Hi I need help how to solve this equation with explanation thank you

Hello there!

Previously, we learnt that to solve the equation, we have to isolate the sin, cos, tan, etc first.

First Question

The first question has sin both sides. Notice that if we move sin(theta) to left. We get:-

[tex] \displaystyle \large{2 {sin}^{2} \theta - sin \theta = 0}[/tex]

We can common factor out the expression.

[tex] \displaystyle \large{sin \theta(2sin \theta - 1) = 0}[/tex]

It is a trigonometric equation in quadraric pattern.

We consider both equations:-

First Equation

[tex] \displaystyle \large{sin \theta = 0}[/tex]

Remind that sin = y. When sin theta = 0. It means that it lies on the positive x-axis.

We know that 0 satisfies the equation, because sin(0) is 0.

Same goes for π as well, but 2π does not count because the interval is from 0 ≤ theta < 2π.

Hence:-

[tex] \displaystyle \large { \theta = 0,\pi}[/tex]

Second Equation

[tex] \displaystyle \large{2sin \theta - 1 = 0}[/tex]

First, as we learnt. We isolate sin.

[tex] \displaystyle \large{sin \theta = \frac{1}{2} }[/tex]

We know that, sin is positive in Quadrant 1 and 2.

As we learnt from previous question, we use π - (ref. angle) to find Q2 angle.

We know that sin(π/6) is 1/2. Hence π/6 is our reference angle. Since π/6 is in Q1, we only have to find Q2.

Find Quadrant 2

[tex] \displaystyle \large{\pi - \frac{\pi}{6} = \frac{6\pi}{6} - \frac{\pi}{6} } \\ \displaystyle \large{ \frac{5\pi}{6} }[/tex]

Hence:-

[tex] \displaystyle \large{ \theta = \frac{\pi}{6} , \frac{5\pi}{6} }[/tex]

Since both first and second equations are apart of same equation. Therefore, mix both theta from first and second.

Therefore, the solutions to the first question:-

[tex] \displaystyle \large \boxed{ \theta = 0,\pi, \frac{\pi}{6} , \frac{5\pi}{6} }[/tex]

Second Question

This one is a reciprocal of tan, also known as cot.

[tex] \displaystyle \large{cot3 \theta = 1}[/tex]

For this, I will turn cot to 1/tan.

[tex] \displaystyle \large{ \frac{1}{tan3 \theta} = 1}[/tex]

Multiply whole equation by tan3 theta, to get rid of the denominator.

[tex] \displaystyle \large{ \frac{1}{tan3 \theta} \times tan3 \theta = 1 \times tan3 \theta } \\ \displaystyle \large{ 1= tan3 \theta }[/tex]

We also learnt about how to deal with number beside theta.

We increase the interval, by multiplying with the number.

Since our interval is:-

[tex] \displaystyle \large{0 \leqslant \theta < 2\pi}[/tex]

Multiply the whole interval by 3.

[tex] \displaystyle \large{0 \times 3 \leqslant \theta \times 3 < 2\pi \times 3} \\ \displaystyle \large{0 \leqslant 3 \theta < 6\pi }[/tex]

We also know that tan is positive in Quadrant 1 and Quadrant 3.

and tan(π/4) is 1. Therefore, π/4 is our reference angle and our first theta value.

When we want to find Quadrant 3, we use π + (ref. angle).

Find Q3

[tex] \displaystyle \large{\pi + \frac{\pi}{4} } = \frac{5\pi}{4} [/tex]

Hence, our theta values are π/4 and 5π/4. But that is for [0,2π) interval. We want to find theta values over [0,6π) interval.

As we learnt previously, that we use theta + 2πk to find values that are in interval greater than 2π.

As for tangent, we use:-

[tex] \displaystyle \large{ \theta + \pi k = \theta}[/tex]

Because tan is basically a slope or line proportional graph. So it gives the same value every π period.

Now imagine a unit circle, and make sure to have some basic geometry knowledge. Know that when values addition by 180° or π would give a straight angle.

We aren't using k = 1 for this because we've already found Q3 angle.

Since we know Q1 and Q3 angle in [0,2π).

We can also use theta + 2πk if you want.

First Value or π/4

[tex] \displaystyle \large{ \frac{\pi}{4} + 2\pi = \frac{9\pi}{4} } \\ \displaystyle \large{ \frac{\pi}{4} + 4\pi = \frac{17\pi}{4} }[/tex]

Second Value or 5π/4

[tex] \displaystyle \large{ \frac{5\pi}{4} + 2\pi = \frac{13\pi}{4} } \\ \displaystyle \large{ \frac{5\pi}{4} + 4\pi = \frac{21\pi}{4} }[/tex]

Yes, I use theta + 2πk for finding other values.

Therefore:-

[tex] \displaystyle \large{3 \theta = \frac{\pi}{4} , \frac{5\pi}{4} , \frac{9\pi}{4}, \frac{17\pi}{4} , \frac{13\pi}{4} , \frac{21\pi}{4} }[/tex]

Then we divide every values by 3.

