The area of a rectangle is 245.25. If it has a width of 14 1/4, what is the length?

babunello [35]

Answer:

Step-by-step explanation:

In all of these problems, the key is to remember that you can undo a trig function by taking the inverse of that function. Watch and see.

a. $sin2\theta =-\frac{\sqrt{3} }{2}$

Take the inverse sin of both sides. When you do that, you are left with just 2theta on the left. That's why you do this.

$sin^{-1}(sin2\theta)=sin^{-1}(-\frac{\sqrt{3} }{2} )$

This simplifies to

$2\theta=sin^{-1}(-\frac{\sqrt{3} }{2} )$

We look to the unit circle to see which values of theta give us a sin of -square root of 3 over 2. Those are:

$2\theta =\frac{5\pi }{6}$ and

$2\theta=\frac{7\pi }{6}$

Divide both sides by 2 in both of those equations to get that values of theta are:

$\theta=\frac{5\pi }{12},\frac{7\pi }{12}$

b. $tan(7a)=1$

Take the inverse tangent of both sides:

$tan^{-1}(tan(7a))=tan^{-1}(1)$

Taking the inverse tangent of the tangent on the left leaves us with just 7a. This simplifies to

$7a=tan^{-1}(1)$

We look to the unit circle to find which values of <em>a</em> give us a tangent of 1. They are:

$7\alpha =\frac{5\pi }{4},7\alpha =\frac{\pi }{4}$

Dibide each of those equations by 7 to find that the values of alpha are:

$\alpha =\frac{5\pi}{28},\frac{\pi}{28}$

c. $cos(3\beta)=\frac{1}{2}$

Take the inverse cosine of each side. The inverse cosine and cosine undo each other, leaving us with just 3beta on the left, just like in the previous problems. That simplifies to:

$3\beta=cos^{-1}(\frac{1}{2})$

We look to the unit circle to find the values of beta that give us the cosine of 1/2 and those are:

$3\beta =\frac{\pi}{6},3\beta =\frac{5\pi}{6}$

Divide each of those by 3 to find the values of beta are:

$\beta =\frac{\pi }{18} ,\frac{5\pi}{18}$

d. $sec3\alpha =-2$

Let's rewrite this in terms of a trig ratio that we are a bit more familiar with:

$\frac{1}{cos(3\alpha) } =\frac{-2}{1}$

We are going to simplify this even further by flipping both fraction upside down to make it easier to solve:

$cos(3\alpha)=-\frac{1}{2}$

Now we will take the inverse cos of each side (same as above):

$3\alpha =cos^{-1}(-\frac{1}{2} )$

We look to the unit circle one last time to find the values of alpha that give us a cosine of -1/2:

$3\alpha =\frac{7\pi}{6},3\alpha =\frac{11\pi}{6}$

Dividing both of those equations by 3 gives us

$\alpha =\frac{7\pi}{18},\frac{11\pi}{18}$

And we're done!!!

8 0

3 years ago

Supposed the population of deer in a region was 3,500 in the year 2000.since then population has grown by 3.5% annually. What wi

sergejj [24]

Y = a (b^x)

1) x = 0, y = 3500

=> 3500 = a (b^0)

=> 3500 = a (1)

=> a = 3500

2) growth percent = 3.5% => growth rate = 1.035 = b

=> y = 3500 (1.035)^ x

3) year 2020 => x = 2020 - 2000 = 20

4) y = 3500 (1.035)^ 20 = 6964

Answer: 6964.

3 0

3 years ago

How do you answer number 4 & number 6 ?‍♀️ explain ! ?

SVEN [57.7K]

For 4 you just need to multiply the 7 and 33 together and add 32. Then put your awnser over 33. (if it is asking for the fraction)

3 0

3 years ago

Kathy’s customer base is 2/3 residential and 1/3 business if she has 350 residential customers how many total customers does she

Scorpion4ik [409]

If we made it into a ratio of residential customers to business customers, it would be a 2:1

350/2 = 175

350 + 175 = 525

525 total customers

4 0

3 years ago

The area of these shapes are?

kipiarov [429]

Answer:
Figure 1:
Area = 390ft^2

Figure 2:
Area = 325.17 ft^2

7 0

3 years ago