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2 years ago

Solve the question below

Mathematics

2 answers:

Svet_ta [14]2 years ago

5 0

Answer:

Step-by-step explanation:

Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just don’t want to waste my time in case you don’t want me to :)

zheka24 [161]2 years ago

3 0

I’m pretty sure it’s HK too

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Please solve 5 f <br> (Trigonometric Equations)<br> #salute u if u solved it

Zanzabum

Answer:

$\beta=45\degree\:\:or\:\:\beta=135\degree$

Step-by-step explanation:

We want to solve $\tan \beta \sec \beta=\sqrt{2}$ , where $0\le \beta \le360\degree$ .

We rewrite in terms of sine and cosine.

$\frac{\sin \beta}{\cos \beta} \cdot \frac{1}{\cos \beta} =\sqrt{2}$

$\frac{\sin \beta}{\cos^2\beta}=\sqrt{2}$

Use the Pythagorean identity: $\cos^2\beta=1-\sin^2\beta$ .

$\frac{\sin \beta}{1-\sin^2\beta}=\sqrt{2}$

$\implies \sin \beta=\sqrt{2}(1-\sin^2\beta)$

$\implies \sin \beta=\sqrt{2}-\sqrt{2}\sin^2\beta$

$\implies \sqrt{2}\sin^2\beta+\sin \beta- \sqrt{2}=0$

This is a quadratic equation in $\sin \beta$ .

By the quadratic formula, we have:

$\sin \beta=\frac{-1\pm \sqrt{1^2-4(\sqrt{2})(-\sqrt{2} ) } }{2\cdot \sqrt{2} }$

$\sin \beta=\frac{-1\pm \sqrt{1^2+4(2) } }{2\cdot \sqrt{2} }$

$\sin \beta=\frac{-1\pm \sqrt{9} }{2\cdot \sqrt{2} }$

$\sin \beta=\frac{-1\pm3}{2\cdot \sqrt{2} }$

$\sin \beta=\frac{2}{2\cdot \sqrt{2} }$ or $\sin \beta=\frac{-4}{2\cdot \sqrt{2} }$

$\sin \beta=\frac{1}{\sqrt{2} }$ or $\sin \beta=-\frac{2}{\sqrt{2} }$

$\sin \beta=\frac{\sqrt{2}}{2}$ or $\sin \beta=-\sqrt{2}$

When $\sin \beta=\frac{\sqrt{2}}{2}$ , $\beta=\sin ^{-1}(\frac{\sqrt{2} }{2} )$

$\implies \beta=45\degree\:\:or\:\:\beta=135\degree$ on the interval $0\le \beta \le360\degree$ .

When $\sin \beta=-\sqrt{2}$ , $\beta$ is not defined because $-1\le \sin \beta \le1$

4 0

3 years ago

can someone help me with this I have to do like 18 other questions so if you can help me with those I would appreciate it!

GenaCL600 [577]

Answer:

see below

Step-by-step explanation:

1.)

(0, 4)

(1, 7)

$\frac{7-4}{1-0} = 3$

y = 3x + b

(4) = 3(0) + b

b = 4

y = 3x + 4

Rate of change: 3 initial value: 4

2.)

(0, -5)

(1, -3)

$\frac{-3-(-5)}{1-0} = 2$

y = 2x + b

(-5) = 2(0) + b

b = -5

Rate of change: 2 initial value: -5

4 0

2 years ago

Im just gonna waste my points. first to comment gets the points I guess.

Aliun [14]

Answer:

Hey

Step-by-step explanation:

8 0

3 years ago

On a map of a town, a school is located at (–6, 2) and a movie theater is located at (–6, –15). What is the distance from the sc

sweet-ann [11.9K]

I think it’s 17 units

3 0

3 years ago

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Using the graph as your guide, complete the following statement.

iogann1982 [59]

Answer:

Step-by-step explanation:

The discriminant tells you where the graph of the parabola goes through the x-axis, if at all. If the discriminant is negative there are no real zeros and the parabola does not cross or touch the x-axis; if the discriminant is positive the parabola will go through the x axis in 2 places; if the discriminant is 0 the parabola will touch the x-axis in 1 place. Our discriminant is 0 since the parabola only touches the x-axis but does not go through.

8 0

2 years ago

Read 2 more answers