[tex] \displaystyle \large \boxed{\theta = \frac{\pi}{12} , \frac{5\pi}{12} , \frac{9\pi}{12}, \frac{17\pi}{12} , \frac{13\pi}{12} , \frac{21\pi}{12} }[/tex]

Let me know if you have any questions!

Answer:

I will choose (a) I did a problem like this last week

Answer:

y=105

Step-by-step explanation:

82+75+x=180

157+x=180

x=23

82+23=y

105=y

can you zoom in on my pic more or no does it say 1/z

Answer:

Option A. Reciprocal

Answered by GAUTHMATH

Answer:

40141

Step-by-step explanation:

Answer:

8 cm^2

Step-by-step explanation:

If the triangle is isosceles the sides are the same

Let the sides be x

We know that we can use the Pythagorean theorem

a^2+b^2 = c^2 where a and b are the sides and c is the hypotenuse

x^2+x^2 = (4 sqrt(2))^2

2x^2 =16(2)

2x^2 = 32

Divide by 2

2x^2/ 32/2

x^2 = 16

Taking the square root of each side

sqrt(x^2) = sqrt(16)

x = 4

The area of the triangle is

A =1/2 bh

A = 1/2 (4) (4)

A = 1/2(16)

A = 8

Answer:

8

Step-by-step explanation:

a^2 + b^2 = c^2

c = [tex]4\sqrt{2}[/tex]

[tex]c^{2} = 32[/tex]

a^2 + b^2 = 32

a=b (isosceles triangle)

a=b=4

base = 4

height = 4

area = 1/2 bh = 1/2(4)(4) = 8

Answer:

The solution is:

(1) 0.0104

(2) 0.0008

Step-by-step explanation:

Given:

Mean,

[tex]\mu = 43.7[/tex]

Standard deviation,

[tex]\sigma = 1.6[/tex]

(1)

⇒ [tex]P(X<40) = P(\frac{x-\mu}{\sigma}<\frac{40-43.7}{1.6} )[/tex]

                      [tex]=P(z< - 2.3125)[/tex]

                      [tex]=P(z<-2.31)[/tex]

                      [tex]=0.0104[/tex]

(2)

As we know,

n = 15

⇒ [tex]P(\bar X > 45)= P(\frac{\bar x - \mu}{\frac{\sigma}{\sqrt{n} } } >\frac{45-43.7}{\frac{1.6}{\sqrt{15} } } )[/tex]

                      [tex]=P(z> 3.15)[/tex]

                      [tex]=1-P(z<3.15)[/tex]

                      [tex]=1-0.9992[/tex]

                      [tex]=0.0008[/tex]

Answer:

Step-by-step explanation:multiple 5 times 108 and that gives you your answer..

Answer:

y = 6/5x-1

Step-by-step explanation:

We have two points so we can find the slope

(-5,-7) and (5,5)

The slope is

m = ( y2-y1)/(x2-x1)

   = ( 5- -7)/( 5 - -5)

   = (5+7)/(5+5)

    = 12/10

   = 6/5

The slope intercept form of a line is

y = mx+b

y = 6/5x+b

Using the point (5,5)

5 = 6/5(5)+b

5=6+b

b=-1

y = 6/5x-1

Answer:

(a) Monomial

(b) Cubic

Step-by-step explanation:

Given

[tex]-9m^2n^3[/tex]

Required

Classify

By number of terms

The above polynomial is single term.

Single term polynomials are referred to as monomial

By degrees

To determine the degree, we consider the variable farthest from the constant.

In this case, n is farther from 9 than m.

And the power or degree of n is 3.

Polynomials with degree 3 are referred to as cubic polynomial

Step-by-step explanation:

a) Weight of the water:

Volume of bottle:

b) Weight of brine:

Density of brine:

9514 1404 393

Answer:

  13064 feet

Step-by-step explanation:

We can rewrite the formula so that x is in feet. Equating the new formula to 8.743 PSI, we have ...

  8.743 = 14.7e^(-0.21x/5280)

Dividing by 14.7 and taking natural logs, we have ...

  ln(8.743/14.7) = -0.21x/5280

Multiplying by the inverse of the coefficient of x gives ...

  x = 5280·ln(8.743/14.7)/-0.21 ≈ 13064.0806

The peak of the mountain is about 13,064 feet high.

Answer:

625 (answer A)

Step-by-step explanation:

Sorry for no explanation I can't explain stuff I just do it.

Answer:

By the Empirical Rule, approximately 68% of the bulbs have lifetimes that lie within 1 standard deviation to either side of the mean.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

What percentage of the bulbs have lifetimes that lie within 1 standard deviation to either side of the mean?

By the Empirical Rule, approximately 68% of the bulbs have lifetimes that lie within 1 standard deviation to either side of the mean.

Answer:

The x-intercept is -8, the y-intercept is 4, and the slope is 1/2.

Step-by-step explanation:

The x-intercept is -8, the y-intercept is 4, and the slope is 1/2.

