(Sinθ-cosθ)(sinθ+cosθ)=1-2cos^2θ

Answers

Answer 1

Answer:

See below

Step-by-step explanation:

[tex]( \sin \theta - \cos \theta)( \sin \theta + \cos \theta) = 1 - 2 { \cos}^{2} \theta \\ \\ LHS = ( \sin \theta - \cos \theta)( \sin \theta + \cos \theta) \\ \\ = \sin^{2} \theta - \cos^{2} \theta \\ \\ =1 - \cos^{2} \theta - \cos^{2} \theta \\( \because \sin^{2} \theta =1 - \cos^{2} \theta) \\ \\ = 1 - 2 { \cos}^{2} \theta \\ = RHS[/tex]

Thus proved


Related Questions

write a possible equation for each graph. Help me please​

Answers

Answer:

a. y = -x² + 2x - 8

b. y = [tex]\frac{1}{x-2}[/tex]

c. y = x³+ 3

Step-by-step explanation:

What is the variable in Samuel is six inches taller than his brother Elijah.if Samuel is 48 inches tall,how tall is Elijah

Answers

Answer: Elijah would be 42 inches tall

Step-by-step explanation:

We all know that Samuel is 48 inches while Elijah is 6 inches shorter.

You subtract 6 from 48 to get 42.

Hopefully, this helped. :D

Can someone help? I really don’t understand this at all!

Answers

is this pathogroem therom?

(GIVING EXTRA POINTS ON THIS ONE!! IM ALSO GIVING AWAY BRAINLIEST TO WHO EVER HELPS ME OUT :D)


If you roll a ball down a ramp, which factor will have the greatest effect on the amount of friction created?

A) Force applied to the ball

B) Speed of the ball

C) Texture of the surface

D) Weight of the ramp

(Here is an image if needed) :

Answers

Answer:

C. The Texture of the Surface

Step-by-step explanation:

I know it's confusing because of A.. But if you think about what would happen if you were to bounce a ball with a lot of force onto the surface, it wouldn't cause a difference in the friction because it would still just bounce right back up. D. is also not applicable because the weight of the ramp wouldn't matter if the ball is rolling on top of it.

A recent study investigated whether renowned violinists were able to classify the age of a violin. In the study, violins constructed before 1900 and violins constructed after 2010 were used. The violinists played each violin and were asked to classify the violin as old (constructed before 1900) or new (constructed after 2010). The responses are shown in the following table.

Which of the following statements is supported by the results in the table?
1.)The proportion of all new violins that are correctly classified is equal to the proportion of all old violins that are correctly classified.
2.)The proportion of all new violins that are incorrectly classified is equal to the proportion of all old violins that are correctly classified.
3.)The proportion of all incorrectly classified violins that are old is equal to the proportion of all correctly classified violins that are new.
4.)The proportion of all incorrectly classified violins that are new is equal to the proportion of all correctly classified violins that are new.
5.)The proportion of all correctly classified violins that are old is equal to the proportion of all new violins that are incorrectly classified.

Answers

Answer:

The proportion of all correctly classified violins that are old is equal to the proportion of all new violins that are incorrectly classified.

Step-by-step explanation:

According to the table, we have that the correct option is:

5.)The proportion of all correctly classified violins that are old is equal to the proportion of all new violins that are incorrectly classified.

Statement 1:

15 of 33 new are correctly classified, thus, the proportion is:

[tex]p_N = \frac{15}{33} = 0.4545[/tex]

18 out of 31 old, thus:

[tex]p_O = \frac{18}{31} = 0.58[/tex]

Proportions are different, thus, statement 1 is false.

Statement 2:

13 out of 31 old are incorrectly classified, thus:

[tex]p = \frac{13}{31} = 0.4194[/tex]

Different than 0.4545, thus, statement 2 is false.

Statement 3:

Out of 31 incorrectly classified, 13 are old.

Out of 33 correctly classified, 15 are new.

