Mathematics High School

HURRY What is the solution to the trigonometric inequality
2sin(x)+3> sin^2(x) over the interval 0<=x<=2pi radians?

Answers

Answer 1

Answer:

C on edge 2021

Step-by-step explanation:

Answer 2

The solution of x for the trigonometric inequality [tex]2sin(x)+3 > sin^2(x)[/tex] is x will lie between  0≤x< [tex]\frac{3\pi}{2}[/tex]  

What is trigonometric inequality?

An inequality of the standard form R(x) > 0 (or < 0) that consists of 1 or a few trigonometric functions of the variable arc x is a trigonometric inequality. Finding a solution to the inequality means determining the values of the variable arc x whose trigonometric functions make the inequality true.

According to the question

The trigonometric inequality :

[tex]2sin(x)+3 > sin^2(x)[/tex] and the interval 0<=x<=2pi radians

Let sin(x) = t  

Now, inequality is :

[tex]2t+3 > t^{2}[/tex]

0 > t² - 2t - 3

0>  t² - (3-1)t - 3

0>  t² - 3t + t - 3

0> t( t - 3) + 1(t - 3)

0> ( t - 3) (t+1)

t < -1 or t < 3

sin(x) < -1 or sin(x) < 3

as sin(x) can not be 3  because sin oscillates between 1 and -1. Sine will never result in 3 so we disregard this as a solution.

sin(x) < -1

sin(x) < sin ([tex]\frac{3\pi}{2}[/tex] )

x < [tex]\frac{3\pi}{2}[/tex]  

And the given interval for x

0<=x<=2pi radians

Therefore,  

x will lie between

0≤x< [tex]\frac{3\pi}{2}[/tex]  

Hence, The solution of x for the trigonometric inequality [tex]2sin(x)+3 > sin^2(x)[/tex] is x will lie between  0≤x< [tex]\frac{3\pi}{2}[/tex]  

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Related Questions

y=5x^2-8x-12


linear , exponential , or quadratic and why

Answers

Answer:

Quadratic

Step-by-step explanation:

This is a quadratic equation because it's in the form of y=ax^2+bx+c

If it were linear, the graph would be a straight line and wouldn't contain a second degree term

If it were exponential there would be a growth or decay factor

Your closet has 5 shirts for every 2 sweaters. Your closet has 45 shirts. How many sweaters are in your closet. .

Answers

Answer:

18

Step-by-step explanation:

Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)

Answer:

18

Step-by-step explanation:

You have to divide 45 by 5. You get 9. 9 times 2 is 18. So that's your answer.

The length and width of a rectangular park are determined by the polynomials (3x + 2) and (62-5). Which expression
represents the area of the park?

Answers

Answer:

If the perimeter of the triangle is 9x + 12 inches, which expression represents the length, in inches, of the third side of the triangle? 6x^2 - x - 12 The length and width of a rectangular park are determined by the polynomials (3x + 4) and (2x - 3).

Step-by-step explanation:

PLEASE HELP!!!!!
The question is in the image below!!!!

Answers

Step-by-step explanation:

We must realise that the image of the quadratic curve shown is not showing the full curve. Instead it extends further out.

For all quadratic curves, the domain is all x-values.

We see here that this quadratic curve has an absolute minimum at y = -4 and the curve stretches towards positive infinity.

Hence the range is y >= 4.

The correct answers are the 1st and 5th options.

Find the slope from the graph

Answers

rise/run 1/4 so it can be

Answer:1/4

Step-by-step explanation:

How do I find a,b and c

Answers

the picture isn’t loading

Please help me with this

Answers

ok so basically you need to cut the shape in half so it makes two squares. all you gotta do from there is times L x W of both squared and add both together if that makes sense. if you don't understand, comment below and i'lol try to help you more.

If 9 is subtracted from two thirds of a number, the result is 7. Find the number
the number is 3
the number is 10,67
the number is 24

Answers

Answer: 24

Step-by-step explanation:

x/2*3-9=7. So you want to know what x is. So lets start reverse thinking. 7+9=16, 16=x/2*3. That means 16 is 2/3 of x. 16/2=8, 8*3=24! The answer is 24.

An item on sale costs 85% of the original price. The original price was $57. What is the answer?