Answer: See below

Concept:

There are different forms of linear equations:

Solve:

Given: y - 3 = 1/2 (x + 2)

Here, we can see the linear equation is in the form of point-slope form.

x₁ = -2

y₁ = 3

m = 1/2

Point included in the graph = (-2, 3)

Slope of the graph = 1/2

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Your wrong, it's 65%.

Step-by-step explanation:

The reason why: You can calculate the percentage by dividing the number of accepted students by the total of business students, 65/100 which equals 65%.

yw :)

The probability that a student was accepted is 5.0% since option  b be the correct answer.

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1,

We have to find out the probability of the selection of a student applied for the business program.

We know that, Probability= Total number of events occurred÷ Total number of possible outcomes/events

So, Probability that a student applying to the business program got selected= No of accepted students for business program÷Total number of students applied for business program=65÷100=0.65For converting a number into percentage we multiply the number by 100 that is 0.65*100=65%So, probability that a student applying for business program gets selected is 65%.

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Answer:

The cube root parent function:

Horizontally stretched by a factor of 4:

Translated 5 units right:

Translated 3 units up:

Answer:

The answer is "18".

Step-by-step explanation:

In the given graph by concluding we observe that  on the x-axis, one step is 2 units, and when we half each of the steps it will= 1 unit

[tex]\therefore\\\\CD = distance\ from\ -(8+1)\ to\ (8+1)\ = \text{distance between} -9 \ to\ 9\ = 18[/tex]

Answer:

3/56

Step-by-step explanation:

Probability is the ratio of the number of possible outcome to the number of total outcome.

Given that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles.

The total number of marbles in the box

= 1 + 3 + 2 + 2

= 8 marbles

The probability that the first marble is white and the second marble is blue

= 3/8 * 1/7

= 3/56

9514 1404 393

Answer:

  (9√3 -3π/2) ft^3 ≈ 10.88 ft^3

Step-by-step explanation:

The area of the hexagon is given by the formula ...

  A = (3/2)√3·s^2 . . . . for side length s

The area of the hexagonal face of this solid is ...

  A = (3/2)√3·(2 ft)^2 = 6√3 ft^2

__

The area of the circular hole in the hexagonal face is ...

  A = πr^2

The radius is half the diameter, so is r = (2 ft)/2 = 1 ft.

  A = π(1 ft)^2 = π ft^2

Then the area of the "solid" part of the face of the figure is ...

  A = (6√3 -π) ft^2

__

The volume is ...

  V = Bh . . . . . where B is the area of the base of the prism, and h is its height

  V = ((6√3 -π) ft^2)(3/2 ft) = (9√3 -3π/2) ft^3 ≈ 10.88 ft^3

Answer:

4 scoops of ice cream

Step-by-step explanation:

Plug in the total cost, number of scoops of nuts, and number of liquid toppings into the formula. Then, solve for s:

C = 0.50s + 0.35n + 0.25t

3.55 = 0.50s + 0.35(3) + 0.25(2)

3.55 = 0.50s + 1.05 + 0.5

3.55 = 0.50s + 1.55

2 = 0.50s

4 = s

So, the sundae had 4 scoops of ice cream.

Answer:

15

Step-by-step explanation:

1-0 =1

3-1 =2

6-3=3

10-6=4

We are adding 1 more each time

10+5 = 15

Answer:

A definition and a theorem can be used as a reason in a two-column proof. A two column proof is assembled into statement and reason columns, where each statement should have verified reason.

Step-by-step explanation:

Answer:

Definitions and algebraic properties

Step-by-step explanation:

Step-by-step explanation:

here is your answer it may help you

There are 700 don't like to admit in both faculties.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given that;

In a survey, survey of 1200 students who have passed SEE 150 like to admit in science Faculty 600 in humanity first and 240 like to admit either of faculties and the rest were found not to be admitted in both faculties​

Hence, not to be admit in any faculty =   N

Science +  Humanity -  Either   + None  = 200

=> 150 + 600 - 240 + N = 1200

=> 750 - 240 + N = 1200

=> N = 700

Hence, 700 don't like to admit in both faculties.

Learn more about the addition visit:

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Step-by-step explanation:

1 since a tank holds 121/2 gallons of gas 121/2 multiplied by two it gives 25 -30 it gives 5 450 divided by two it gives 225-25 i guess.

There are 365 ways of forming an executive Committee of four in a social club consisting of 15 members

If a particular man must be in the committee, we can choose the remaining 3 members from the remaining 14 members. The number of ways to choose 3 members from 14 is given by the combination:

14Cr3 = [tex]\frac{14!}{3! 11!}[/tex] = [tex]\frac{14x13x12}{3x2x1}[/tex] = 364

Therefore, there are 364 ways of forming an executive committee of four in a social club consisting of 15 members, if a particular man must be in the committee.

Learn more about combination here:

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Answer:

It's the last one.

Step-by-step explanation:

For example, if you have 0, the absolute valeu of 0 is 0. A postive number like 2, has an absolute value of 2. 0 is not greater than 0 and 2 is not greater than 2. Hope this helps!

Answer: Kayla is incorrect. The absolute value of 0 or a positive number is equal to the number.