use an identity to solve the equation on the interval [0,2pi) sin x cos x = -1/4 x=

Answers

Answer 1

Answer:

The solution of the given equation is    x = 105 °∈ ( 0 , 2pi)

Step-by-step explanation:

Step(i):-

Given equation is sin x cos x = -1/4

                           [tex]2(2sinxcosx) = -1[/tex]

we know that trigonometry formula

                             2 sin x  cos x = sin 2x

                            2 ( sin 2 x) = -1

                                sin2x = -1/2

Step(ii):-

                            sin2x =    [tex]\frac{-1}{2} = sin (\pi +\frac{\pi}{6}[/tex]

                 sin2x = sin 210                       2x = 7π/6                       2x = 210°                                x = 105 °The solution of the given equation is    x = 105 °∈ ( 0 , 2pi)

Related Questions

Point E is located at (-5,2). Point M is the reflection of point E across the y-axis. What is the distance between E and M?

Answers

Answer:

The distance is Ten

If f(x)= -4x + 3 and g(x) = 3x² + 2x - 4 find (f+g)(x)

Answers

Answer:

A

Step-by-step explanation:

We have the two functions:

[tex]f(x)=-4x+3\text{ and } g(x)=3x^2+2x-4[/tex]

And we want to find (f+g)(x).

Note that this is the same thing to f(x)+g(x). Therefore:

[tex]\begin{aligned} (f+g)(x)&=f(x)+g(x) \\ &=(-4x+3)+(3x^2+2x-4) \end{aligned}[/tex]

We simply substituted them for their equations.

Simplify. Combine like terms:

[tex]=(3x^2)+(-4x+2x)+(3-4)[/tex]

Add:

[tex]=3x^2-2x-1[/tex]

Hence, our answer is A.

Triangle ABC IS an isosceles triangle AB=BC m

Answers

Answer:

The measure of angle A is 73°

Step-by-step explanation:

Isosceles Triangles

An isosceles triangle is a triangle with exactly two congruent sides. The angles the congruent sides form with the third side are also equal.

The triangle ABC is isosceles and AB congruent with BC. The angle at B measures 34°.

The other two angles are congruent, i.e. their measures are the same. Since the internal angles of a triangle sum 180°:

[tex]2*m\angle A=180^\circ - 34^\circ =146^\circ[/tex]

Thus:

[tex]m\angle A=146^\circ /2=73^\circ[/tex]

The measure of angle A is 73°

Determine if this data is an example
of a function.
(-2,5); (0, 3); (-2, 8); (1, 14)
Relation
Function

Answers

Answer:

Step-by-step explanation:

it is not a function because -2 has two y values

Find the dimensions of the right circular cylinder of maximum volume that can be placed inside of a sphere of radius R.

Answers

This question is incomplete, the complete question is;

Find the dimensions of the right circular cylinder of maximum volume that can be placed inside of a sphere of radius R(10cm)

What is the maximum volume?

Answer:

a) Dimensions of the cylinder are; Radius = 8.1650 cm , Height = 11.547 cm

b) the maximum volume is 2418 cm³

Step-by-step explanation:

From the image

radius of the sphere is 10cm

radius of the cylinder is x and its height is 2y

so

The volume of cylinder  is V = πr²h = πx²(2y)

Get V as function of just one variable x² + y² = 100

x² = 100 - y²

Therefore V = π( 100-y² )(2y) = 200πy-2πy³

V will be a maximum when V' = 0

V' = 200π - 6πy² =0

y² = 200π / 6π = 100/3

y = √(100/3) = 5.7735

x² = 100 - y²

x² =100 - (100/3)

x = √(200/3)

x = 8.1650

So The maximum volume will occur when the radius is 8.1650 cm

and the height 2y is 2(5.7735) = 11.547 cm

The maximum volume is

πr²h = π(8.1650)² (11.547 )  

= 2418 cm³

Therefore the maximum volume is 2418 cm³

put 1.12 2.10 3.11.40 4.10.48 5.10.95 6.10.72 7.11.53 in a number line

Answers

Answer:Add them up

Step-by-step explanation:

answer if you have the ability to​

Answers

Answer:

A is the answer.

What is a3 of the sequence 13, 18, 23, 28, 33, 38...

Answers

Answer:

23

Step-by-step explanation:

cuz it starts with 13 as a1

Helps PLEASE?!
What is the equation of line A? and
What is the equation of line B?

Answers

Answer:

Line A: [tex]y=1.5x+1[/tex]

Line B: [tex]y=-1/3 x[/tex]

I hope this helps and good luck!

