Fern is doing her holiday shopping. She wants to buy a game for her little sister. The game is regularly priced at $32, but it is on sale for $20.80. What is the percentage of the discount for the game?

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.

Answer:70

Step-by-step explanation: notice the pattern is adding by 8 after the first term

Answer:

Hii, I believe your answer would be $3,360

Hope this helps!

Step-by-step explanation:

[tex]▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ { \huge \mathfrak{Answer}}▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ [/tex]

Let's find the slope :

now, the equation is in the general form of a straight line.

and here, the coefficient of x will be the slope of given line.

that is :

Answer:

Option D portrays that

Matrix A multiplied by an identity matrix equals Matrix A

Answer:

x = 11/9

Step-by-step explanation:

Answer:

Pls take a clearer picture or type down the values pls. Is angle D=6x+3 or something else?

The graphical device that divides data according to the percentage they represent is a pie-chart.

Frequency distribution, relative frequency distribution, or percent frequency distribution all are statistical measures that want to establish the part of the distribution corresponding to each measure, that is, percentages, thus they are represented by pie-charts.

An example, suppose that among 50 people sampled, 20 prefer the NBA and 30 the NFL.

A similar problem is given at https://brainly.com/question/14354536

And.......what........

Answer: [tex]3\sqrt{3[/tex]

Step-by-step explanation: use pythagorean theorem to solve this. which is a^2 + b^2 = c^2

lets say b=3 and c=6. plug this into the equation.  (6)^2 - (3)^2 + = 36 - 9 which is 27 = c^2. to get c from c^2, square root the c^2 value

the square root of 27 is [tex]3\sqrt{3[/tex] in simplest radical form

Answer:

x=64

Step-by-step explanation:

x/8+4=12

x/8=12-4

=8

x=8×8

=64

The value of expression is equivalent to given expression is,

⇒ 126y²

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 3 √2y³ × 7 √18y

Now, We can simplify as;

⇒ 3 √2y³ × 7 √18y

⇒ 21 √36y⁴

⇒ 21 × 6y²

⇒ 126y²

Thus, The value of expression is equivalent to given expression is,

⇒ 126y²

Learn more about the mathematical expression visit:

brainly.com/question/1859113

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Answer: b

Step-by-step explanation:

Answer:

15 bags left

Step-by-step explanation:

360/6=60

60-45=15

Answer:

83.3%

Step-by-step explanation:

Answer:

You answer can be written for Solving X two different ways

The inquitly form is

x[tex]\geq[/tex]-6

Interval Notation is

{-6,∞)

Step-by-step explanation:

In order to graph put a close dot on the number -6 and then color your line to the right of the number line.  Because the infinity sign is positive so all the number after the -6 is positive. So a close dot on the number -6 and then draw a line or color a line to the right of the number line

Answer:

=  2

=  − 5

Step-by-step explanation:

Answer:

hope my answer helps you

Step-by-step explanation:

Yes that is definitely possible. You will have to either double up on geometry and algebra II or algebra II and pre-calculus. At my high school, there were multiple people that did the latter. I also knew someone that doubled up on pre-calculus and calculus I, but I don't recommend that.

Answer:

Ok so I don't have a graphing thing on my computer but on the y axis you are going to put a dot on the one then go up 47 and to the right 1 and put a dot sorry that is as much as i can help you

Answer:

He ate 1/4 of a pizza.

Step-by-step explanation:

1/3 basically means: There are 3 parts, you take 1 of those parts

so 3/4 means that there are three fourths. 3/4 divided by 3 = 1/4. He ate 1/4 of a pizza.

The answer is $309

Since its $3 extra per 3 months and 9 months pass it has to be an extra $9 for the $9 months.You already had to pay back the 300 so the equation would be (300+9=309)

Answer:

x= 104

Step-by-step explanation:

Angle in a triangle is 180

35+41+x=180

76+x=180

x=180-76

x=104

Answer:

AB

Step-by-step explanation:

They are the shortest combined side