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jonny [76]
3 years ago
8

Find the equation of the problem

Mathematics
1 answer:
pogonyaev3 years ago
5 0
6\sin^2\theta-\sin\theta=1\ \ \ -1\\\\6\sin^2\theta-\sin\theta-1=0\\\\6\sin\theta-3\sin\theta+2\sin\theta-1=0\\\\3\sin\theta(2\sin\theta-1)+1(2\sin\theta-1)=0\\\\(2\sin\theta-1)(3\sin\theta+1)=0\iff2\sin\theta-1=0\ \vee\ 3\sin\theta+1=0\\\\2\sin\theta=1\ \ |:2\ \ \vee\ \ 3\sin\theta=-1\ \ |:3\\\\\sin\theta=\dfrac{1}{2}\ \vee\ \sin\theta=-\dfrac{1}{3}\\\\
\theta=30^o\ \vee\ \theta=150^o\ \vee\ \theta=360^o-\sin^{-1}\left(\dfrac{1}{3}\right)\ \vee\ \theta=180^o+\sin^{-1}\left(\dfrac{1}{3}\right)

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You order the hardcover book shown from a website that offers free shipping on orders of $25 or more. Write and solve an inequal
jenyasd209 [6]

Answer:

If P= price of the hardcover book, then

We have to spend $25-P, if P<$25; or $0 if P>= $25

Step-by-step explanation:

Lets call P the price of the hardcover book, in $. We can suppose that P is less than 25, otherwise we shoudnt spend on anything else to get the free shipping. If X is the amount that we have to spend to reach 25, then we get that P+X = 25. If P is known, we can obtain X by substracting P in both sides, therefore

X = 25-P

We conclude that if the price of the book P is less than 25, then we have to spend $25-P. Otherwise we have to spend 0.

6 0
3 years ago
31-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece and the third piece
pychu [463]

"31-inch piece of steel is cut into three pieces"

Call the pieces a,b,c

a + b + c = 31

"second piece is twice as long as the first piece"

b = 2a

"third piece is one inch more than seven times the length of the first piece"

c = 1 + 7a

Ok, we have our equations, let's substitute the second and third into the first.

a + 2a + 1 + 7a = 31

10a + 1 = 31

10a = 30

a = 30/10 = 3

b = 2a = 6

c = 1 + 7a = 22

Check: 3 + 6 + 22 = 31, good

Answer: 3 inches, 6 inches, 22 inches


4 0
3 years ago
In 1/8 days, a construction crew built 1/4 miles of a road. What is the unit rate in miles per day.
tigry1 [53]

The unit rate of road construction is 2 miles per day.

Step-by-step explanation:

Given,

In \frac{1}{8} days \frac{1}{4} miles road is constructed.

To find

The rate of road constructed per day

Method

We will apply unitary method to solve it.

Now,

In \frac{1}{8} days \frac{1}{4} miles road is constructed.

In 1 day the road will be constructed = \frac{1}{4} ÷ \frac{1}{8} miles

= 2 miles

4 0
3 years ago
A teacher randomly chooses a two-person leadership team from a group of four qualified students. Three of the
Slav-nsk [51]

Answer:

what is P(A), the probability that the first student is a boy? 3/5


what is P(B), the probability that the second student is a girl? 3/4


what is P(A and B), the probability that the first student is a boy and the second student is a girl? 1/2


No, évents A and B are not independent events

Step-by-step explanation:

3 0
2 years ago
A team won 9 of its first 12 games. At that rate, how many games will the team win if it plays 64 games in all?
Feliz [49]
9 out of 12 = 9/12 which can be simplified to 3/4.  So the team wins 3/4 of its games.  3/4 of 64 = 64 divided by 4 = 16.  16 x 3 = 48. 
3 0
3 years ago
Read 2 more answers
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