It takes a groundskeeper 35 minutes to prepare a Little League baseball field for a game. It takes his assistant 45 minutes to prepare the same field. How long will it take if they work together to prepare the field?

Answers

a) It takes a groundskeeper 45 minutes to prepare a softball field for a game. It takes his assistant 50 minutes to prepare the same field. How long will it take if they work together to prepare the field?

G does 1/45 job per minute

A does 1/50 job per minute

Together, they do 1/45 + 1/50 = 19/450 jobs/minute

--> 450/19 minutes to do the job

You can use a shortcut, product/sum

50*45/(50+45) = 2250/95

= 450/19

--------------------------------

b) It takes the owner/operator of a dog kennel 7 hours to clean all of the cages. It takes his assistant 4 hour(s) more than that to clean the same cages. How long will it take if they work together?

This is 7 and 11 hours.

7*11/(7+11) = 77/18 hours

= ~ 4.28 hours

The 7th-grade class took a survey on their favorite ice cream. 58 people said they prefer vanilla, while 28 people said they prefer chocolate. Write a ratio comparing chocolate to vanilla. (Write it in a :b form)

Answers

Answer:

[tex]a : b = 14 : 29[/tex]

Step-by-step explanation:

Given:

[tex]Vanilla = 58[/tex]

[tex]Chocolate = 28[/tex]

Required

Represent as ratio

Let chocolate be represented with a and vanilla be represented with b

So, we have:

[tex]a : b[/tex]

[tex]a : b = 28 : 58[/tex]

Divide ratio by 2

[tex]a : b = 14 : 29[/tex]

Hence, the required ratio is [tex]14:29[/tex]

What is the Greatest Common Factor of 16 and 18
06
8
O 4
02

Answers

Answer:

2

Step-by-step explanation:

2 is the hfc or gfc (depending on if you say highest or greatest) becausee it is the largest factor in both numbers

ions
How many solutions does this equation have?
1 solution
x + 3 + x + 3 = - (x + 4) + (3x - 2)
No solution
Infinite solutions
Explain your thinking

Answers

Answer:

I am not certain but I think it's no solution but how the number of X's their is and won't have it's value, it's by themselves

what is 71 3/7% equal to in simplest form?

Answers

23 2/3 simplest form

Answer:

23 2/3 i think sorry for the other my sponese  my sister came and typed the response

what is 2/5 of 1 7/8

Answers

Answer:

0.75

Step-by-step explanation:

I think

Answer:

0.75 or something like that

Step-by-step explanation:

Which equation correctly shows the relationship between the numbers 6,560 and 656?

Answers

Answer:

656×1000

Step-by-step explanation:

I don’t understand this at all pls help I will mark brainliest

Answers

Answer:

D

Step-by-step explanation:

-2/3 is -.666

-3/5 is -.60

1/2 is .5

and 5/8 is a little more than half since 4/8 is half. so -2/3, -3/5, 1/2, 5/8, or D


Name the relationship: complementary, linear pair, vertical, alternate interior, corresponding, or
alternate exterior.

Answers

Answer:

Linear pair

Step-by-step explanation:

Angle a and angle b are adjacent angles formed at the point of interception of two straight lines that intersects.

Thus, they are angles formed on a straight line. Angles on a straight line sum up to give 180°, since a straight line angle measures 180°.

Thus, angle a and angle b are regarded as linear pair angles. They are supplementary.

Suppose a team is to be formed consisting of a head chef, sous chef, and dishwasher, in that order. What is the probability of forming such a team with 6 people?

Answers

Answer:

0.0083

Step-by-step explanation:

From the given information;

The total number of individual in the team = 3

The number of ways the team, which comprises of head chef, sous chef, and dishwasher can be arranged = [tex]^{6}P_3[/tex]

= (6×5×4×3!)/3!

= 6×5×4

= 120 ways

The probability of forming such a team with 6 people = 1/120

= 0.0083

Hola me pueden explicar por favor el punto 1 es para hoy muchas gracias

Answers

Answer:

las soluciones estan abajo. En algunos incisos se debe suponer que el numero en cuestion es entero. De lo contrario no es posible hablar del siguiente o del anterior al numero.

Step-by-step explanation:

Sea x un numero, entonces

1)2x

2)5x

3)x-1 (aqui x es un numero entero)

4)[tex]\frac{x}{2}[/tex]

5)[tex]\frac{x}{10}[/tex]

6)x+1 (aqui x es un numero entero

7) x(x+1) (aqui x es un numero entero

8) x(x+1)(x+2) (aqui x es un numero entero

-11, -8,-5, -2...
What is the 100th term in this sequence?

Answers

Answer:

298.

