Mathematics High School

)Suppose is a real number with 0 < < 4 . Set = sin( − ), = cos( + ), = sin( − ), and = cos(2 − ). Arrange the values , , , and in increasing order, and explain how you determined their order.

Answers

Answer 1

Answer:

b < c < a < d

Step-by-step explanation:

P.S - The exact question is -

Given - Suppose x is a real number with 0 < x < [tex]\frac{\pi }{4}[/tex] . Set a = sin([tex]\pi[/tex] - x) ,

b = cos([tex]\pi[/tex] + x) , c = sin( x - [tex]\pi[/tex]) , d = cos(2[tex]\pi[/tex] - x)

To find - Arrange the values of a, b, c, d in increasing order , and explain

how you determined their order.

Proof -

Firstly draw a unit circle where you indicate the following

A = ( cos(x), sin(x) )

B = ( cos( [tex]\pi[/tex] - x) , sin ([tex]\pi[/tex] - x) )

C = ( cos([tex]\pi[/tex] + x), sin ([tex]\pi[/tex] + x) )

D = ( cos (2[tex]\pi[/tex] - x) , sin (2[tex]\pi[/tex] - x) )

As we have given that 0 < x < [tex]\frac{\pi }{4}[/tex]

⇒sin (x) and cos(x) are positive and sin(x) < cos(x)

The figure is as follows :

Now

By seeing point B , we can say that

sin ([tex]\pi[/tex] - x) = sin (x) = a

By seeing point C , we can say that

cos([tex]\pi[/tex] + x) = -cos (x) = b

By seeing point C , we can say that

sin( x - [tex]\pi[/tex]) = -sin(x) = c

By seeing point D , we can say that

cos(2[tex]\pi[/tex] - x) = cos(x) = d

As sin(x) < cos(x) ⇒ a < d

-sin(x) > -cos(x) ⇒ c > b ⇒ b< c

and as we know that -sin(x) < sin(x) ⇒ c < a

∴ we get

b < c < a < d

)Suppose Is A Real Number With 0 < < 4 . Set = Sin( ), = Cos( + ), = Sin( ), And = Cos(2 ). Arrange

Related Questions

Aylin went to the store to buy some new folders for school . She bought a total of 7 folders and spent a total of $12. She bought two different types of folders. Plain folders that cost $1 each and folders with cartoons that cost $2 each. How many did each type of folder did Aylin buy?

Answers

Answer:

2 plain folders and 7 folders with cartoons

Step-by-step explanation:

Given data

Let the number of plain folders be x

and the number of folders with cartoons be y

x+y=7------------1

x+2y=12----------2

from 1

x= 7-y

put this in 2

7-y+2y=12

7+y= 12

y= 12-7

y=5

Put y=5 in 1

x+5= 7

x= 7-5

x= 2

Hence Ayin bought 2 plain folders and 7 folders with cartoons

PLEASE HELP ME. I WILL GIVE BRAINLIEST IF CORRECT

Answers

Answer:

c) [tex]h(t)=-16(t-1.5)^{2}+676[/tex]

Step-by-step explanation:

Each of the given equations is written in vertex form. This means that the vertex is written in the equation. The quadratic term (the term to the second degree), contains (x), and a value that is either added or subtracted to it. The additive inverse (meaning a number times negative one) of that number is the x-coordinate of the vertex. Therefore, the term inside the parenthesis is (-1.5). The constant is the y-coordinate of the vertex, and therefore it is 676. Since the object is being thrown off a cliff, gravity acts on it. The gravitational constant in feet per second is (-16), hence the coefficient of the quadratic term is (-16).

5x+y=2
Solve for y my teacher said to write the answer in this form y=-5x+2 because it goes with y=mx+b can it be written like that?

Answers

Y=2-5x hope this is correct

Answer:yes it can be written like that.