Different proportions, thus, statement 3 is false.

Statement 4:

Out of the 33 new, 15 are correctly classified and 18 incorrectly, different proportions, thus, statement 4 is false.

Statement 5:

18 out of 33 correctly classified are old.

18 out of 33 new violins are incorrectly classified.

Same proportion, thus, statement 5 is true.

A similar problem is given at https://brainly.com/question/12612621

There were 5 ice cream cones for every 3 brownies sold at the ice cream shop. If there were 24 brownies sold, how many ice cream cones were sold?

Answers

Answer:

THe answere is 40

Step-by-step explanation:

If 24 brownies are sold, the number of ice cream cones sold is 40.

A linear equation is in the form:

y = mx + b;

where y, x is variable, m is the rate of change and b is the y intercept.

Let y represent the number of ice cream cones and x represent the number of brownies sold.

Since there were 5 ice cream cones for every 3 brownies sold at the ice cream shop. Hence:

y = (5/3)x

If 24 brownies are sold:

y = (5/3)x

y = (5/3) * 24 = 40

If 24 brownies are sold, the number of ice cream cones sold is 40.

Find out more at: https://brainly.com/question/13911928

The odds that it will snow tomorrow are 9 to 6. What is the probability that it will not snow tomorrow?a) 0.1818
b) 0.2222
c) 0.1111
d) 0.1667
e) 0.8182

Answers

Answer:

a) 0.1818

Step-by-step explanation:

Given that:

The odd that it'll snow tomorrow is 9 to 6

The probability that it will snow tomorrow  [tex]=\dfrac{9}{9+6}[/tex]

[tex]=\dfrac{9}{15}[/tex]

= 0.6

The probability that it'll not snow tomorrow [tex]= 1 - \dfrac{9}{15}[/tex]

[tex]= \dfrac{15-9}{15}[/tex]

[tex]=\dfrac{6}{15}[/tex]

= 0.4

Let assume that the odd that it'll snow tomorrow is 9 to 2

The probability that it will snow tomorrow  [tex]=\dfrac{9}{9+2}[/tex]

[tex]=\dfrac{9}{11}[/tex]

= 0.8181

The probability that it'll not snow tomorrow  [tex]= 1 - \dfrac{9}{11}[/tex]

[tex]= \dfrac{11-9}{11}[/tex]

[tex]=\dfrac{2}{11}[/tex]

= 0.1818

None of the  options is correct.

Probability that it will not snow tomorrow = 0.4

The odds of an event E is defined as formulated in equation (1)

[tex]\rm Odd\; of\; event\; E = P(E)/P(\bar E) = P(E)/(1-P(E)).......(1)[/tex]

Let P(E) represents the probability that it will snow tomorrow.

Let event E represents the event that " it will snow tomorrow "

So the odds of the event that it will snow tomorrow

[tex]\rm \dfrac{P(E)}{P(\bar E)} =\dfrac{9}{6} = \dfrac{P(E)}{1-P(E)}.......(2)[/tex]

On solving equation (2) we get

[tex]\rm P(E) = \dfrac{9}{15}[/tex]

So the probability that it will snow tomorrow is 9/15

Hence the probability that it will not snow tomorrow

[tex]\rm P(\bar E) = 1- \dfrac{9}{15} = \dfrac{6}{15} =\bold{0.4}[/tex]

Probability that it will not snow tomorrow = 0.4

For more information please refer to the link below

https://brainly.com/question/7538150

Please answer the bottom one

Answers

Answer:

The first one is 109, the 2nd one is the 2nd and 4th choices

Step-by-step explanation:

Fill in the blanks to complete the sentence.
Last month, the online price of a powered ride-on car was $250. This month, the online price is $330. What is the percent of increase in the price of the car? Round the percent to the nearest tenth if necessary. :)

Answers

Answer:32%

Step-by-step explanation:

330-250=80

80/250=0.32 or 32%

Solve four and six eighths minus two and three fifths.

