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3 years ago

2. Solve the following equations for 0° Sx < 180°.

Mathematics

1 answer:

diamong [38]3 years ago

5 0

Answer:

See below in bold.

Step-by-step explanation:

(1) cosec ( x + 10) = 3

Now cosec x = 1/sin x so

1 / sin (x + 10) = 3

3 sin (x + 10) = 1

sin (x + 10) = 1/3

x + 10 = 19.47 , 160.53 degrees

x = 9.47, 150.53 degrees.

(ii) cot (x - 30) =0.45

cot (x - 30)= 1 /tan (x- 30) so we have

tan (x - 30) = 1 / 0.45 = 2.2222

x - 30 = 65.77 degrees

x = 95.77 degrees.

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cricket20 [7]

Recall that

$\tan(\alpha-\beta)=\dfrac{\tan\alpha-\tan\beta}{1+\tan\alpha\tan\beta}$

$\cos^2\theta+\sin^2\theta=1$

From the second identity, we find

$\cos x=\pm\sqrt{1-\sin^2x}$

$\sin y=\pm\sqrt{1-\cos^2y}$

We're told that $0$ and $0$ , which means we should take the positive roots above. Then

$\cos x=\sqrt{1-\left(\dfrac8{17}\right)^2}=\dfrac{15}{17}$

$\sin y=\sqrt{1-\left(\dfrac35\right)^2}=\dfrac45$

Then we compute the tangents:

$\tan x=\dfrac{\sin x}{\cos x}=\dfrac{\frac8{17}}{\frac{15}{17}}=\dfrac8{15}$

$\tan y=\dfrac{\sin y}{\cos y}=\dfrac{\frac45}{\frac35}=\dfrac43$

so we end up with

$\tan(x-y)=\dfrac{\frac8{15}-\frac43}{1+\frac8{15}\cdot\frac43}=-\dfrac{36}{77}$

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4 years ago

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Oliga [24]

Answer:

as a fraction = 75/92

as a percentage = 81.52%

Step-by-step explanation:

total no of students = 92

probability that a student has hazel or brown eyes = Pr(hazel or brown)

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