Recall the triple angle identity for sine:
sin(3x) = 3 sin(x) cos²(x) - sin³(x)
… = 3 sin(x) (1 - sin²(x)) - sin³(x)
… = 3 sin(x) - 4 sin³(x)
So the equation is equivalent to
sin²(x) - 2 sin(x) + 2 = sin²(3x)
sin²(x) - 2 sin(x) + 2 = (3 sin(x) - 4 sin³(x))²
sin²(x) - 2 sin(x) + 2 = 9 sin²(x) - 24 sin⁴(x) + 16 sin⁶(x)
16 sin⁶(x) - 24 sin⁴(x) + 8 sin²(x) + 2 sin(x) - 2 = 0
or, by replacing y = sin(x),
16y ⁶ - 24y ⁴ + 8y ² + 2y - 2 = 0
By inspection, y = 1 is a root, since
16 - 24 + 8 + 2 - 2 = 0
so we get one family of solutions,
sin(x) = 1 ===> x = arcsin(1) + 2nπ = π/2 + 2nπ
Now suppose y ≠ 1. Dividing both sides of the sextic equation by y - 1 then gives
(16y ⁶ - 24y ⁴ + 8y ² + 2y - 2)/(y - 1) = 0
16y ⁵ + 16y ⁴ - 8y ³ - 8y ² + 2 = 0
Unfortunately, the remaining roots can only be obtained through numerical methods. Using a calculator, you would find
y ≈ -1.127
y ≈ -0.475 ± 0.368i
y ≈ 0.539 ± 0.127i
But if you're solving over the reals, you can ignore these solutions. Remember that sin(x) is bounded between -1 and 1, and its value goes outside this interval only when x is complex.
The side length of a cube is 8 cm, and the side length of a smaller cube is 2 cm.
The volume of the larger cube is how many times the volume of the smaller cube?
Answer:
64 times larger
Step-by-step explanation:
8^3=512
2^3=8
512/8=64
Evaluate the expression for
c = 3 and d = -1
cd2
Answer: 3
Step-by-step explanation:
3(-1)^2
Answer: 3
Step-by-step explanation:
hope this helps
HELP PLEASE ASAP!!!!!!!!!!!!!!!!!!!!!!!
Answer:
3
Step-by-step explanation:
(plz mark as branliest if correct)
Answer:
3
Step-by-step explanation:
P to S is 3 and the other side must be equal so its 3.
An adult ticket to the school play cost $14.75. A child ticket cost $5.25. Mr. Montes bought 2 adult tickets and 4 child tickets.
Answer:
$50.50
Step-by-step explanation:
From the above question, we are to find the total cost of the tickets Mr Montes bought
An adult ticket to the school play cost $14.75.
A child ticket cost $5.25.
Mr. Montes bought 2 adult tickets and 4 child tickets.
Hence, the total cost is
= 2 × $14.75 + 4 × 5.25
= $29.5 + $21
= $50.50
In what form is the following linear equation written?
3.x - 2y=4
A. Rise-run
B. Standard
C. Slope-intercept
D. Point-slope
Answer:
Step-by-step explanation:
The format of the "standard equation of a line" is Ax + By = C
Which measurement is closest to the area of the circle in square meters?
115 divided by 356................
Answer:
0.32
:)
brainliest greatly appretiated
The system of equations
(2x - y = 2(x+1)
has
ly=-2
no solution
one solution
infinitely many solutions
Brainly Reward (mathematics)
Answer:
1: 45
2: 32
3: 35
4: 32
Step-by-step explanation:
when finding the area of a trapezium you can also just split the rectangle and triangle to have 2 different areas then combine to have the same area. but also this would be more difficult if you needed to separate the trapezium into more than 3 shapes.
so if there is like a trapezoid that you split and there is a rectangle and 2 triangles it is harder than doing the formula.
so use the formula sometimes too if it is easier.
Answer:
1 would be 45, 2 would be 32, 3 would be 35, 4 would be 32
Step-by-step explanation:
what is aproxamently the answer to 5 pi
Answer:
It turns into the decimal: 15.70796...
Step-by-step explanation:
8th grade math !!
g(x) = x+6/2
Determine for each x-value whether it is in the domain of g or not.
-6
0
2
Answer:All in domain
Step-by-step explanation:
Answer:all in domain
Step-by-step explanation:I did it on khan
Write an exponential function in the form y=ab^x that goes through points (0,6) and (7, 768)
Answer:y=6(2)*x
Step-by-step explanation:
Determine the value of y for y=x-2
Answer:
y=7, -3, 3, -9, 1 (in the empty boxes from left to right)
Step-by-step explanation:
Since y=x-2, all you have to do is take an x value from the top box and subtract 2 from that number to find the value of y.