(GIVING EXTRA POINTS AND GIVING BRAINLIEST!!)

A) one and six thirteenths

B) one and three fortieths

C) two and six fortieths

D) two and three thirteens

(Here is an image if needed) :

Answers

Answer:

I am not really sure but I asume it is C honestly I am sorry if I am wrong. But if I am right I really hope this helps

What is 2s + 5 > 49 ?

Answers

Answer:

s>22

Step-by-step explanation:

2s>49−5

2s>44

s>44/2

s>22

what is the absolute minimum and maximum of this graph ​

Answers

Answer:

The minimum is 0 because the lowest point the line reaches is 0. The maximum is infinity because the arrow keeps going up.

Answer:

There is no max since the arrow is continuous and the minimum is zero

Step-by-step explanation:

X
I ㅗ
]
Factor: -2/3
out of -3X
- 12

Answers

Answer:what is this

Step-by-step explanation:

bruh

What is the midpoint of the segment below?
(2,3)
(-3,-2)
O A. (2.5, 2.5)
O B. (5,5)
O C. (-0.5, 0.5)
O D. (0,0)

Answers

The midpoint is C, (-0.5,0.5)

Find the middle between the x and y coordinates and that is the midpoint

Answer:

C

Step-by-step explanation:

use midpoint formula

midpt = ((2 + (- 3))/2 , (3 + (- 2))/2) = (-0.5, 0.5)

The graph shows the number of centimeters a particular plant grows over time. Given the points​ (0,0) and ​(6​,9​), how many centimeters does the plant grow per​ week?

Answers

Answer: 4/5 or 0.8

Step-by-step explanation: To find how much it grows over time, we have to find the slope. to do that, we need to have two points with exact points on the graph, so (0,0) and (4,5). the equation for slope is rise/run. it rises 4, and runs 5. so 4/5.

What is the equation of the line that passes through the point (-1,7) and has a slope of -2?

Answers

Y = -2x + b
Plug in the point
7 = -2(-1) + b
7 = 2 + b
b = 5
Final equation y = -2x + 5

Write an explicit formula for an, the nth term of the sequence 19,24,29

Answers

Answer:

explicit formula for an, the nth term of the sequence 19,24,29

[tex]a_1=19 ; \ a_n=a_{n-1}+5[/tex]

Step-by-step explanation:

We need to Write an explicit formula for an, the nth term of the sequence 19,24,29

In the sequence the First term a₁= 19

Common Difference d= 5

The Formula used for explicit formula is: [tex]a_1=First \ term ; \ a_n=a_{n-1}+d[/tex]

Where d is common difference and n is nth term of sequence.

So, explicit formula for an, the nth term of the sequence 19,24,29

[tex]a_1=19 ; \ a_n=a_{n-1}+5[/tex]

What is the slops of this line? Enter your answer as a fraction in simplest term in the box.

Answers

The slope is 1/4 cause it goes up 1 and right 4 meaning slope=1/4

Answer:

It is 1/4

Step-by-step explanation:

If you go from dot to dot on the line, starting with the first dot:

you go to the right 4 times and then up 1 to get to the next dot.

If you put that into a fraction it is [tex]\frac{rise}{run}[/tex] so going up (1) is ontop of going to the right (4), which is 1/4.

Question 6
Ryan spent half of his weekly allowance on candy. To earn more money, his parents let him clean the windows in his house for $9. He
ended with $15. Which equation would represent this situation?

Answers

Answer:

x=6

Step-by-step explanation:

Let X = Rob's weekly allowance

If he spent 1/2 of it on candy, then he had 1/2 of it left (1/2)X

After he earned $6 for cleaning the oven, he had $9.