Step-by-step explanation:  

formula- n in the next term is (n+3)

basically adding three

3x100=300

-2+300=298

PLZZ help me wit this I won’t the right answers no facts

Answers

Answer:

C. No, because not all of the pairs represent the same ratio

Step-by-step explanation:

6/2 = 3

12/5 = 2.4

14/6 = 2.3

18/8 = 2.25

Tell whether the lines through the given points are parallel, perpendicular, or neither.
Line 1: (10,5), (-8,9)
Line 2: (2, - 4), (11, -6)
The slope of line 1 is...
The slope of line 2 is...
These 2 lines are...

Answers

Answer:

The Slope of Line 1 is ->  [tex]-\frac{2}{9}[/tex]

The Slope of Line 2 is -> [tex]-\frac{9}{2}[/tex]

These two lines are - >  Perpendicular

Step-by-step explanation:

To find the slope of line one, you follow these steps:

First Coordinate 10 -> x1, 5 -> y1

Second Coordinate -8 -> x2, 9 -> y2

Then insert the assigned values into this equation:  [tex]\frac{y2-y1}{x2-x1}[/tex] -> [tex]\frac{9-5}{-8-10}[/tex] which equals [tex]\frac{4}{-18}[/tex] which simplifies to [tex]-\frac{2}{9}[/tex]

Then do the same process to find the slop of line 2:

First Coord: 2 -> x1, -4 -> y1

Second Coord: 11 -> x2, -6 -> y2

Then insert the values into this equation: [tex]\frac{y2-y1}{x2-x1}[/tex]  ->[tex]\frac{11-2}{-6-(-4)}[/tex] which equals [tex]\frac{9}{-2}[/tex].

We know the lines are perpendicular by:

a. Typing the equations of the lines into a graphing calculator and observing the graph

b. Looking at the slopes. By looking at the slopes, we see that the slope of line 1 is the reciprocal of line 2, and vice versa. Since reciprocal slopes indicate perpendicular lines, the lines 1 and 2 are perpendicular to each other.

Hope this helps!

Help please this is urgent☹️

Answers

All of the are correct

CAN SOMEONE PLZ HELP MEI BEG U ILL DO ANYTHING JUST HELP ME!!!!

Answers

Answer:

you can draw < > ≤ ≥ as duck mouths or something.

and the symbol ≠ can be inputed as a wire or dog leash, so if I had to draw this, draw a park where there is a lake on the right side then have a bench where an old man or a little child is feeding ducks with little bits of breab with its beaks opened then have like, a girl jogging with her dog and put ≠ as a leash for the dog and that's all I got. If you want more add street lights hanging above like triangles.

plz help me
is 7/3 less than 6 ​

Answers

Answer:

yes

Step-by-step explanation:

I figured this out by determining how many times 3 fits into 7.

7/3 is equal to 2 and 1/3

2 1/3 < 6

Hope this helps <3

please give brainliest

Imena earned $261 last week. If she worked 18 hours and earned the same amount each hour, how much was she paid per hour?

Answers

The answer to your question is $14.50 a hour

The amount paid to Imena per hour will be $14.5

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Imena earned $261 last week. She worked 18 hours and earned the same amount each hour.

Imena's earnings for an hour will be calculated as:-

Earning per hour = 261 / 18

Earning per hour = $14.5

Therefore, the amount paid to Imena per hour will be $14.5

To know more about an expression follow

https://brainly.com/question/24392720

#SPJ5

Which graph shows a proportional relationship between the number of hours of renting a canoe and the total amount spent to rent the canoe?

Answers

Answer:

Uh pick a graph that is straight line and passes through 0

Step-by-step explanation:

You don't have screenshot

Answer:

This would be simaler to the answer

Step-by-step explanation:

A graph is shown. The values on the x axis are 0, 2, 4, 6, 8, 10. The values on the y axis are 0, 18, 36, 54, 72, and 90. Points are shown on ordered pairs 0, 0 and 2, 18 and 4, 36 and 6, 54 and 8, 72. These points are connected by a line. The label on the x axis is Number of Hours. The title on the y axis is Total Amount in dollars.

fred can complete a work in 6 days and Paul can complete a work in 3 days. if fred and Paul work together, how many days can the work be completed?​

Answers

Answer:

I think its 3 or 2 days bc if paul can get two works done by the time fred can get one done then the days should be divided.

Step-by-step explanation:

What is the equation you would set up to solve the following problem? DO NOT SOLVE THE EQUATION.
You bought a magazine for $5 and four erasers. You spent a total of $25. How much did each eraser cost?

Answers

4x + 5 = 25

x being the cost of each eraser
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