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dlinn [17]
2 years ago
15

What are the sine and cosine ratios for a 30°–60°–90° triangle with a hypotenuse of 6, when θ = 60°?

Mathematics
1 answer:
Margaret [11]2 years ago
4 0

Answer:

There are two ways to do this problem algebraically or trigonometrically.

Algebraically/geometrically

The ratios of the sides of a 30/60/90 tri. are x, x√3, 2x (short leg, long leg, hyp). Therefore, if the long leg is 6 'units'. then 6 = x√3. x = 6√3.

The hyp is 2x then the hypotenuse is 2(6√3) = 12√3, rationalizing is 12√3/3 = 4√3

Using Trig.

We can use sinx = y/r = opp/hyp. The long leg of 6 is opposite 60 degrees (pi/3).

Therefore, sin(pi/3) = 6/r =

r = 6/sin(pi/3) = 6/(√3/2) = 12/√3, when you rationalize you get 12√3/3 = 4√3

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3 years ago
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Irina18 [472]

Answer:

x ≅ 20.10 torr

Step-by-step explanation:

Given that the equation which models blood pH in the question is;

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x = partial pressure of carbon dioxide in arterial blood, measured in torr.

we are asked to find (x)

In order to do that, we use the given equation:

pH(x)=6.1+log(800/x)

since pH = 7.7

7.7 = 6.1 + log (800/x)

7.7 - 6.1 =  log (800/x)

1.6 =  log (800/x)

10^{1.6}= \frac{800}{x}

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4 0
3 years ago
Two researchers are studying the decline of orangutan populations. In one study, a population of 784 orangutans is expected to d
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Step 1:
Set Variables (We will use x & y)

x = years
y = total orangutan population

Step 2:
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784 - 25x = y
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Step 3:
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784 - 25x = 817 - 36x
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3 years ago
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Which equation is best represented by the graph above (x+1)(x-3)(x+2). please explain why
Nat2105 [25]
<h3>Answer:</h3>

y = (x +2)(x -1)(x -3) . . . . or . . . . y = x³ -2x² -5x +6

<h3>Step-by-step explanation:</h3>

The graph shows y=0 at x=-2, x=1, and x=3. These are called the "zeros" or "roots" of the function, because the value of the function is zero there.

When "a" is a zero of a polynomial function, (x -a) is a factor. This means the factors of the graphed function are (x -(-2)), (x -1) and (x -3). The function can be written as the product of these factors:

... y = (x +2)(x -1)(x -3) . . . . . the equation represented by the graph

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... y = x³ -2x² -5x +6 . . . . . the equation represented by the graph

7 0
3 years ago
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