Mathematics High School

Solve the equation for the interval [0, 2pi). 2sin^2x = sin x
A) 0, pi, pi/6, 5pi/6
B) pi/6, 5pi/6
C) pi/3, 2pi/3
D) pi/2, 3pi/2, pi/3, 2pi/3​

Answers

Answer 1

Answer:

A

Step-by-step explanation:

We want to solve the equation:

[tex]2\sin^2(x)=\sin(x)[/tex]

For the interval [0, 2π).

First, we can move all the terms to one side. Start off by subtracting sin(x) from both sides:

[tex]2\sin^2(x)-\sin(x)=0[/tex]

We can factor:

[tex]\sin(x)\left(2\sin(x)-1\right)=0[/tex]

By the Zero Product Property:

[tex]\sin(x)=0\text{ or } 2\sin(x)-1=0[/tex]

Solve for each case:

[tex]\displaystyle \sin(x)=0\text{ or } \sin(x)=\frac{1}{2}[/tex]

Use the unit circle to solve:

[tex]\displaystyle x=\left\{0, \frac{\pi}{6},\frac{5\pi}{6}, \pi\right\}[/tex]

Hence, our answer is A.

*Please note that we should not simply divide both sides by sin(x) to acquire 2sin(x) = 1. The problem with the operation is that we are dividing by sin(x), yet we do not know what the value of x is. Thus, one or more values of x may result in sin(x) = 0, and we cannot divide by 0. Hence, we are required to subtract and then factor, unless the question specifically states that sin(x) ≠ 0.

Related Questions

if a wind turbine costs 1.3 million per megawatts how much would it cost to build a 2.6 megawatts wind turbine​

Answers

Answer:

It would cost 3.38 million for 2.6 megawatts.

Step-by-step explanation:

1.3 X 2.6 = 3.38

3.38 million for 2.6 megawatts.

A quantity with an initial value of 220 grows continuously at a rate of 9.5% per hour. What is the value of the quantity after 255 minutes, to the nearest hundredth?

Answers

Answer:

i need help

Step-by-step explanation:

There are 15 plates in a kitchen cabinet. The diameter of each plate is either 7 inches or 12 inches. The diameter of all 15 plates combined is 140 inches. Which system of equations can be can be used to find the number of 7-inch plates, x, and the number of 12-inch plates, y, that are in the cabinet? A. x + y = 140 12x + 7y = 15 B. 7x + 12y = 140 7x + 12y = 15 C. x + y = 15 7x + 12y= 140 D. x + y = 15 12x + 7y= 140

whats the answers​

Answers

Answer:

37 There are 15 plates in a kitchen cabinet. The diameter of each plate is either 7 inches or

Step-by-step explanation:

12 inches. The diameter of all 15 plates combined is 140 inches.

Which system of equations can be used to find the number of 7-inch plates, x, and the

number of 12-inch plates, y, that are in the cabinet?

A

x + y = 140

12x + 7y = 15

B

7x +12y = 140

7x + 12y = 15

cx + y = 15

7x + 12y = 140

D

x + y = 15

12x + 7y = 140

What must be true when solving a quadratic equation when using factoring?
The equation must be equal to

Answers

Answer:

Step-by-step explanation:

The function must be factorable.

For example, x^2 + x - 6= 0  factors to (x + 3)(x - 2) = 0 so the roots are -3 and 2.

x^2 + x - 7 = 0  will not factor so you need another method to solve this.

Which is the correct solution to the cubic equation,
3/ 3x-2=1

-3
-1
1
3

Answers

Answer:

x = 1

Step-by-step explanation:

[tex]\sqrt[3]{3x - 2} = 1[/tex]        Cube both sides of the equation

3x - 2 = 1

3x = 3

x = 1

Check:  [tex]\sqrt[3]{3(1) - 2} = \sqrt[3]{3 - 2} = \sqrt[3]{1} = 1[/tex]   Since x = 1 makes the original equation true, then x = 1 is the solution.

The correct solution for the given equation is x = 1.

What is an equation?

