 point throw is 5, the number of 2 point throw is 8 and the number of 3 point throw is 4
Step-by-step explanation:
Let x represent the number of 1-point free throws, y is the number of 2-point field goals, and z is the number of 3-point field goals. A basketball player scored 33 points during a game by shooting 1-point free throws, 2-point field goals, and 3-point field goals. Each of 1 point free throw is 1 point, each of 2 point free throw is 2 points and each of the 3 point free throw is 3 points. This is represented by the equation:
x + 2y + 3z = 33 (1)
Also, The player scored 17 times, therefore it is represented by:
x + y + z = 17 (2)
The player scored 3 more 2-point field goals than 1-point free throws, it is represented by:
y = x + 3
-x + y = 3 (3)
Solving equation 1, eqn 2 and eqn 3 simultaneously:
x = 5, y = 8, z = 4.
The number of 1 point throw is 5, the number of 2 point throw is 8 and the number of 3 point throw is 4
Answer:
No. of 1 pt free throws = 5, No. of 2 pt goals = 8, No. of 3 pt goals = 4
Step-by-step explanation:
Equations : x + y + z = 17 [ Total times taken to score ]
1x + 2y + 3z = 33 [ Total Score ]
Also, y = x + 3
Putting the value of 'y' in both equations :
x + (x + 3)+ z = 17 → 2x + 3 + z = 17 → 2x + z = 14 (i)
1x + 2 (x + 3) + 3z = 33 → x + 2x + 6 + 3z = 33 → 3x + 3z = 27 (ii)
Solving these equations :
From (i), z = 14 - 2x
Putting this value in (ii), 3x + 3(14 - 2x) = 27 → 3x + 42 - 6x = 27
42 - 3x = 27 → 3x = 15 → x = 5
y = x + 3 = 5 + 3 → y = 8
z = 17 - x - y → z = 17 - 5 - 8 = 17 - 13 → z = 4
HELPPPP
A penny has a mass of 2.5 grams, I just cashed in 75$ in pennies at the coin star.
How many Kg is that? *
Answer:
18.750kgStep-by-step explanation:
If a mass of 2.5 grams costs a penny, we want to know the amount of mass that will cost $75. Before we get the mass, we need to convert 75 dollars to penny. Using the conversion:
$1 = 100pennies
$75 = (75*100)pennies
$75 = 7,500 pennies
Using the law of equivalence
1 penny = 2.5 grams
7,500pennies = x grams
Cross multiply
1 * x = 2.5 * 7500
x = 18,750 grams
Hence 18,759 grams will cost $75
Converting grams to kilograms
If 1000 grams = 1kg
18,750grams -= y
cross multiply
1000*y = 18750
Divide both sides by 1000
1000y = 18750/1000
y = 18.750kg
Hence the amount in kilogram of $75 coin in pennies is 18.750kg
what's the answer for (2+i)(i+2i)?
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{3 {i}^{2} + 6i}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{(2 + i)(i + 2i)}[/tex]
Use the distribute property to multiply each term of the first binomial by each term of the second binomial.
⇒[tex] \sf{2(i + 2i) + i(i + 2i)}[/tex]
⇒[tex] \sf{2i + 4i + {i}^{2} + 2 {i}^{2} }[/tex]
Collect like terms
⇒[tex] \sf{3 {i}^{2} + 6i}[/tex]
Hope I helped!
Best regards!
The theatre has 4 chairs in a row. there are 5 rows. Using rows as your unit of measurement,what is the perimeter.
Answer: 18 rows.
Step-by-step explanation:
The theatre has 4 chairs in a row.
There are 5 rows.
If we consider rows as unit, then we observed that
Length = 4 rows
Width = 5 rows
Perimeter of Rectangle = 2(length +breadth)
= 2(5+4)
= 2(9)
=18 rows
Hence, the perimeter is 18 rows.
Choose all of the expressions that are equal to -9.
the opposite of nine
-191
1-91
-1-91
-(-9)
the distance from zero to nine
Answer:
[tex]-|9|[/tex] and [tex]-|-9|[/tex]
Step-by-step explanation:
Given
Expression = -9
Required
Select all equivalent expressions
To do that, we examine each of the options.
First Option
[tex]-|9|[/tex]
This can be rewritten as
[tex]-|9| = -1 * |9|[/tex]
[tex]|9| = 9[/tex]
So, the expression becomes
[tex]-|9| = -1 * 9[/tex]
[tex]-|9| = -9[/tex]
Hence, |-9| is equivalent to -9
Second Option
[tex]|-9|[/tex]
[tex]|-9| = 9[/tex]
So, the expression is not equivalent to -9
Third Option
[tex]-|-9|[/tex]
This can be rewritten as
[tex]-|-9| = -1 * |-9|[/tex]
[tex]|-9| = 9[/tex]
So, the expression becomes
[tex]-|-9| = -1 * 9[/tex]
[tex]-|-9| = 9[/tex]
Hence, -|-9| is equivalent to -9
Fourth Option
[tex]-(-9)[/tex]
This can be rewritten as
[tex]-(-9) = -1 *(-9)[/tex]
[tex]-(-9) = -1 *-9[/tex]
[tex]-(-9) = 9[/tex]
Hence, -(-9) is not equivalent to -9
Fifth Option
The distance from 0 to 9
This is calculated as thus;
[tex]Difference = 9 - 0[/tex]
[tex]Difference = 9[/tex]
Hence, the difference from 0 to 9 is not equivalent to -9
Given that P(A|B) =......... rest of question is on the diagram.
Answer:
C. 2/25
Step-by-step explanation:
The probability that Events A and B both occur is the probability of the intersection of A and B. The probability of the intersection of Events A and B is denoted by P(A ∩ B). It is calculated by Rule of Multiplication.P(A ∩ B) = P(A) P(A|B)
P(A ∩ B) = 2/5 * 1/5 = 2/25
Answer option is:
C. 2/25
Let y = [5 5] and u = [6 8] . Compute the distance from y to the line through u and the origin.
Answer:
The distance d = 1
Step-by-step explanation:
The objective is to compute the distance from y to the line through u and the origin.
Given that :
[tex]y = \left[\begin{array}{cc}5\\5\end{array}\right][/tex] and [tex]u = \left[\begin{array}{cc}6\\8\end{array}\right][/tex]
Recall that:
from the slope - intercept on the graph, the equation of line can be expressed as :
y = mx + b
where;
m = slope = [tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]
b = y - intercept
Similarly, we are being informed that the line passed through [tex]u = \left[\begin{array}{cc}6\\8\end{array}\right][/tex] and origin, so ;
[tex]x_1 = 0 , y_1 = 0 \\ \\ x_2 =6 , y_2 = 8[/tex]
the slope m = [tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]=\dfrac{8 - 0}{6-0}[/tex]
[tex]= \dfrac{4}{3}[/tex]
Also, since the line pass through the origin:
Then
y = mx + b
0 = m(0) + b
b = 0
From y = mx + b
y = mx + (0)
y = mx
[tex]y = \dfrac{4}{3}x[/tex]
3y = 4x
3y - 4x = 0
4x - 3y =0
The distance of a point (x,y) from a line ax +by + c = 0 can be represented with the equation:
[tex]d = \dfrac{|ax+by +c|}{\sqrt{a^2 +b^2}}[/tex]
∴ the distance from [tex]y = \left[\begin{array}{cc}5\\5\end{array}\right][/tex] to the line 4x - 3y = 0 is
[tex]d = \dfrac{|4x-3y +0|}{\sqrt{4^2 +3^2}}[/tex]
[tex]d = \dfrac{|4(5)-3(5) +0|}{\sqrt{16+9}}[/tex]
[tex]d = \dfrac{20-15 }{\sqrt{25}}[/tex]
[tex]d = \dfrac{5}{5}[/tex]
The distance d = 1
The distance from y(5,5) to the line through u(6,8) and the origin(0,0) is √2 units.
What is the distance between the two points on a graph?The distance or length of any line on the graph is given by the formula,
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
where,
d = distance/length of the line between points 1 and 2,
(x₁, y₁) = coordinate of point 1,
(x₂, y₂) = coordinate of point 2,
In the given equation, we need to find the distance between the line and the point u (6,8). Now, we try to find the equation of the line, with points y=(5,5) and origin (0,0). Therefore, the slope of the equation can be written as,
[tex]m = \dfrac{y_2-y_1}{x_2-x_1} = \dfrac{5-0}{5-0} = 1[/tex]
Now, if we substitute the value of the slope and a point in the general equation of the line, we will get,
[tex]y = mx+c\\\\0 = 1(0)+c\\\\c = 0[/tex]
Further, if we draw the line on the graph, the nearest point to point u(6,8) is a(7,7). Therefore, the distance between the two points can be written as,
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\D = \sqrt{(7-6)^2+(7-8)^2}\\\\D = \sqrt2[/tex]
Hence, the distance from y(5,5) to the line through u(6,8) and the origin(0,0) is √2 units.
Learn more about the Distance between two points:
https://brainly.com/question/16410393
x+2/5=6/15 solve for x
Answer:
0
Step-by-step explanation:
First, simplify for both sides
6/15 -> 2/5
2/5 -> 2/5
x+2/5 = 2/5
Subtract 2/5 from each side.
(x+2/5)-2/5-> x
2/5-2/5 -> 0
x = 0
A question includes logarithm and trigonometry. Could anybody help me to solve this,please?
[tex]\log_2(2\sin x)+\log_2(\cos x)=-1[/tex]
Condense the logarithms on the left side:
[tex]\log_2(2\sin x\cos x)=-1[/tex]
Recall the double angle identity for sine, [tex]\sin(2x)=2\sin x\cos x[/tex]:
[tex]\log_2(\sin(2x))=-1[/tex]
Write both sides as powers of 2:
[tex]2^{\log_2(\sin(2x))}=2^{-1}[/tex]
Simplify this:
[tex]\sin(2x)=\dfrac12[/tex]
Solve for [tex]2x[/tex]:
[tex]2x=\sin^{-1}\left(\dfrac12\right)+2n\pi\text{ OR }2x=\pi-\sin^{-1}\left(\dfrac12\right)+2n\pi[/tex]
(where [tex]n[/tex] is any integer)
Recall that [tex]\sin^{-1}\left(\frac12\right)=\frac\pi6[/tex]:
[tex]2x=\dfrac\pi6+2n\pi\text{ OR }2x=\dfrac{5\pi}6+2n\pi[/tex]
Solve for [tex]x[/tex]:
[tex]x=\dfrac\pi{12}+n\pi\text{ OR }x=\dfrac{5\pi}{12}+n\pi[/tex]
We get solutions in the interval [tex]2\pi <x<\frac{5\pi}2[/tex] when [tex]n=2[/tex], giving
[tex]\boxed{x=\dfrac{25\pi}{12}}\text{ OR }\boxed{x=\dfrac{29\pi}{12}}[/tex]