So,

(1/2)X + 6 = 9

(1/2)X = 3

X = 6

PLEASE HELP MATH 100%: How does Newton’s Second Law apply to the field of robotics? why is this a litreal math question like i know-

Answers

I- I’m bouta SUE that math teacher-
Also the answer is

2.2.1 Newton's Second Law of Motion Applied to Mechanical Systems Modeling
Newton's second law of motion states that the acceleration of a particle
(
a
=
x
¨
=
d
2
x
(
t
)
/
d
t
2
)
is proportional to the force applied to it and is in the direction of this force. The proportionality constant is the mass m for a constant-mass particle or a rigid body undergoing translatory motion whose inertia can be reduced to a point. In cases where several external forces act on the particle in the motion direction, the acceleration is proportional to the algebraic sum of external forces fj
(2.34)
m
x
¨
=

j
=
1
n
f
j
An equation similar to Eq. (2.34) can be derived from Newton's second law of motion (which is formulated for translation), expressing the dynamic equilibrium of a body of constant mass moment of inertia J rotating about a fixed axis:
(2.35)
J
θ
¨
=

j
=
1
n
m
t
j
where mtj are the torques acting on the rotating body and the rotary acceleration is
θ
¨
=
d
2
θ
(
t
)
/
d
t
2
(the symbol mt has been used for moments to avoid confusion with the mass symbol m). Equation (2.35) is also valid for a particle rotating about an external axis.
Equation (2.34) for translation and Eq. (2.35) enable deriving mathematical models formed of the differential equation(s) connecting the input and the output through system component parameters. Instrumental to correctly applying these equations is the free-body diagram, which isolates a mechanical element from its system using external forcing as well as reaction forces and moments from the elements that have been separated from the studied element. The equations based on Newton's second law of motion and the free-body diagrams are utilized for the remainder of this chapter, as well as in Chapter 3, to determine the free and forced responses of mechanical systems
PHEW thank GOD for copy and paste-
Take what you will from this

can someone please help me thank you

Answers

Answer:

Neither of the students are correct.

Step-by-step explanation:

Sarah:

P = 3x + x +7 + 3x + x +7 ..... this first step is correct

    = 6x + 14 .... this step is incorrect, Sarah forgot to add the other 2 xs

John:

P = 2(x + 7) + 2(3x)

  =  2x + 7 + 6x .... this step is incorrect, John forgot to distribute the 2 to the 7

  =  8x + 7 .... incorrect because of the previous step

The answer should've been 8x + 14.

DONT HAVE MUCH TIME LEFT, THIS WILL BE DUE SOON!!!

What is the slope?

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Answers

Answer:

the slope is 2 I am pretty sure

2
2,0) (6,8)
8-0/6-2
8/4= 2

1. Jared borrowed $300 from his mother to buy an x-box 360. Jared will pay her back in 4 years with 3.5% simple interest. How much total money will he payback to his mother at the end of the 4 years? (Hint: which formula should you use simple or compound, what is the principal, what is the rate, what is the time.)

2. Jackie deposits $225 in an account that pays 4.1% interest compound annually. How much money would Jackie have in her account after 1.5 years? (Hint: which formula should you use simple or compound, what is the principal, what is the rate, what is the time.)

3. Stephanie placed $1,700 in an account that earns 6% interest compounded annually. How much money will she have in the account at the end of 48 months? (Hint: which formula should you use simple or compound, what is the principal, what is the rate, what is the time.) ​

Answers

Answer:

1) future value = present value x [1 + (i x n)] = $300 x [1 + (3.5% x 4)] = $342

2) using the compound interest formula:

future value = $225 x (1 + 4.1%)¹°⁵ = $238.98

Using the simple interest formula doesn't yield the same answer = $225 x [1 + (4.1% x 1.5)] = $238.84. In this case it is close due to a very short period of time and low interest rate.