Step-by-step explanation:

Solve each problem. Explain or show your reasoning.
What is 25% of 160?
What is 39% of 200?
What is 150% of 32?
13 is 50% of what number?
18 is 120% of what number?
21 is what percentage of 30?
I NEED HELP

Answers

1: 40 2: 78 3: 48 4: 26 5: 15 6: 70

Someone help me please

Answers

Answer: Blue is longer

Step-by-step explanation: Blue islonger because it strtches a

corss more than 3 it almost reaches 4 ( no it is 4 dots long )

THE QUESTION IS ABOVE

Answers

Answer:

The box would be 14

Step-by-step explanation:

It would be 14 because 7/14 is equal to 1/2. And 2/4 is also equal to 1/2.

Answer:

7/14

Step-by-step explanation:

Have a nice day.....

Function 1 is defined by the following table.

x. y

0. 5

5. 7.5

10. 10

15. 12.

Function 2 is defined by h

Which function has a greater slope?

Answers

Function 1 I think because it’s has the greater slope

Find the slope and y-intercept from the following graph of a linear equation.

Answers

Answer:

The slope is 4x and the y intercept is 3

Hope this helps. :)

Answer:

Step-by-step explanation:

mark me brainiest

and look up slope calculator and use omni calculator

If Mia has brings 14 donuts to the party and Lizzy brings 14 also then how many cookie's is there all together

Answers

add the two donuts together, which is 28

Arnie is mixing red and yellow paints to make two different shades of orange. To make 1 cup of dark orange paint, he needs 7 ounces of red paint and 1 ounce of yellow paint. To make 2 cups of light orange paint, he needs 13 ounces of yellow paint and 3 ounces of red paint. Answer parts a and b.

Answers

Answer:

Arnie has enough red paint

Step-by-step explanation:

step 1

Find out the number of ounces of red paint needed to make 3 cups of dark orange paint

Let

x -----> number of ounces of red paint

y -----> number of ounces of yellow paint

z ----> cups of dark orange

we know that

\frac{x}{z}=\frac{7}{1}\ \frac{ounces\ red\ paint}{cups\ dark\ orange}

cups dark orange

ounces red paint

For z=3 cups

substitute and solve for x

\frac{x}{3}=\frac{7}{1}

x=21\ ounces\ of\ red\ paintx=21 ounces of red paint

step 2

Find out the number of ounces of red paint needed to make 3 cups of light orange paint

Let

x -----> number of ounces of red paint

y -----> number of ounces of yellow paint

z ----> cups of light orange

we know that

\frac{x}{z}=\frac{3}{2}\ \frac{ounces\ red\ paint}{cups\ light\ orange}

cups light orange

ounces red paint

For z=3 cups

substitute and solve for x

\frac{x}{3}=\frac{3}{2}

x=4.5\ ounces\ of\ red\ paintx=4.5 ounces of red paint

step 3

Adds the ounces of red paint

21+4.5=25.5\ ounces\ of\ red\ paint21+4.5=25.5 ounces of red paint

25.5\ ounces < 32\ ounces25.5 ounces<32 ounces

therefore

Arnie has enough red paint

Why does the value of money in a savings account increase overtime

Answers

Answer:

Because it earns interest

Step-by-step explanation:

We save money in the financial institutions like banks and micro-finance institutions. This money increase is known as interest. So the money you save increase in value over the time because it earns interest.

Answer:

the bank pays you interest

Step-by-step explanation:

The bank is paying you to keep your money and their storage because they give their money to other people so for that they give you like a cent or more a month based on how much money you put in annually

Simplify the expression:
(14 - 3a) + (5a+4)
show work if u can

Answers

Answer:

(2a + 18)

Step-by-step explanation:

Rearrange Terms

(14−3)+(5+4)

(−3+14)+(5+4)

Eliminate the brackets

(−3+14)+(5+4)

−3+14+5+4

Add the numbers

−3+14+5+4

−3+18+5

Combine like terms

−3+18+5

Answer:

multiplication...

