A set of four stars form the shape of a rectangle in space. The length of the rectangle is approximately 510,000,000 miles, while the width of the rectangle is approximately 366,000,000 miles. What is the approximate area of the rectangle?

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:

(2x^(3)y^(2))^(3) the little ^ means "sub"

Step-by-step explanation:

Use the power rule to distribute the exponent.

Raise 2 to the power of 3

Multiply the exponents in (x^3)^3

Multiply the exponents in (y^2)^3

Answer:

9. A, C,

10. A, B,

Step-by-step explanation:

Answer:Correct option is

A

10

Given y=(x−11)  

2

⇒y=x  

2

−22x+121

After substitute y=25. we get,

x  

2

−22x+121−25=0

⇒x  

2

−22x+96=0

⇒(x−16)(x−6)=0

⇒x=16,x=6

∴ two points are  A,B are (16,25),(6,25).

Distance between A and B is  

(16−6)  

2

−(25−25)  

2

​

=10

Hence, option A is correct.

Answer:

2/3

Step-by-step explanation:

y2 - y1 / x2 - x1

5 - 3 / 9 - 6

2/3

Answer:

-2 i think

Step-by-step explanation:

We want to find the total change in the volume of water of a tub, given that we know how much water is used.

The change in volume is: -(9 + 7/10) quarts.

To find the change in volume, we need to find the total volume of water used.

We do know that:

The total amount used is the sum of the two quantities above, we get:

(3 + 1/5) quarts + (6 + 1/2) quarts

(3 + 6 + 1/2 + 1/5) quarts

(9 + 7/10) quarts.

So the change in volume is related to this, and we should write:

Final Volume - Initial Volume = -(9 + 7/10) quarts.

Where the negative sign is because at the end we have less volume than at the beginning.

If you want to learn more, you can read:

https://brainly.com/question/18013877

so I don't know the answer but need to answer a question

Answer:

X is the opposite of X

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

4 > -8 negative numbers (-1, -2, -3) are always smaller than whole numbers (1, 2, 3)

Answer:

87 Adult tickets were sold

Step-by-step explanation:

This type of question relates to a system of equations. These types of questions are pretty easy to spot and they are just about solved all the same way.

So what we first want to do is see that there is a total of 159 tickets sold. Now obviously that number consists of the adult and children tickets, therefore we need to add those two unknown numbers to get 159, so x will be for adults and y will be for children tickets. this will give us the equation x + y= 159.

Next, we want to associate the amount those tickets are with those variables, because you can only have so many adult tickets and children tickets with the given $1794. So what we need to do is similar, we just have those totals added to get the equation 14x + 8y = 1794.

Now we want to use the process of elimination to find the value of x (because we are solving how many adult tickets were sold). IN order to do elimination, we need to have the equation x + y= 159 cancel the y value to leave us with the x value. In order to do this, you need to multiply y by a value that cancels 8y in 14x + 8y = 1794, which is -8.

So we multiply the entire equation of x + y= 159 by -8 to get. Now we would add these equations together where you subtract by like terms so:

[tex]14x + 8y = 1794\\-8x - 8y = -1272[/tex]

This leaves us with 6x=522 now you would divide by 6 to isolate x which leaves you with 87.

Answer:

Pythagorean theorem = [tex]a^2+b^2=c^2[/tex] or [tex]c=\sqrt{a^2+b^2}[/tex]

a & b are the sides

c is hypotenuse

1. [tex]9^2+5^2=c^2[/tex]

[tex]81+25=c^2[/tex]

[tex]106 = c^2[/tex]

[tex]c=\sqrt{106}[/tex]

c = 10.3 cm

And you keep doing that to the other triangles.

2. x = 8.1

3. x = 39.2

4. x = 108.5

Brainly plz :)

Step-by-step explanation:

(1.6 x 10^*5)(6.7 x 10^*18)

=10.72 × 10²³

=1.072×10²⁴

Hello there!

(1.6x10^5)(6.7x10^18)

1.072x10^24

Hope this helps you! :)

[tex](: GraceRosalia :) *^**^**^**^[/tex]

Answer:

9875 dollars I believe is your answer

Answer:

9,875

Step-by-step explanation:

u just multiply the number of boxes by 395

Answer:

65 and 325

Step-by-step explanation:

(l+w)*2 = 780

l+w = 390

l = 5w

5w + w = 390

6w = 390

w = 65

length = 325

Step-by-step explanation:

Since Q and R are complementary,

⇒ Q + R = 90°

Since Q is 26° less than the measure of R

⇒ R - 26° = Q

We can therefore say that ( R - 26°) + R = 90°

⇒              2 R = 90° + 26°

                    R = 58 °

Also, since  R - 26°   = Q

                   58° - 26° =  Q

                            32 ° = Q

Answer:

it's 88.9

Step-by-step explanation:

Answer: 88.9

Step-by-step explanation .....

Answer:

0.35

Step-by-step explanation:

Answer:

Just one

Step-by-step explanation:

Got it right on Edge 2022

Answer:

15 bears

Step-by-step explanation:

Answer:

ion know if this is a joke but 15 bears

Answer:

-204ºC

Step-by-step explanation:

The third option.

Emma will not have enough glue since she'll have 10 2/3 rather than 11 batches.

Note that 1 gallon = 16 cups

Since Emma has half of 1-gallon bottle of white school glue, this means that she has 1/2 × 16 = 8 cups

Since Emma uses 3/4 cup of white school glue for each batch, therefore the number of batches that van be made with 8 cups will be:

= 8 ÷ 3/4

= 8 × 4/3

= 10 2/3

Therefore, Emma will not have enough glue since she'll have 10 2/3 rather than 11 batches.

Read related link on:

https://brainly.com/question/24963824

Answer:

5.99g in one dose.

Step-by-step explanation:

Add up all the chemicals in the mix and divide by 5 to get how many grams are in one dose of medicine. We divide by 5 cause we get 5 doses out of the entire mixture.

[tex]\frac{10.384+12.061+7.505}{5} =\frac{29.95}{5}=5.99g[/tex]

Answer:

The answer to your equation is 7x4.

Answer:

It is 8.5 meters tall

Step-by-step explanation:

28.05 / 3.3 = 8.5

Answer:

350$

Step-by-step explanation:

he usually makes $250, 60% more is $400, and 7/8 of $400 is $350