Answers

Answer:

85%oforiginal price=selling cost

selling cost=85/100×$57=$48.45

A circle diameter is 11 cm a square has a side length of 7 cm

Answers

Answer:

By the Pythagorean theorem, the diagonal length (d) of the square is

 d² = 7² + 7²

 d = √98 ≈ 9.8995

Since the diameter of the circle (11 cm) is greater than the diagonal length of the square (9.9 cm), you know the square will fit into the circle without touching.

Step-by-step explanation:

Answer:

what is the question ?

Step-by-step explanation:

Which table shows a proportion relationship between the time spent reading and number of pages read?

Answers

None of them is right.

What is proportionality?

The concept of proportionality in mathematics denotes the linear relationship between two numbers or variables. The size of one item increases by twofold, whereas the size of the other quantity decreases by one-tenth of the earlier amount.

Given a table that has work and time spent on that theoretical work has to be proportional to the time such as the Spend time ∝ number of pages read but none of the options match the criteria. Therefore no option is correct for this problem.

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A car is traveling at a steady speed. It travels 2 1/2 miles in 3 1/3 minutes. How far will it travel in 41 minutes? In 1 hour

Answers

Answer:

120 miles

Step-by-step explanation:

You multiply 41 times 4 equal 120 miles.

Answer:

30 3/4 miles, 45 miles

Step-by-step explanation:

First we find the unit rate, in miles per minute:

 2 1/2 miles            5/2 mi          1/2 mi         1 mi

--------------------- = --------------- = ------------- = -------------- = 3/4 mile/min

 3 1/3 minutes       10/3 min        2/3 min       4/3 min    

In 41 minutes the car will travel (3/4 mi/min)(41 min) = 123/4 mi = 30 3/4 mi

In 1 hour, or 60 minutes, the car will travel (3/4)(60) mi = 45 mi

help me please i don’t get this

Answers

Answer:

angle 8= 120 degrees

angle 7= 60 degress

Step-by-step explanation:

So since it's a line, they will equal 180. So since angle 7 is half of 8 we need to a pair of numbers that add to 180. So you can find out that 120/2 is 60. Then 60+120=180

I need to do these factor trees for 60 and 96

Answers

60
2 and 30
30
2 and 15
15
3 and 5
96
8 and 12
circle for 8 is 2 and the square is 4
circle for 12 is 2 and the last circle is also 2

Select the correct answer. How can you write the expression 2 - (p + 6) in words? O A two minus the sum of p and six OB. two added to the difference of p and six OC. the difference of two and p times six OD. the sum of two and padded to six​

Answers

Answer:

the correct one is the first option

Step-by-step explanation:

hope I'm helpful to you, please mark me as a brainlist

what is the slope of the line in the graph?

Answers

the rise is 1 and the run is 2 so 1/2 since slope is rise over run.

HELP ASAP PLSS!!!
1. Sophia is trying to save money for the new Iphone 12. She is currently has $50 in her savings account and plans on adding $25 a month to that same account. She needs exactly $1600 to buy the new phone.
50x+25=1600
50+25x=1600
1600+25x=50
25+1600x=50

Answers

Answer:

50 + 25x = 1600

Step-by-step explanation:

Find the balance in the account after the given period.
$3000 principal earning 4% compounded annually, 7 years
The balance after 7 years will be $
(Round to the nearest cent as needed.)

Answers

Answer:

3,947.80

Step-by-step explanation:

Harry has $110 in his savings account. He decides to save $15 every month to buy a bike. An equation for this relation is C = 110 + 15m, where C represents the amount of money, in dollars, in his account and M represents the number of months. How many months does it take Harry to have $185 in his account?

Answers

Answer:

5 MONTHSSSSSS only 5

Step-by-step explanation:

K here we go

y=110+15x

185=110+15x

75=15x

x=5

Louise is 56 3 /4 inches tall. Theresa is 1 1 /2 inches shorter than Louise and Jane is 1 1/ 5 inches shorter than Theresa. How tall is Jane?

Answers

Answer: [tex]54\dfrac1{20}\text{ inches}[/tex]

Step-by-step explanation:

Given:  Height of Louise  = [tex]56\dfrac34 \text{ inches }=\dfrac{4\times56+3}{4}=\dfrac{227}{4}\text{ inches}[/tex]

Then , height of Theresa = Height of Louise  [tex]-1\dfrac{1}{2}\text{ inches}[/tex]

[tex]=\dfrac{227}{4}-\dfrac{3}{2}\text{ inches}\\\\=\dfrac{227-6}{4}=\dfrac{221}{4}\text{ inches}[/tex]

Height of jane = height of Theresa - [tex]1\dfrac15[/tex] inches

[tex]=\dfrac{221}{4}-1\dfrac15\text{ inches}\\\\=\dfrac{221}{4}-\dfrac{6}{5}\text{ inches}\\\\=\dfrac{5\times221-6\times4}{20}\text{ inches}\\\\=\dfrac{1105-24}{20}=\dfrac{1081}{20}\text{ inches}\\\\= 54\dfrac1{20}\text{ inches}[/tex]

Hence,  Jane is  [tex]54\dfrac1{20}\text{ inches}[/tex] tall.

what is the value of ???????