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given is a cubic equation, [tex]\sqrt[3]{3x-2}[/tex] = 1

Solving for x,

[tex]\sqrt[3]{3x-2}[/tex] = 1

Cubing both the sides,

([tex]\sqrt[3]{3x-2}[/tex])³ = 1

3x - 2 = 1

3x = 3

x = 1

Hence, the correct solution for the given equation is x = 1.

Learn more about equations, click;

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Can a real person help me out all the hackers just want me to delete the app

Answers

Answer:

Question 7: x = 36

Question 4: x = 14

Question 9: D

Step-by-step explanation:

A small business earns a profit of $6500 in January and $17,500 in May. What is the rate of change in profit for this time period?

The rate of change in profit for this time period is per month.

Answers

Answer:
Rate of change of profit for this period = $2750 / month

Explanation

Can someone help me, please? Also, can someone explain it?

Answers

Answer:60m^2

Step-by-step explanation:you have to find the height of the triangle first which is easy bc it’s been split in half so the are now two right triangles. use the pythagorean theorem to determine the height, the height is 12, the formula for the area of a triangle is 1/2bxa and half of the base is already given to you, 5 so 5 x 12 equals 60

A quadratic in factored form is given as (x + 5) (2x - 3) = 0, what are the solutions of this given equation?
X = and x =

Answers

Answer:

x = -5, x = 1.5

Step-by-step explanation:

If the two expressions multiplied together is 0, that means that one of the expressions would have to equal 0. This gives us two possible answers. Our two equations are now:

x + 5 = 0

2x - 3 = 0

We will first solve the first one!

To isolate x, we subtract 5 from both sides to get:

x = -5

Onto the second one!

We begin to isolate x by adding 3 to both sides.

2x = 3

Now we divide both sides by 2.

x = 3/2 or 1.5

Answer:

Step-by-step explanation:

Simplify
(20n−36)−54​(35n−20)​

Answers

Answer:

-1870n + 1044

Step-by-step explanation:

what is 500 times 10​

Answers

Answer:

500*10=5,000

hope this helps

Answer:

5,000

Step-by-step explanation:

please correct me if im wrong

find the function. f(-7) if f(x) = 8x+15
f(-7) =
-4?
7
0 ​

Answers

Answer:

-41.

Step-by-step explanation:

Replace the x by -7:

f(-7) = 8(-7) + 15

= -56 + 15

= -41.

Graph the following exponential function given the table of
values.

Answers

Answer:

D

Step-by-step explanation:

Here, we want to select the graph of the given exponential function values

Let us take a look at the y-intercept

At the y-intercept, the value of x is 0

The y-intercept for this particular equation is 1

This mean that the y-intercept value is 1

hence, the graph will touch the y-axis at the point y = 1

looking at the graphs , only the graph D provides this, and that should be our answer

The quotient of 4,768 divided by 4.22 is greater than which of the following ? A. 1,000 B. 1,400 C .1,600 D. 2,000

Answers

Answer:

a.

Step-by-step explanation:

someone pls just comment something again​

Answers

Answer:

?

Step-by-step explanation:

Answer:

こんにちは、お元気ですか？

あなたの質問があれば、私もうまくやっています。日本での生活はとても楽しいです！日本に来てください。

Step-by-step explanation:

Solve for x and show your work! For each equation choose if there are:
• zero solutions for x • exactly one solution for x • or an infinite number of solutions for x.
3x + 5 = 7 + 3x

Answers

3x+5 = 7 +  3x

3x+5= 3x + 7

3x + 5 = 3x + 7

3x + 5 - 5 = 3x + 7 - 5

3x = 3x + 2

3x - 3x = 3x + 2 - 3x

Answer : 0 = 2

Hope this helps!

someone please tell me how to work out this type of problem i completely forgot

Answers

Answer:

Plug the x-values into the equation to get the y values. This will give you coordinates that you can graph a line with.

Step-by-step explanation:

For x = -5:  y = -3 - 2 * (-5) = 7, so the coordinates are (-5, 7)

For x = -2:  y = -3 - 2 * (-2) = 1, so the coordinates are (-2, 1)

(Etc.)

