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iragen [17]
3 years ago
5

Find all solutions to the equation in the interval [0, 2TT). Cos x= sin 2x (1 point)

Mathematics
1 answer:
igomit [66]3 years ago
6 0

You can use the formula for the double angle of the sine to write

\sin(2x)=2\sin(x)\cos(x)

To turn the equation into

2\sin(x)\cos(x)=\cos(x)

Move everything to the left hand side to have

2\sin(x)\cos(x)-\cos(x)=0

Factor \cos(x) to have

\cos(x)(2\sin(x)-1)=0

A factor equals zero if and only if one of its factor equals zero. So, either

\cos(x)=0

or

2\sin(x)-1=0 \iff 2\sin(x)=1\iff \sin(x)=\dfrac{1}{2}

I assume that you have a table to lookup for these known values. If you have troubles solving for x, hit me up in the comments

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Consider the example of finding the probability of selecting a black card or a 6 from a deck of 52 cards.
Marina86 [1]

Answer:

The probability of selecting a black card or a 6 = 7/13

Step-by-step explanation:

In this question we have given two events. When two events can not occur at the same time,it is known as mutually exclusive event.

According to the question we need to find out the probability of black card or 6. So we can write it as:

P(black card or 6):

The probability of selecting a black card = 26/52

The probability of selecting a 6 = 4/52

And the probability of selecting both = 2/52.

So we will apply the formula of compound probability:

P(black card or 6)=P(black card)+P(6)-P(black card and 6)

Now substitute the values:

P(black card or 6)= 26/52+4/52-2/52

P(black card or 6)=26+4-2/52

P(black card or 6)=30-2/52

P(black card or 6)=28/52

P(black card or 6)=7/13.

Hence the probability of selecting a black card or a 6 = 7/13 ....

7 0
3 years ago
G(x)= 3/4x+6<br> What is the value of g(12)?
gizmo_the_mogwai [7]

Answer:

G(12) = 15

Step-by-step explanation:

When doing g(x) equations, all you do is substitute the value inside the parentheses to x in the equation.

So you get 3/4(12) + 6.

Then simplify to get g(12) = 15

4 0
3 years ago
Substitution for {2x-3y=11 and -x + 2y = -6
Svetradugi [14.3K]

Step-by-step explanation:

-x+2y=-6

x-2y=6

x=2y+6

substitute in 2x-3y=11 gives us 2(2y+6)-3y=11

4y+12-3y=11

y=-1

-x+2(-1)=-6

-x=-4

x=4

7 0
3 years ago
In which measurement situations would the most appropriate unit of measurement be feet?
nikklg [1K]
The answer would be the distances that are not too large and not too small

A.legnth and width of a ball room
this would work because the next measurement is 1  mils and ball rooms are not that big


B. width of an eyelash. that is rediculously small so this is wrong

C. distanc from chicaco to san fransisco
way too far, use miles

D. height of a door
corect, door is apout 8 feet aprox


answer is A and D
5 0
3 years ago
Find the volume of the cylinder. Use 3.14 for Pi. Round your answer to the nearest hundredth.the height is 13 and the radius is
NikAS [45]

Answer:

The volume of the cylinder is 2002 square units.

Step-by-step explanation:

It is given that,

Height of the cylinder, h = 13 units

Radius of the cylinder, r = 7 units

We need to find the volume of the cylinder. The formula of the volume of cylinder is given by :

V=\pi r^2 h\\\\V=\dfrac{22}{7}\times 7^2 \times 13\\\\V=2002\ \text{unit}^2

So, the volume of the cylinder is 2002 square units.

4 0
3 years ago
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