Please help me with this

Answer:

[tex]\theta = \frac{\pi}{3} , \pi, \frac{5\pi}{ 3}[/tex]

Step-by-step explanation:

we want to solve the following trigonometric equation:

[tex] \displaystyle - 2 { \sin}^{2} (\theta )+ \cos( \theta) + 1 = 0, \: \theta \in [0,2\pi)[/tex]

The first step of solving trigonometric equation is to rewrite the equation in terms of one trigonometric function . With Pythagorean theorem, we know that sin²x=1-cos²x . It will be helpful to rewrite the equation in terms of one trig functions. Therefore, substitute 1-cos²[tex]\theta[/tex] in the place of sin²[tex]\theta[/tex]:

[tex] \displaystyle - 2 (1 - \cos ^{2} ) + \cos( \theta) + 1 = 0, \: \theta \in [0,2\pi)[/tex]

simplify:

[tex] \displaystyle\implies - 2 (1 - \cos ^{2} (\theta) + \cos( \theta) + 1 = 0, \: \theta \in [0,2\pi)\\\implies- 2 + \cos ^{2} (\theta)+ \cos( \theta) + 1 = 0, \: \theta \in [0,2\pi)\\\implies\cos ^{2} (\theta)+ \cos( \theta) -1 = 0 [/tex]

Consider cos² [tex]\theta\implies[/tex] x. Thus,

[tex]2 {x}^{2} + x - 1 = 0[/tex]

solving the quadratic equation yields:

[tex]{x}^{} = \frac{1}{2} \\ x = - 1[/tex]

back-substitute:

[tex] \begin{cases} \cos( \theta) = \dfrac{1}{2} \\ \cos( \theta) = - 1 \end{cases} \theta \in[0,2\pi)[/tex]

take inverse trig in both sides

[tex] \implies \begin{cases} \theta = \dfrac{\pi}{3} + 2n\pi\\\theta= \frac{5\pi}{3} + 2n\pi \\ \theta = \pi + 2n\pi\end{cases} \theta \in[0,2\pi) \\\\\implies\theta= \frac{\pi}{3}+\dfrac{2n\pi}{3},\theta\in [0,2\pi)\\\text{when n=0}\\ \implies \theta = \frac{\pi}{3} \\ \text{when n=1}\\ \theta= \pi\\ \text{when n=2}\\\theta=\frac{5\pi}{ 3} [/tex]

In conclusion,

[tex]\displaystyle\theta = \frac{\pi}{3} , \pi, \frac{5\pi}{ 3}[/tex]

Answer:

A, 3/7.

Step-by-step explanation:

There are 7 shapes overall shown. Since there are 3 triangles, we need to do 3/7.

Answer: 3/7

Step-by-step explanation:

Number of triangles / total number of shapes

Answer:

Mean 27

Median 9

Mode 12, 2, 64, 0, 48, 4, 6, 80

Step-by-step explanation:

Answer:

1320

Step-by-step explanation:

12 x 11 x 10 = 1,320

Answer:

A to C is [tex]37.51\ ft[/tex]

Step-by-step explanation:

We are given an angle and the base length. Recall:

[tex]tan(x) = \frac{opposite}{adjacent}[/tex]

Add the values:

[tex]tan(15) = \frac{x}{140}[/tex]

Solve for x:

[tex]tan(15) = \frac{x}{140}\\tan(15) * 140 = x\\37.51 = x[/tex]

Answer:

Scale factor = 4

If you multiply by 4 the two sides of ABCD, you will get the corresponding sides of A’B’C’D’

Answer:

Step-by-step explanation:

1 and 4 are adjacent supplementary angles. This will mean that 180-68=112

<4=112 degrees

<3 is the same as 1 which is 68 since they are vertical angles.