Step-by-step explanation:

50 x 12 = 600

SO...

j = 600

SOO...

600 / 12 = 50

there u go

can i be brainiest...

Multiplication should be the correct answer

fractions equivalent to - 9/16

Answers

Answer:

Equivalent Fractions for 9/16: There are infinity equivalent fractions to 916. See some examples: 916, 1832, 2748, 3664, 4580, 5496, 63112, 72128, 81144, 90160, 99176, 108192, 117208, 126224, 135240, 144256, 153272, 162288, 171304

Step-by-step explanation:

NOT my answer, got it from g0ogle..

Pt.2 of my other question

Answers

Answer:

x = 5, supplementary

Step-by-step explanation:

6x + 13 + 14x - 33 = 180

20x - 20 = 80

20x = 100

x = 5

PLEASE HELP I DO NOT UNDERSTAND AT ALL AND SHOW YOUR WORK !!

write the equation of the line given the y- and x- intercepts
y intercept (-6,0), x-intercept (0,-8)
y intercept (0,-6), x-intercept (-2,0)
y intercept (0,8), x-intercept (1.6,0)
y intercept (0,7), x-intercept (-1.4,0)

Answers

Answer:

y intercept (-6,0), x-intercept (0,-8) : [tex]y = \frac{-4}{3}x -8[/tex]

y intercept (0,-6), x-intercept (-2,0): [tex]y = -3x -6[/tex]

y intercept (0,8), x-intercept (1.6,0): [tex]y = -5x + 8[/tex]

y intercept (0,7), x-intercept (-1.4,0): [tex]y = 5x + 7[/tex]

Step-by-step explanation:

y = mx + b

*note: b is the y intercept

1. y intercept (-6,0), x-intercept (0,-8)

[tex]m = \frac{-8 - 0}{0 - (-6)}= \frac{-8}{6} = \frac{-4}{3}\\y = \frac{-4}{3}x + b\\y = \frac{-4}{3}x -8[/tex]

2.y intercept (0,-6), x-intercept (-2,0)

[tex]m = \frac{0 - (-6)}{-2 - 0} = \frac{6}{-2} = -3\\y = -3x + b \\y = -3x -6[/tex]

3. y intercept (0,8), x-intercept (1.6,0)

[tex]m = \frac{0 - 8}{1.6 - 0}= \frac{-8}{1.6} = -5\\y = -5x + b\\y = -5x + 8[/tex]

4. y intercept (0,7), x-intercept (-1.4,0)

[tex]m = \frac{0 - 7}{-1.4 - 0} = \frac{-7}{-1.4}= 5 \\y = 5x + b\\y = 5x + 7[/tex]

Determine the slope & y intercept for the line shown. Then write the equation of the line. If you hurry I’ll mark you brainliest

Answers

Answer:

y = -3/7x + 1

Step-by-step explanation:

from the first point to the second point it goes down 3 and right 7 so this is your slope

the y intercept is 1

How do you do 5+5?
I'm serious!
I don't know how to add 5 and 5!
Help!
It's due in .5 seconds!

Answers

A=D where is picture . it is required

In a parallelogram ABCD is given. Find the measurement of angle A.

Answers

I don’t see the parallelogram. Which angle is A?

help me please don't understand (see picture)

Answers

Answer:

< F would be 140 degrees

Step-by-step explanation:

So what you would do is that since they told you angle D is 40 degrees and you know that the 2 lines in there are parallel, and since they are asking for angle F, whne you add angle F and angle H they should equal 180 degrees which you know so you just subtract 40 degrees from 180 and you get 140 degrees which if angle F and you can subtract 40 since angle H and angle D would be congruent.

Evaluate x + 23
when x=7

Answers

Answer:

Step-by-step explanation:

x + 23 = ?

x = 7

All we need to do is plug in x =7 to the first equation:

7 + 23 = ?

We simplify and get:

30 = ?

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