State the domain of the function. (5 points) 2 1 1 3 -6

[Pre-Calc] Please Help! I don’t know where to start. How do I do this?

sertanlavr [38]

Answer:

See Below.

Step-by-step explanation:

Problem A)

We have:

$\displaystyle \csc^2\theta \tan^2\theta -1=\tan^2\theta$

When in doubt, convert all reciprocal trig functions and tangent into terms of sine and cosine.

So, let cscθ = 1/sinθ and tanθ = sinθ/cosθ. Hence:

$\displaystyle \left(\frac{1}{\sin^2\theta}\right)\left(\frac{\sin^2\theta}{\cos^2\theta}\right)-1=\tan^2\theta$

Cancel:

$\displaystyle \frac{1}{\cos^2\theta}-1=\tan^2\theta$

Let 1/cosθ = secθ:

$\sec^2\theta -1=\tan^2\theta$

From the Pythagorean Identity, we know that tan²θ + 1 = sec²θ. Hence, sec²θ - 1 = tan²θ:

$\tan^2\theta =\tan^2\theta$

Problem B)

We have:

$\sin^3x=\sin x-\sin x \cos^2 x$

Factor out a sine:

$\sin x(\sin^2 x)=\sin x-\sin x\cos^2 x$

From the Pythagorean Identity, sin²θ + cos²θ = 1. Hence, sin²θ = 1 - cos²θ:

$\sin x(1-\cos^2 x)=\sin x-\sin x\cos^2x$

Distribute:

$\sin x- \sin x \cos^2 x=\sin x-\sin x\cos^2 x$

Problem C)

We have:

$\displaystyle \frac{\cos 2x+1}{\sin 2x}=\cot x$

Recall that cos2θ = cos²θ - sin²θ and that sin2θ = 2sinθcosθ. Hence:

$\displaystyle \frac{\cos^2 x-\sin^2 x+1}{2\sin x\cos x}=\cot x$

From the Pythagorean Identity, sin²θ + cos²θ = 1 so cos²θ = 1 - sin²θ:

$\displaystyle \frac{2\cos^2 x}{2\sin x\cos x}=\cot x$

Cancel:

$\displaystyle \frac{\cos x}{\sin x}=\cot x$

By definition:

$\cot x = \cot x$

3 0

3 years ago

Help me pleeeaaaasssseeee!!!!!!!

Gnesinka [82]

Sorry cant help you, that's a tough nut to crack! good luck though!

3 0

3 years ago

Read 2 more answers

Urgente!!! Doy 20 puntos

andre [41]

Answer:

7
4
-7, 0, +9

Step-by-step explanation:

Hope this helps

4 0

2 years ago

4. Is rap music more popular among young Indians than among young Asians? A sample survey compared 634 randomly chosen Indians a

bulgar [2K]

Answer:

H0 is accepted

there is no difference between the proportions of Indian and Asian young people who listen to rap music every day.

Step-by-step explanation:

Given a sample survey compared 634 randomly chosen Indians aged 15 to 25 with 567 randomly selected Asians in the same age group.

$p_{1} = \frac{368}{634} =0.580$

It found that 368 of the Indians and 130 Asians listened to rap music every day.

$p_{2} = \frac{130}{567} =0.229$

Null hypothesis H0: there is no difference between the proportions of Indian and Asian young people who listen to rap every day.

$p_{1} = p_{2}$

Alternative hypothesis:- $p_{1} \neq p_{2}$

Level of significance α = 0.05

The test of statistic

$z = \frac{p_{1} - p_{2}}{\sqrt{pq(\frac{1}{n_{1} }+\frac{1}{n_{2} }) } } }$

where $p = \frac{n_{1}p_{1} + n_{1}p_{2}}{n_{1}+n_{2}} = \frac{634(0.580)+567(0.229)}{634+567}$

p = 0.414

and q = 1-p = 1- 0.414 =0.586

$Z = \frac{0.580-0.229}{\sqrt{0.414(0.586)(\frac{1}{634} +\frac{1}{567} } } }$

on calculation , we get

z = 0.300 ><1.96 at 95 % level of significance

H0 is accepted

there is no difference between the proportions of Indian and Asian young people who listen to rap every day.

3 0

3 years ago

Tasha invests $5000 annually at 6% and an additional $5000 annually at 8%. Thomas invests $10000 annually at 7%. Which statement

REY [17]

Answer:

Answer:

Option B is correct.

Step-by-step explanation:

We will compare the interest earned by both.

Tasha: p = $5000

r = 6% or 0.06

n = 1

So, Amount after a year will be = = $5300

And amount the next year with p = 5300: 5300*1.06= $5618

Additional $5000 at 8%

Here the amount will be = =5400

Next year amount with p = 5400 : 5400*1.08 = $ 5832

Amount in total Tasha will have in 2 years = 5618+5832 = 11450

Thomas:

p = 10000

r = 7% or 0.07

n = 1

After a year the amount will be = =$10700

Amount Next year with p = 10700 : 10700*1.07 = $11449

*****Just after 1 year we can see that Tasha's total amount is high than Thomas. This means at the same consistent rate, each year Tasha's amount will always be higher than Thomas.

So, option B is correct. Tasha’s investment will yield more over many years because the amount invested at 8% causes the overall total to increase faster.

6 0

3 years ago

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State the domain of the function. (5 points) 2 1 1 3 -6​

State the domain of the function. (5 points) 2 1 1 3 -6