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3 years ago

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kondaur [170]3 years ago

5 0

Answer:

D

Ur welcome sir

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If sin(x) = 5/13, and x is in quadrant 1, then tan(x/2) equals what?

Rufina [12.5K]

$x$ is in quadrant I, so $0$ , which means $0$ , so $\dfrac x2$ belongs to the same quadrant.

Now,

$\tan^2\dfrac x2=\dfrac{\sin^2\frac x2}{\cos^2\frac x2}=\dfrac{\frac{1-\cos x}2}{\frac{1+\cos x}2}=\dfrac{1-\cos x}{1+\cos x}$

Since $\sin x=\dfrac5{13}$ , it follows that

$\cos^2x=1-\sin^2x\implies \cos x=\pm\sqrt{1-\left(\dfrac5{13}\right)^2}=\pm\dfrac{12}{13}$

Since $x$ belongs to the first quadrant, you take the positive root ( $\cos x>0$ for $x$ in quadrant I). Then

$\tan\dfrac x2=\pm\sqrt{\dfrac{1-\frac{12}{13}}{1+\frac{12}{13}}}$

$\tan x$ is also positive for $x$ in quadrant I, so you take the positive root again. You're left with

$\tan\dfrac x2=\dfrac15$

4 0

3 years ago

A rectangular swimming pool is twice as long as it is wide. A small concrete sidewalk surrounds the pool and is a constant 2 fee

Naddika [18.5K]

Answer:

The dimensions of the pool are:

Width: 8.944 feet

Length: 17.888 feet

Step-by-step explanation:

From Geometry, the area of a rectangle ( $A$ ), measured in square feet, is determined by the following equations:

$A = w\cdot l$ (1)

Where:

$w$ - Width, measured in feet.

$l$ - Length, measured in feet.

If we know that $w = x$ , $l = 2\cdot x$ and $A = 160\,ft^{2}$ , then we get the following second order polynomial:

$2\cdot x^{2}-160 = 0$ (1)

And we solve the expression for $x$ :

$2\cdot x^{2} = 160$

$x^{2} = 80$

$x = \sqrt{80}\,ft$

$x \approx 8.944\,ft$

Then, the dimensions of the pool are, respectively:

$w \approx 8.944\,ft$ and $l \approx 17.888\,ft$

5 0

2 years ago

Order the set of numbers from least to greatest 64 8 1/7 8.14 15/2

Marianna [84]

Answer:

Step-by-step explanation:

1/7 15/2 8 8.14 64

4 0

2 years ago

HELP ME ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing. Check ALL that apply.

Elena L [17]

Answer:

x = -2 or x = 1/3 thus: B & C

Step-by-step explanation:

Solve for x over the real numbers:

2 x^2 + 7 x - 2 = 2 x - x^2

Subtract 2 x - x^2 from both sides:

3 x^2 + 5 x - 2 = 0

The left hand side factors into a product with two terms:

(x + 2) (3 x - 1) = 0

Split into two equations:

x + 2 = 0 or 3 x - 1 = 0

Subtract 2 from both sides:

x = -2 or 3 x - 1 = 0

Add 1 to both sides:

x = -2 or 3 x = 1

Divide both sides by 3:

Answer: x = -2 or x = 1/3

3 0

2 years ago

Someone do this plz ill pay u when im rich

lbvjy [14]

Answer:

11307.19 rounded and exact is 11307.1875

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers