MATHEMATICS HIGH SCHOOL

Find all solutions to the equation.

sin x = sqrt(3)/2

Answers

Answer 1
Answer:

Answer:

x=(\pi)/(3) and x=(2\pi)/(3)

Step-by-step explanation:

We are given that sin x=(\sqrt3)/(2)

We have to find all solutions of the given equation

We know that sin (\pi)/(3) =sin60^(\circ)=(\sqrt3)/(2)

sin x is positive then  the value of sin x will lie in I quadrant and II quadrant.The value of sin x is negative in III and IV quadrant .

We are given that sin x is positive then the solution will lie in I and II quadrant only.Therefore, the solution of sin x will not lie in III and  IV quadrant .

sin x =sin (\pi)/(3) ...(I equation )and sin x =sin(\pi-(\pi)/(3))...(II equation)

In II quadrant \theta change into(\pi-\theta )

Cancel  sin on both side of equation I

Then, we get

x=(\pi)/(3)

sin x =sin ((3\pi-\pi)/(3))

sin x =sin (2\pi)/(3)...(II equation )

Cancel sin on both side of equation II

Then we get

x=(2\pi)/(3)

Hence, the solutions of equation are

x=(\pi)/(3) and x=(2\pi)/(3)
Answer 2
Answer:

The solutions of the equation are:

x = 60 degrees

x = 120 degrees

x = 420 degrees

x = 480 degrees, and so on.

We have,

The solutions to the equation sin(x) = √3/2 are any angles where the sine of the angle is equal to √3/2.

So,

sin 60 = √3/2

sin 120 = sin (π - 60) = sin 60 = √3/2

In trigonometry 180 is written as π.

Since (π - 60) is in the secondquadrant sin 60 is positive.

sin 420 = sin (360 + 60) = sin 60 = √3/2

In trigonometry 360 is written as 2π.

Since (2π + 60) is in the Firstquadrant sin 60 is positive.

Similarly,

sin 480 = sin (2π + 120) = sin 120 = sin (π - 60) = sin 60 = √3/2

Thus,

The solutions of the equation are:

x = 60 degrees

x = 120 degrees

x = 420 degrees

x = 480 degrees, and so on.

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What is 40+40×0+1=?
and can the answer be squared

Answers

order of opertations
PEMDAS
parenthasees
exponnents
multipication or division
additon or subtraction

first multiply since no exponents or partnehasees

40 times 0=0


now we have
40+0+1
now we add
40+0+1=41


any number can be squared

You have 160 boxes of cookies. In each case you can pack 8 boxes of cookies. How many cases would be filled from these boxes of cookies ?

Answers

160 boxes of cookies / 8 boxes per case = 20 cases that can be filled.
you divide 160 by 8 and you get 20. 20 cases will be filled

Barbara has $70.00 in her pocket and a $20 gift card. which purchase will she be able to make without having to use her credit card?

Answers

if Barbara has $ 70.00 in her pocket and a $ 20 gift card. then the maximumm amount she can pruchase is $ 70 + $ 20 = $ 90
so let x be purchase will she be able to make without having to use her credit card
x >= $ 90

Answer:

Step-by-step explanation:

six puzzles for $11.99 each and a board game for $15.89

If the nth term of a sequence is 7n-1 what is the 6th term?

Answers

To find the 6th term in the sequence whose nth term is represented by the formula 7n-1, substitute 6 in place of n into the formula. This gives 7*6 - 1, which equals 41.

The question is: If the nth term of a sequence is 7n-1, what is the 6th term?

In order to find this, we can substitute 6 into the formula for the nth term, in place of n.

Following the formula, we get 7n-1, replace n with 6, hence, the formula looks like 7*6 - 1.

Therefore, we get 42 - 1 = 41. Hence, the 6th term of the sequence is 41.

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The only thing you should do is to put 6 for n so you will have:
7(6) -1 = 42 - 1 = 41 :)))
I hope this is helpful
have a nice day

Simplify this expression (5)^ -5 (5)^ 7 please explain how you got the answer A.1/25
B.25
C.10
D. 5^ -35

Answers

Answer:

( {5}^( - 5) ) * ( {5}^(7) ) \n \n \frac{ {5}^(7) }{ {5}^(5) } = {5}^(7 - 5) = {5}^(2)

the answer is b. 25

If h(x)=x-7 and g(x)=x^ which expression is equivalent to (g•h)(5)?A) (5-7)^
B) (5)^-7
C) (5)^ (5-7)
D) (5-7)x^

Answers

Answer:

A (5-7)^

Step-by-step explanation:

We have the next two functions h(x)=x-7 and g(x)=x^. We need to find (g•h) that is equal to g(h(x)) then:

(g•h)=g(h(x))=(x-7)^

Finally in the poin x=5 we have:

(g•h)=g(h(x))=(x-7)^

(g•h)=g(h(5))=(5-7)^

Then the answer is A
Assuming that by ^, you mean ², here's how you do this:
(g•h)(5) means that you need to solve g(h(5)). So, you plug 5 in for x in h(x), then you plug the solution of that in for x in g(x) like so:
h(5)=5-7 \n g(h(5))= (5-7)^(2)

The answer is A. (5-7)²

Hope this helps!
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