3) future value = present value x (1 + i)ⁿ = $1,700 x (1 + 6%)⁴ = $2,146.21

since the interest is annual, we must convert 48 months to 4 years

help with this question please ​

Answers

It is : D

Hope this helps

24 = 3(n–5)

What is the answer​

Answers

Step-by-step explanation:

24=3n-15 or,25+15=3n or,39=3n or,39/3=n or,n=13 therefore the value of n is 13. I think this answer is helpful for you

Answer: n = 13

Step-by-step explanation:

24=3(n-5) - First  distribute the 3 to the n and the 5. Which you would than get 3n and -15

24=3n-15 - Now add the 15 to both sides which would cause it to cancel out on the left side of the equal side.

39=3n - Now divide the 3 from 3n on both sides of the equal side.

n=13 - Once you do that you will get n = 13. That is your answer!

Find the measure of the arc or angle indicated. Assume GE is the diameter of
the circle
O 70°
0 47
O 54
O 60°

Answers

Answer: 70 degrees (i had that question got it right)

Step-by-step explanation:

Wow, using grammar makes me feel like an adult!

Answers

Answer:

I asked my teacher if we could use that she said it's considered cheating, I still use it

Step-by-step explanation:

helppppp pleaseee!!

Evaluate the function

Answers

Answer:

10

Step-by-step explanation:

go to mathaway.com and type in the equation and when x=-6. Press show graph and it says 10. The graph is my proof.

Number of Certified Organic Farms in the United States, 2001–2008


Year Farms


2001 6,231


2002 6,574


2003 7,237


2004 7,211


2005 7,701


2006 8,581


2007 10,302


2008 11,796


Click here for the Excel Data File


(a) Fit three trends (linear, quadratic, exponential) to the time series. (A negative value should be indicated by a minus sign. Do not round the intermediate calculations. Round your final answers to 2 decimal places.)


(b) Use each of the three fitted trend equations to make numerical forecasts for the next 3 years. (Round the intermediate calculations to 2 decimal places and round your final answers to 1 decimal place.)

Answers

Answer:

ŷ = 739.49X + 4876.43

y = 6755.98 - 388.24x + 125.30x²

y = 5428.98(1.09)^x

B.)

Linear:

ŷ = 739.49(9) + 4876.43

y = 11531.8

Year 2010 ; x = 10

y = 739.49(10) + 4876.43

y = 12271.3

Year 2011 ; x = 11

y = 739.49(11) + 4876.43

y = 13010.8

Quadratic :

Year 2009 ; x = 9

y = 6755.98 - 388.24(9) + 125.30(9^2)

y = 13411.1

Year 2010 ; x = 10

y = 6755.98 - 388.24(10) + 125.30(10^2)

y = 15403.6

Year 2011 ; x = 11

y = 6755.98 - 388.24(11) + 125.30(11^2)

y = 17646.6

Exponential:

Year 2009 ; x = 9

y = 5428.98(1.09)^9

y = 11791.2

Year 2010 ; x = 10

y = 5428.98(1.09)^10

y = 12852.4

Year 2011 ; x = 11

y = 5428.98(1.09)^11

y = 14009.1

Step-by-step explanation:

X :

1

2

3

4

5

6

7

8

Y:

6231

6574

7237

7211

7701

8581

10302

11796

Using the online linear regression calculator :

The linear trend :

ŷ = 739.49X + 4876.43

Where x = year

With 2006 representing 1 ; and so on

Slope = m = 739.49

Intercept (c) = 4876.43

y = predicted variable

The quadratic model:

General form:

y = A + Bx + Cx²

y = 6755.98 - 388.24x + 125.30x²

The exponential model:

y = AB^x

y = 5428.98(1.09)^x

B.) Next three years :

Year 2009 ; x = 9

Year 2010 ; x = 10

Year 2011 ; x = 11

Linear:

ŷ = 739.49(9) + 4876.43

y = 11531.8

Year 2010 ; x = 10

y = 739.49(10) + 4876.43

y = 12271.3

Year 2011 ; x = 11

y = 739.49(11) + 4876.43

y = 13010.8

Quadratic :