Then, plot these coordinates and draw a line through them to complete the graph.  

The area of a circle is 0.5024 square centimeters. What is the circle's radius?

Answers

r≈0.4cm
A Area
Hope this helps

This oblique cylinder has a volume of 90\pi\text{ m}^390π m
3
90, pi, start text, space, m, end text, cubed and a base area of 12\pi\text{ m}^212π m
2
12, pi, start text, space, m, end text, squared.
whats the height?

Answers

Answer:

7.5

Step-by-step explanation:

The height of the cylinder is equal to 7.5 meters.

Given that,
An oblique cylinder has a volume of 90π m ^3 and a base area of 12π m^2.

What is a cylinder?

A cylinder is defined as it is geometric shape when a rectangle sheet fold into a circular shape the figure arises looks same as the tube structure.

What is volume?

Volume, is defined as the ratio of the mass of object to its density.


The volume of the oblique cylinder = height * base area

90π = 12π  * height
height = 7.5 m                                

Hence, the height of the cylinder is equal to 7.5 meters.

Learn more about Cylinder here:

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The question seems to be incomplete or improperly written,
So Correct Question could be given as,


This oblique cylinder has a volume of 90π m ^3 and a base area of 12π m^2.

what is the height of the cylinder?

ANSWER ASAP ILL GIVE BRAINLIEST

Answers

Answer: C

Step-by-step explanation: There are 9 cards. 3 are vowels. 3/9 reduces to 1/3

HELP PLEASE!! No websites allowed please, complete 1,2,3, and 4.

NO WEBSITES! OR YOU ARE REPORTED thank you

Answers

Answer:

1: 31.5. 2: 5. 3: 4.6 4: 45

Can anyone help me with these questions? I am sorry if they aren’t a lot of points.

Answers

Answer:

Question 1: A

Question 2: B

Question 3: C

Step-by-step explanation:

Please give me brainliest if this helps! :)

Find m∠E

*geometry problem*

Answers

8x+4=9x-5
when you solve that out you get x =9
then you plug in x everywhere in the chart

3(9)=27
9(9)-5=76
180-76-27= 77°

angle E =77°

please mark brainiest if you can

If a triangle has a side length of 5 inches and another side length of 7 inches, which of the
following choices for the third side length will make a triangle?
a. 1 inch
b. 2 inches
c. 6 inches
d. 13 inches

Answers

Answer:

d. 13 inches

Step-by-step explanation:

When we need to solve the side length and length of triangles, we need to remember one thing.

Coming to a right triangle, there are two short sides and one long side, and the two short sides need to add up to something less than the one long side.

Therefore, since we know our two short sides, add them :

7in. + 5in.

= 12in.

Looking at the answers, we can point out that d. is greater than 12 inches, therefore making it the correct answer.

Someone plz help me giving brainliest

Answers

It would be a=16/25 or 0.64


If the line segment at right is subdivided
into equal parts, what is the length of
the marked portion of the line?
75

Answers

Answer:

50

Step-by-step explanation:

75 dived into 3 parts can also be written as 75/3. 75/3 is 25 making each part worth 25. 2 segments are included in the marked portion so its 50 or (25 + 25)

A skateboarding ramp is 13 inches high and rises at an angle of 12 degrees. How long is the base of the ramp?

Answers

144 + 13 !!!!!!!!!!!!!!!
144 + 13 is ur andwerrrrrrrrrrr

36/c=45/10 please help me

Answers

Answer:

c = 8

Step-by-step explanation:

36/c = 45/10

36 * 10 = 45 * c

360 = 45c

c = 360/45

c = 8

11. Cory owns x shoes. Nico has y shoes. The
number of shoes Cory owns is 1 less than 2 times
the number Nico owns. Together they have a total of
11 pairs of shoes. How many shoes does Cory and
Nico have each?

Answers

Answer:

5 and 6

Step-by-step explanation:

Answer: Cory owns 7 shoes, Nico owns 4.

Question :
25+25 -25 = ____​

Answers

Answer:

25+25-25=25+0=25 is your answer

Answer:

25 +25-25=25

Have a nice day!

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