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2 years ago

16. Solve for the angle x. cos(¹/2x) = ¹/2

Mathematics

1 answer:

Basile [38]2 years ago

6 0

Answer:

We know that ,

$\rightarrow \tt \cos( \frac{\pi}{3} ) = \frac{1}{2}$

So ,

$\: \rightarrow \tt \cos( \frac{1}{2}x ) = \cos( \frac{\pi}{3} ) \\ \\ \rightarrow \tt \frac{1}{2}.x = \frac{\pi}{3} \\ \\ \rightarrow \tt x = \frac{2\pi}{3}$

we can add 2 pi to it since there will be no change in the value

Also,

$\: \rightarrow \tt \cos( \frac{14\pi}{6} ) = \frac{1}{2} \\ \\ \\ \rightarrow \tt \frac{1}{2} x = \frac{14\pi}{6} \\ \\ \rightarrow \tt x = \frac{7\pi}{3}$

Answer : Option B

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Help! Picture attached

schepotkina [342]

Answer:

minimum maximum parabolas are equal then because of the circumference

Step-by-step explanation:

5 0

2 years ago

Can somebody explain how these would be done? The selected answer is incorrect, and I was told "Nice try...express the product b

trapecia [35]

Answer:

Solution ( Second Attachment ) : - 2.017 + 0.656i

Solution ( First Attachment ) : 16.140 - 5.244i

Step-by-step explanation:

Second Attachment : The quotient of the two expressions would be the following,

$6\left[\cos \left(\frac{2\pi }{5}\right)+i\sin \left(\frac{2\pi \:}{5}\right)\right]$ ÷ $2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi \:}{2}\right)\right]$

So if we want to determine this expression in standard complex form, we can first convert it into trigonometric form, then apply trivial identities. Either that, or we can straight away apply the following identities and substitute,

( 1 ) cos(x) = sin(π / 2 - x)

( 2 ) sin(x) = cos(π / 2 - x)

If cos(x) = sin(π / 2 - x), then cos(2π / 5) = sin(π / 2 - 2π / 5) = sin(π / 10). Respectively sin(2π / 5) = cos(π / 2 - 2π / 5) = cos(π / 10). Let's simplify sin(π / 10) and cos(π / 10) with two more identities,

( 1 ) $\cos \left(\frac{x}{2}\right)=\sqrt{\frac{1+\cos \left(x\right)}{2}}$

( 2 ) $\sin \left(\frac{x}{2}\right)=\sqrt{\frac{1-\cos \left(x\right)}{2}}$

These two identities makes sin(π / 10) = $\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}$ , and cos(π / 10) = $\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}$ .

Therefore cos(2π / 5) = $\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}$ , and sin(2π / 5) = $\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}$ . Substitute,

$6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right]$ ÷ $2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi \:}{2}\right)\right]$

Remember that cos(- π / 2) = 0, and sin(- π / 2) = - 1. Substituting those values,

$6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right]$ ÷ $2\sqrt{2}\left[0-i\right]$

And now simplify this expression to receive our answer,

$6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right]$ ÷ $2\sqrt{2}\left[0-i\right]$ = $-\frac{3\sqrt{5+\sqrt{5}}}{4}+\frac{3\sqrt{3-\sqrt{5}}}{4}i$ ,

$-\frac{3\sqrt{5+\sqrt{5}}}{4}$ = $-2.01749\dots$ and $\:\frac{3\sqrt{3-\sqrt{5}}}{4}$ = $0.65552\dots$

= $-2.01749+0.65552i$

As you can see our solution is option c. - 2.01749 was rounded to - 2.017, and 0.65552 was rounded to 0.656.

________________________________________

First Attachment : We know from the previous problem that cos(2π / 5) = $\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}$ , sin(2π / 5) = $\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}$ , cos(- π / 2) = 0, and sin(- π / 2) = - 1. Substituting we receive a simplified expression,

$6\sqrt{5+\sqrt{5}}-6i\sqrt{3-\sqrt{5}}$

We know that $6\sqrt{5+\sqrt{5}} = 16.13996\dots$ and $-\:6\sqrt{3-\sqrt{5}} = -5.24419\dots$ . Therefore,

Solution : $16.13996 - 5.24419i$

Which rounds to about option b.

7 0

3 years ago

Suppose that each semester at a particular community college Manuel has to pay $1478 in tuition and $121 in fees.

Kamila [148]

Answer:

Step-by-step explanation:

Let x be time, in semesters, remaining before Manuel graduates. We find that Manuel's expenses are:

$1478/semester in tuition, and

$121/semester in fees

1. x semesters remaining: fees

Remaining cost for fees, y, is the product of the fee times the number of semesters, x:

y =($121/semester)*x

y = ($121)*x

2. x semesters remaining: tuition

Remaining cost, y, is the product of the tuition (times the number of semesters, x.

y = ($1478/semester)*x + ($121/semester)*x

y = ($1599)*x

3. x semesters remaining: tuition and fees

Remaining cost, y, is the sum of the products of the tuition (times the number of semesters, and the fees (tix.

y = ($1478/semester)*x + ($121/semester)*x

y = ($1599)*x

5 0

1 year ago

Two lawn care companies are competing for a landscaping contract. Company A charges a $300 consulting fee plus $7 per square foo

kkurt [141]

The square feet of landscaping will the two companies carry out that enables them to charge the same amount is 30

What is the total of the landscaping contract for each company?

The total cost of the landscaping contract for each of the two companies is the sum of the fixed consulting fee plus the multiple of variable charge per square foot multiplied by the number of square feet of landscaping

Company A:

Total cost=300+7S

S=square foot

Company B:

Total cost=120+13S

At the point where the square foot are the same they charge the same amount

300+7S=120+13S

300-120=13S-7S

180=6S

S=180/6

S=30 square foot

Find out more about total cost on: brainly.com/question/15686427

#SPJ1

4 0

1 year ago

Solve the equation and state the value of x w - 2 = -8- 5w

Wewaii [24]

Answer:

x=-1

Step-by-step explanation:

w-2=-8-5w

-2=-8-6w

+8 +8

6=-6w

divide 6 in both side

x=-1

hope this help.

4 0

3 years ago