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3 years ago

6

5. On the fifth day of my winter break, I got five golden rings. BUT—— the golden rings were five separate water rings around my

hot tub caused by too high a concentration of iron in the water. The radius of my cylindrical hot tub is 3 feet. How many feet of “golden ring” did I have to scrub off the hot tub? Round to nearest foot.

1 answer:

kvv77 [185]3 years ago

4 0

Answer:

Step-by-step explanation:

1 ring has a radius of 3 feet

1 ring has a circumfrence of 2*pi*r = 2 * 3.14 * 5 = 10*Pi

5 rings would have a length of 50 * pi length = 50*3.14 = 157 feet

That's a lot of Brillo pads.

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Josh and Anthony have a lemonade stand.They charge $1 for 2 cups of lemonade.They sell 14 cups each afternoon.Is it reasonable t

Rudik [331]

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3 years ago

How do I solve: 2 sin (2x) - 2 sin x + 2√3 cos x - √3 = 0

ziro4ka [17]

Answer:

$\displaystyle x = \frac{\pi}{3} +k\, \pi$ or $\displaystyle x =- \frac{\pi}{3} +2\,k\, \pi$ , where $k$ is an integer.

There are three such angles between $0$ and $2\pi$ : $\displaystyle \frac{\pi}{3}$ , $\displaystyle \frac{2\, \pi}{3}$ , and $\displaystyle \frac{4\,\pi}{3}$ .

Step-by-step explanation:

By the double angle identity of sines:

$\sin(2\, x) = 2\, \sin x \cdot \cos x$ .

Rewrite the original equation with this identity:

$2\, (2\, \sin x \cdot \cos x) - 2\, \sin x + 2\sqrt{3}\, \cos x - \sqrt{3} = 0$ .

Note, that $2\, (2\, \sin x \cdot \cos x)$ and $(-2\, \sin x)$ share the common factor $(2\, \sin x)$ . On the other hand, $2\sqrt{3}\, \cos x$ and $(-\sqrt{3})$ share the common factor $\sqrt[3}$ . Combine these terms pairwise using the two common factors:

$(2\, \sin x) \cdot (2\, \cos x - 1) + \left(\sqrt{3}\right)\, (2\, \cos x - 1) = 0$ .

Note the new common factor $(2\, \cos x - 1)$ . Therefore:

$\left(2\, \sin x + \sqrt{3}\right) \cdot (2\, \cos x - 1) = 0$ .

This equation holds as long as either $\left(2\, \sin x + \sqrt{3}\right)$ or $(2\, \cos x - 1)$ is zero. Let $k$ be an integer. Accordingly:

$\displaystyle \sin x = -\frac{\sqrt{3}}{2}$ , which corresponds to $\displaystyle x = -\frac{\pi}{3} + 2\, k\, \pi$ and $\displaystyle x = -\frac{2\, \pi}{3} + 2\, k\, \pi$ .
$\displaystyle \cos x = \frac{1}{2}$ , which corresponds to $\displaystyle x = \frac{\pi}{3} + 2\, k \, \pi$ and $\displaystyle x = -\frac{\pi}{3} + 2\, k \, \pi$ .

Any $x$ that fits into at least one of these patterns will satisfy the equation. These pattern can be further combined:

$\displaystyle x = \frac{\pi}{3} + k \, \pi$ (from $\displaystyle x = -\frac{2\,\pi}{3} + 2\, k\, \pi$ and $\displaystyle x = \frac{\pi}{3} + 2\, k \, \pi$ , combined,) as well as
$\displaystyle x =- \frac{\pi}{3} +2\,k\, \pi$ .

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3 years ago

Y - 5 = -2x - 4<br><br>Write in simpilest form.

Romashka-Z-Leto [24]

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4 years ago

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3 years ago

-3.75+2(-4x+6.1)-3.25

Pani-rosa [81]

The value of x is 0.65

<u>Step-by-step explanation:</u>

This solution is given by solving the given problem using BODMAS rule.

This means that the steps to be followed to find the solution should be in the order of BODMAS rule.

B- Bracket, O- of, D- Division, M- Multiplication, A- Addition, S- Subtraction.

This rule states that the 1st operation must be done for Brackets.

⇒ -3.75+2(-4x+6.1)-3.25 = 0

⇒ -3.75 -8x + 12.2 -3.25 = 0

The addition operation should be performed next and then followed by subtraction.

⇒ -8x -7+ 12.2 = 0

<u>To find the value of x :</u>

Keeping the x term alone on one side and moving the constants on other side,

⇒ -8x = -12.2 + 7

⇒ -8x = -5.2

⇒ x = 5.2/8

⇒ x = 0.65

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3 years ago