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OverLord2011 [107]
3 years ago
7

On a unit circle, the vertical distance from the x-axis to a point on the perimeter of the circle is twice the horizontal distan

ce
from the y-axis to the same point. What is sin theta?

Mathematics
1 answer:
swat323 years ago
5 0

Check the picture below.

since the vertical distance, namely the y-coordinate, is twice as much as the horizontal, then if the horizontal is "x", the vertical one must be 2x.

let's find the hypotenuse first.

\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{x}\\ b=\stackrel{opposite}{2x}\\ \end{cases} \\\\\\ c=\sqrt{x^2+(2x)^2}\implies c=\sqrt{x^2+4x^2}\implies c=\sqrt{5x^2}\implies c=x\sqrt{5} \\\\[-0.35em] ~\dotfill

\bf sin(\theta )=\cfrac{\stackrel{opposite}{2~~\begin{matrix} x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }}{\stackrel{hypotenuse}{~~\begin{matrix} x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ \sqrt{5}}}\implies \stackrel{\textit{and rationalizing the denominator}~\hfill }{\cfrac{2}{\sqrt{5}}\cdot \cfrac{\sqrt{5}}{\sqrt{5}}\implies \cfrac{2\sqrt{5}}{(\sqrt{5})^2}\implies \cfrac{2\sqrt{5}}{5}}

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Solve for X: <br> 2.5x+12=32
Crank

Step-by-step explanation:

2.5x+12=32

We move all terms to the left:

2.5x+12-(32)=0

We add all the numbers together, and all the variables

2.5x-20=0

We move all terms containing x to the left, all other terms to the right

2.5x=20

x=20/2.5

x=8

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3 years ago
Given the quadratic equation: f(x) = x2+4x-21
ryzh [129]

Answer:

x = - 7, x = 3

Step-by-step explanation:

To find the x- intercepts let f(x) = 0 , that is

x² + 4x - 21 = 0

Consider the factors of - 21 which sum to give the coefficient of the x- term (+ 4)

The factors are + 7 and - 3, since

7 × - 3 = - 21 and 7 - 3 = + 4, then

x² + 4x - 21 = 0

(x + 7)(x - 3) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 7 = 0 ⇒ x = - 7

x - 3 = 0 ⇒ x = 3

6 0
3 years ago
determine The length of the circular arc of a circle with a radius of 49 cm subtended by a central angle of 135°
Katena32 [7]

Given:

Length of the circular arc with circle radius=49cm

θ=135°

Now,

Length of arc = θ/360°×2πr

49=2× 22/7×r×135°/360°

49×20×7/3×22×2

51.96cm

6 0
1 year ago
-9=-3(x+2)<br>solve for x <br>show steps
lianna [129]

SimplifyOkie dokie so first things first, you have to get rid of those parentheses! To do this you use the distributive property. -3(x+2) is the same thing as -3(x)+-3(2). that and you get -9=-3x-6. So you want to get x by itself to be able to find what x is, so you add 6 to both sides of the equation to get rid of the -6. So then you get -3=-3x. Then you must divide both sides by the coefficient of x, which would be -3. When you divide both sides by -3 you get -3/-3=x, which is the same thing as 1=x. Hope this helped!

4 0
3 years ago
Read 2 more answers
AKAJAXOSPAPXODAOAPA HELP
Leya [2.2K]

Answer:

He used 6 bananas at .50 which cost $3.00

12 oranges at .75 which cost $9.00 and

3 papayas at $1.25 which cost $3.75

Step-by-step explanation:

We can set up a system of equations using the information given.

b for banana, r for orange, p for papaya

b + r + p = 21. Also given r = 2b So substitute to simplify for calculating two unknowns:

b + 2b + p = 21 The number of items.

50b + 75(2b) +125p = 1575 The cost.

<em>I </em><em>multiplied</em><em> </em><em>everything</em><em> </em><em>by </em><em>100 </em><em>to </em><em>eliminate</em><em> </em><em>the</em><em> </em><em>decimals</em><em>.</em>

To solve by substituion, rewrite the first equation to get a value for p in terms of b

p = 21 - 3b

Substitute this value in the second equation and solve for b.

50b + 150b + 125(21–3b) = 1575

200b +2625 –375b = 1575 Subtract 2625 from both sides and combine the like terms:

–175b = 1575 –2625

–175b = –1050. Divide both sides by –175

b = 6

Substitute in the original equation to find the amount of each fruit:

b + r + p = 21

b = 6 bananas

r = 2b. 2(6) = 12 oranges. <em>I </em><em>used </em><em><u>r </u></em><em>so </em><em>as </em><em>not</em><em> to</em><em> </em><em>mix </em><em>up </em><em>o </em><em>with </em><em>0</em><em>.</em><em> </em>

6 + 12 + p = 21

p = 21 –18

p = 3 papayas

7 0
3 years ago
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