Can you help me with this like explain how and stuff, Please?
Answer:
Step-by-step explanation:I belive that the 7x+22 needs to equal 50 because they opposite angles. Hope this helped a little and can get you started
Answer:
22.57
Step-by-step explanation:
7x+ 22 =180 180 because its a supplimentary angle -22 from 22 and 180 22 and -22 cancel out the 180 - 22 = 158
then you have 7x = 158 divide both numbers by 7 to isolate x then divide 158 by 7 = 22.57
Maleah turned on the water in the kitchen. For every 1 3/4 minute, 1 2/3 gallons of water went into the sink. How many gallons of water filled the sink per minute?
Answer: 20/21 gallons
Step-by-step explanation:
From the question given, we are informed that Maleah turned on the water in the kitchen and that for every 1 3/4 minute, 1 2/3 gallons of water went into the sink.
The number of gallons of water that filled the sink per minute will then be calculated as:
= Amount of gallons of water that went into sink / Number of minutes used
= 1 2/3 ÷ 1 3/4
= 5/3 ÷ 7/4
= 5/3 × 4/7
= 20/21
Therefore, 20/21 gallons of water filled the sink per minute
HI! please help out ASAP this is due today! Explain it the best you can and send a picture explaining it so I won’t get confused. Thank u!
Answer:
Step-by-step explanation:
Sammie cuts a piece of ribbon that is 2 feet long.
She needs only 18 inches of ribbon.
How much extra ribbon did she cut?
Answer:
the answer is 6 extra inches
Step-by-step explanation:
im assuming she cut off 2 feet of ribbon which is also known as 24 inches so the you just do 24 - 18 = 6
Please help.
Is algebra.
PLEASE HELP NO LINKS OR FILES.
I don't want links.
5ive plus 2wo?
Correct answer gets brainiest!!
!00 bomb
Step-by-step explanation:
The Answer For the solution of
5ive plus 2ow is...........
7even
MARK ME AS BRAINLIST
how do i find the range of a function on a graph
Answer:
#1. First label the function as y=f (x) #2. Express x as a function of y #3. Find all possible values of y for which f (y) is defined y y. #4. Element values of y by looking at the initial function f (x)
Step-by-step explanation:
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP MEEE PLSSSS
Answer:
Ur question? Itz incomplete
6. There are 12 girls and 8 boys in
Ms. Sander's class. Each day, she
randomly asks one student to take
attendance. In 180 school days, which
is the best prediction for the number of
times that the student will be a girl?
A. 72
(B. 90
C. 99
D. 108
Answer:
90
Step-by-step explanation:
its half
165 x 0.38² to two decimal place
Answer:
23.83
Step-by-step explanation:
Find the distance between the two numbers on a number line. Write your answer as a decimal.
2.491, -3.065
Answer:
-0.574
Step-by-step explanation:
Subtract the two numbers to get the solution
Given m||n, find the value of x.
Answer: T be honest i really don't know.
Step-by-step explanation:
Answer:
x=29
Step-by-step explanation:
Based off of the Consecutive Interior Therom, Angle 1= Angle 2. With this given, you get:
6x-1=5x+28
-5x. -5x
x-1=28
ANSWER:
x=29
What are the answer for your these questions?
Answer:
a. 11
b. 9
Step-by-step explanation:
A:
2 x 4 = 8
8 + 3 = 11
B:
-2 x -2 = 4
4 + 5 = 9
Hope this helps! Let me know if it was right!
Jasmine made a line plot to show the lengths of string in inches that the art teacher gave her for a craft project
Which of the following statements that Jasmine made about the string lengths are true? Select all that apply.
A. The difference between the longest length and shortest length is 14 inches.
B .I have twice as many 12-inch strings as I do 8-inch strings.
C. The total length of string that I have is 84 inches.
D. I cannot determine what the shortest string is by looking at my line plot.
E. Since I need 100 total inches of string for my project, I have enough string.
WILL GIVE BRAINLEST
Answer:
B and C
Step-by-step explanation:
I took a test
Answer:
answer is b and c
Step-by-step explanation:
plz plz help its shapes!!!! ill give u brainy !!!!!!
Answer:
Names that describe the shape- Trapezoid, Quadrilateral
Names that don't describe the shape- Square, Rectangle, Parallelogram and rhombus
Step-by-step explanation:
HELP PLEASE!!!!!!!!!! ASAP
Answer:
j - 150
k - 62
l - 52
m - 96
Complete the square for 5x2 - 30x = 5.
Answer:
x=1/6
Step-by-step explanation:
cytktcyrcuhvoui