<2 is also 112

Answer:

2=112

3= 68

4= 112

Step-by-step explanation:

Each line adds to 180

So subtract 68  and it will give you the opposite side(2)  112

the angle across from it has tha same value so 2 and 4 are the same mesure

Answer:

1.D

2.B

3.F

4.E

5.A

6.C

Answer:

88

Step-by-step explanation:

PE M/D A/S

55/ (9-4) *8

9-4=5

55/5*8

11*8

88

Answer:

n = 6

Rule: Times 3

Step-by-step explanation:

Answer:

Richard

Step-by-step explanation:

28 days=4 weeks

40 paintings in 4 weeks

45 paintings in 5 weeks

Richard weekly rate: 40/4=10 paintings per week

Nestor weekly rate: 45/5=9 paintings per week

If richard's rate is 10 while nestor's is 9, richard has a faster rate

Answer:8/25

Step-by-step explanation: 4/25 ×2/1

Answer: hii

Exact form:

8/25

Decimal Form:

0.32

_____________________

Step-by-step explanation:

Simplify the expression.

Hopefully this helps you

- Matthew

Answer:

31.5 in²

Step-by-step explanation:

The area of a triangle is calculated with the following formula:

1/2*b*h (b: base, h: height)

The height of this triangle is given as 9 and base is 7

1/2*7*9 = 31.5 in²

Answer:

31.5 in²

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

because the formula of finding the area of a triangle is base times height divided by 2 so thatshow you get the answer, multiply 10by15 and then divide by 2

Answer:

The answer would be 75 ft ^2

Step-by-step explanation:

Step 1. Do 15x10 (which equals 150)
Step 2. Divide by 2 to get the answer of 75
Step 3. Label to get 75 ft ^2

Answer:

h=6

Step-by-step explanation:

To find the volume of a right angle prism-

Find area of cross-section, in this case an isoscles triangle so we know that both of the parallel lines are 3ft

To find the area of the cross-section, do:

3 x 3 = 9

9 ÷ 2 = 4.5 (Area of cross-section)

Since we don't know the length of h, we need do:

27^3 ÷ 4.5 = 6

Therefore 6 is h

Hope I explained it okay:)

Answer:

√99, 9.8 repeating, π2

Step-by-step explanation:

hope this helped!

Answer:

  4%

Step-by-step explanation:

The interest earned on the investment is the difference between the end-of-year value and the initial value:

  $83.20 -80 = $3.20 . . . . simple interest per year

__

The interest rate is the ratio of this to the initial investment:

  $3.20/$80.00 = 0.04 = 4% . . . . . simple interest rate per year

Answer:

Step-by-step explanation:

Answer:

is that 32 / 3 or 3^2/3 ...?

Step-by-step explanation:

if 32/3 and 51/7

then answer will be 1120/17

Answer:

The Answer is C.

Step-by-step explanation:

f(x) = cos x , g(x) = cos(x - π/4)

Equation: f(x) = a * cos (x - h) + k

Since the equation only has h = π/4, it means that it shift right.

Answer:

-2 square root 5

Step-by-step explanation:

Answer:

526.4

Step-by-step explanation:

560 - 6%

= 526.4 you will pay for the shirt

Answer:

8x=55+73

8x=128

X=128/8

X=16

Step-by-step explanation:

check:

-73+8(16)=55

-73+128=55

55=55

I hope you understand

Answer:

See below ~

Step-by-step explanation:

Solving for x in ΔLMN

Angles in ΔLMN

Solving for y in ΔSTU

Angles in ΔSTU

⇒ Their angles are equal (in ΔLMN and ΔSTU)

⇒ ΔLMN and ΔSTU are similar

The theorem state that the products of the lengths of the line segments on each chord are equal. The value of x from the figure is 15.75

The theorem state that the products of the lengths of the line segments on each chord are equal.

According to the given diagram;

9 * 21 = 12 * x

189 = 12x

Divide both sides by 12

12x/12 .= 189/12

x = 189/12

x = 15.75

Hence the value of x from the figure is 15.75

Learn more on Intersecting chord theorem here:https://brainly.com/question/23732231

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Answer:

3468 students

Step-by-step explanation:

289 x 12 = 3468