Answers

Answer:

70

Step-by-step explanation:

60 + 65 + x = 180

x + 125 = 180

x = 55

55 + 50 + y = 180

y + 105 = 180

y = 75

75 + 35 + ? = 180

? + 110 = 180

? = 70

The $200 digital camera Anne purchased was on sale for 15% off. What amount did Anne get off the price?

Answers

7.50 dollers off the camera

BONUS: What is the standard form of the linear model for Matuba?
Matuba: 312.4 308.6

Answers

Answer:

Step-by-step explanation:  The standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form. When an equation is given in this form, it's pretty easy to find both intercepts (x and y).

I will try to give brainliest for the CORRECT answer​

Answers

Answer:

BC is 40.8

B° is 59.03°

C° is 30.96°

Step-by-step explanation:

classic pythagoras (a² + b² = c²)

35² + 21² = 1666

sqrt1666 = 40.8

you do tan(x) here because you want to find B° and only know the opposite and adjacent sides.

35/21 = 1.66...

tan-¹(1.66..) = 59.03°

you do tan(x) here because you want to find C° and only know the opposite and adjacent sides.

21/35 = 0.6

tan-¹(0.6) = 30.96°

2) -9(18+ 2x)
show work

Answers

Answer:

-162+(-18x)

Step-by-step explanation:

distribute

-9×18=-162

-9×2x=-18x

Answer:

-162-18x

Step-by-step explanation:

-9(18+2x)

distribute the -9 into the (18+2x)

and ur left with -162-18x

-0.72x + 0.42x = 8.4
solve for x

Answers

You first have have to add -0.72 and 0.42 because they both have like terms. Then you will get -0.3x. Then you will divide both sides by -0.3 because you have to get x alone. When you do that you’ll get -28. That’s your answer -28.

What is the answer for
4/5 of 3/4=

Answers

Answer:

3/5

Step-by-step explanation:

4/5 of 3/4 =4/5*3/4 = 3/5

Segment AB falls on line 6x + 3y = 12. Segment CD falls on line 4x + 2y = 8. What is true about segments AB and CD?
A They are parallel because they have the same slope of −2.
B They are parallel because they have the same slope of one half.
C They are lines that lie exactly on top of one another because they have the same slope and the same y-intercept.
D They are lines that lie exactly on top of one another because they have the same slope and a different y-intercept.

Answers

Answer:

C. They are lines that lie exactly on top of one another because they have the same slope and the same y-intercept.

Step-by-step explanation:

Given lines

6x + 3y = 12 ⇒ 2x + y = 4 ⇒ y = -2x + 44x + 2y = 8 ⇒ 2x + y = 4 ⇒ y = -2x + 4

The lines are same as both have same slope and y-intercept.

Correct statement is following:

C. They are lines that lie exactly on top of one another because they have the same slope and the same y-intercept.

Answer:

C. They are lines that lie exactly on top of one another because they have the same slope and the same y-intercep

Step-by-step explanation:

in slope intercept form, what is the equation of the line having a slope of 2 and passing through the point (6,24)?​

Answers

Answer: y = 2x + 12

Explanation: The slope-intercept form is y = mx + b, where m is slope and b is the y-intercept. Substituting 2 for m, 6 for x, and 24 for y, we have 24 = 2(6) + b. Simplifying, we get that b = 12, so the equation is y = 2x + 12.

Answer:

y = 2x + 12

Step-by-step explanation:

Is (12, 14) a solution to the system of equations? 5x-y=74
3x+y=50 ​

Answers

Answer:

For the first equation

5x-y=74

5(12)-14= 46 which is not =74

Then the second is the equation

Or you calculate it also

3x+y=50

3(12)+14=50

Sutable equation this is

First equation would be a no but second would be a yes
Overall tho since it’s asking u if it’s an answer to the both the answer would be NO it’s not
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