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3 years ago

What values for q (0 ≤q≤2π) satisfy the equation? 22√sin q + 2 = 0

Mathematics

2 answers:

Vesna [10]3 years ago

6 0

Answer:
$\frac{3 \pi }{4}$ , $\frac{7 \pi }{4}$

Explanation:
2√2 sin(q) + 2 = 0
2√2 sin(q) = -2
sin(q) = $\frac{-2}{2 \sqrt{2} }$
sin(q) = $\frac{- \sqrt{2} }{2}$

Now, we know that:
sin (45) = $\frac{ \sqrt{2} }{2}$

From the ASTC rule, we know that the sine function is negative in the third and fourth quadrant.
This means that:
either q = 90 + 45 = 135° which is equivalent to $\frac{3 \pi }{4}$
or q = 270 + 45 = 315° which is equivalent to $\frac{7 \pi }{4}$

Hope this helps :)

frutty [35]3 years ago

4 0

Answer:

The value of q are $\frac{5\pi}{4},\frac{7\pi}{4}$

C is correct.

Step-by-step explanation:

Given: $2\sqrt{2}\sin q+2=0$

We need to solve for q.

$2\sqrt{2}\sin q+2=0$

Subtract 2 both side

$2\sqrt{2}\sin q=-2$

Divide both sides by $2\sqrt{2}$

$\sin q=\frac{-2}{2\sqrt{2}}$

$\sin q=\frac{-1}{\sqrt{2}}$

Here, sin q is negative. Sine is negative in III and IV quadrant [0,2π ]

$\sin q=-\sin \frac{\pi}{4}$

In III quadrant, $q=\pi+\frac{\pi}{4}=\frac{5\pi}{4}$

In IV quadrant, $q=2\pi-\frac{\pi}{4}=\frac{7\pi}{4}$

Thus, The value of q are $\frac{5\pi}{4},\frac{7\pi}{4}$

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A manufacturing plant earned $80 per man hour of labor when it opened. Each year, the plant earns an additional 5% per man hour.

Mekhanik [1.2K]

Answer:

The amount that plant earns per man hour after (t) years it open is $80 $(1.05)^{\textrm t}$ .

Step-by-step explanation:

Given as :

The earning of manufacturing plant when it opened = $ 80 per man hour

The rate of plant earning per man hour = 5 %

Let The earning of plant after t years = A( t )

So,

The earning of plant after t years = initial earning × $(1+ \dfrac{\textrm rate}{100})^{\textrm Time}$

Or, A(t) = $ 80 × $(1+ \dfrac{\textrm 5}{100})^{\textrm t}$

or, A(t) = $ 80 × $(1.05)^{\textrm t}$

Hence The amount that plant earns per man hour after (t) years it open is $80 $(1.05)^{\textrm t}$ . Answer

3 0

2 years ago

Read 2 more answers

I need someone who will answer all five questions correctly. Give out 100 bonus points for who will answer all 5 correctly

KATRIN_1 [288]

Answer:

The circumference of the yellow circle is $9\pi$ or $28.27cm^2$ approximately, the circumference of the blue circle is $6\pi$ or $18.85m^2$ approximately, the circumference of the green circle is $80\pi$ or $251.33mm^2$ approximately, the circumference of the red circle is $5\pi$ or $15.71cm^2$ approximately, and the circumference of the pink circle is $7\pi$ or $21.99cm^2$ approximately.

Step-by-step explanation:

To find the circumference of a circle, you need to multiply the diameter of the circle and multiply it by $\pi$ . In this case, the circumferences of the yellow circle are $9\pi$ or approximately $28.27cm^2$ , the circumference of the blue circle is $6\pi$ or approximately $18.85m^2$ , the circumference of the green circle is $80\pi$ or approximately $251.33mm^2$ , the circumference of the red circle is $5\pi$ or approximately $15.71cm^2$ , and the circumference of the pink circle is $7\pi$ or approximately $21.99cm^2$ .