Year 2009 ; x = 9

y = 6755.98 - 388.24(9) + 125.30(9^2)

y = 13411.1

Year 2010 ; x = 10

y = 6755.98 - 388.24(10) + 125.30(10^2)

y = 15403.6

Year 2011 ; x = 11

y = 6755.98 - 388.24(11) + 125.30(11^2)

y = 17646.6

Exponential:

Year 2009 ; x = 9

y = 5428.98(1.09)^9

y = 11791.2

Year 2010 ; x = 10

y = 5428.98(1.09)^10

y = 12852.4

Year 2011 ; x = 11

y = 5428.98(1.09)^11

y = 14009.1

Evaluate 3/11 × 11/13 Give your answer as a fraction in its simplest form.​

Answers

Answer: 3/13

Step-by-step explanation:

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An equation is shown. What factor is missing from the equation? 32 + 20= (8+5)* Alice is opening a savings account which earns 2.2% interest, compounded continuously.How much will she need to deposit in the account so that she has $6200 after 3 years?Round your answer to the nearest dollar. What is 8 times 5 times 6 times 21 In the book code talker, According to chapter 14, why were the corpses so fearful for the Navajos? Frogs use their tongues to catch flies, the longer a frog's tongue the more food he can get. Over time the lengths of frogs tongues became longer, as those frogs with shorter tongues died off quickly and reproduced more slowly. This is an example of which of the following?AdaptionNatural SelectionMutationVariations Which is an example of Identity Property of Addition ?6 + 0 = 623+5=5+307x1 = 7O (5+9) + 8 = 5 + (9 + 8)+ Read and select the best answer to complete the dialogue.You are just meeting a new neighbor, seora Hidalgo, and want to know her name.usted?-Hola, -Seora Hidalgo.O cmo te llamascul es tu nombreO cmo estO cmo se llama what are the possible values for the ones digits when a number is a multiple of 5 Which of the following statements is included in the Bill of Rights? What volume would a 200 g sample of gold have, if its density is known to be 19.3 PLEASE HELPWhich version of the underlined portion of sentence 9 (reproduced below) develops the main idea of the paragraph by explaining an effect of the art piece Passin on to Others ?Words that previously had passed unremarked now joined other aphorisms and sayings that Kennedy has printed on posters.a// (as it is now)b// appeared in a hand-printed format thanks to a technique similar to the process used by professional printers hundreds of years agoc// made up the entire text of the piece, confirming that limitations spark creativity, as Kennedy asserted in a 2010 interview with artist Michael Curtind// spurred consideration and discussion, exchanges that many stylists chose to continue by hanging prints from the show in their salonse// presented an impressive, wall-sized spectacle to visitors who encountered them at the Institute for Contemporary Art Last year, a middle school band had 80 students. This year,the band has 120% of that number of students. How manystudents are in the band this year? 6. f(x) = (x + 2). g(X) = (X+3) Find (fg)(x) Suppose 52R% of the population has a college degree. If a random sample of size 808808 is selected, what is the probability that the proportion of persons with a college degree will be less than 54T% You are at a fruit stand to get some fresh produce. You notice that the person in front of you gets 5apples and 4 pears for 10 dollars. You get 5 apples and 5 pears for 11 dollars. Write a system ofequations that could be used to find the price of an apple and the price of a pear. NEED HELP RLLY BAD!!!!!Which of the following is not an example of a lipid?a. triglycerideb. steroidc. enzymed. phospholipid Why were Democrats challenged during the first years of Oklahoma statehood?A. Oklahoma became a state during a national economic boom.B. Divisions in the Democratic Party grew due to supporters from various backgrounds.C. The party had very low expectations and wanted to impress the public.D. The Republicans fought to move the state capital out of Guthrie. What is the HARDEST part of writing?Where/When do you do the BEST writing? Why?What STEPS do you take writing something good?How could you HELP a struggling writer?2+ paragraphs I suck at math I need help this one is also giving me a hard time