If cosθ = [tex]\frac{2}{\sqrt{19} }[/tex] and angleθ is in Quadrant I, what is the exact value of tan2θ in simplest radical form???

Answers

Answer 1

we know that θ is in the I Quadrant, namely that cosine as well as sine are both positive, well, we know that

[tex]cos(\theta )=\cfrac{\stackrel{adjacent}{2}}{\underset{hypotenuse}{\sqrt{19}}}\qquad\qquad \textit{let's get the \underline{opposite side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{(\sqrt{19})^2-2^2}=b\implies \pm\sqrt{19-4}=b\implies \pm\sqrt{15}=b\implies \stackrel{I~Quadrant}{+\sqrt{15}=b} \\\\[-0.35em] ~\dotfill[/tex]

[tex]tan(\theta)=\cfrac{\stackrel{opposite}{\sqrt{15}}}{\underset{adjacent}{2}}~\hspace{10em} tan(2\theta)=\cfrac{2tan(\theta)}{1-tan^2(\theta)} \\\\[-0.35em] ~\dotfill\\\\ tan(2\theta)=\cfrac{2\cdot \frac{\sqrt{15}}{2}}{1-\left( \frac{\sqrt{15}}{2} \right)^2}\implies tan(2\theta)=\cfrac{\sqrt{15}}{1-\frac{15}{4}}\implies tan(2\theta)=\cfrac{\sqrt{15}}{~~\frac{4-15}{4}~~} \\\\\\ tan(2\theta)=\cfrac{\sqrt{15}}{~~ \frac{-11}{4}~~}\implies tan(2\theta)=-\cfrac{4\sqrt{15}}{11}[/tex]


Related Questions

Please help asap!! (75 points)

Answers

Answer:

B, C, A

Step-by-step explanation:

These form a straight line.

Answer:

The sheet is backwards for some reason i dont know why 12

Step-by-step explanation:

I would answer it but i cant see it.

10) The ratio of boys to girls in Mrs. Ronilo's math class is 3 to 1. What PERCENT of the class is girls

Answers

Answer:

25%

Step-by-step explanation:

ratio is 3B : 1G  (this means, out of 4 sections, 3 are boys and 1 are girls)

this means that 3/4 of class is boys and 1/4 are girls

1/4 equals 25%

Can someone explain this to me please?

Answers

Answer:

123

Step-by-step explanation:

Squaring the given equation gives

[tex]t^2+(2\cdot t \cdot \frac{1}{t} )+ \frac{1}{t^2}=9.[/tex]

The [tex]t[/tex] and [tex]\frac{1}{t}[/tex] terms cancel out nicely, which is one of the reasons for squaring the equation.

Simplifying gives

[tex]t^2+2+\frac{1}{t^2}=9,[/tex]

[tex]t^2+\frac{1}{t^2}=7.[/tex]

The question asks for [tex]t^5+\frac{1}{t^5},[/tex] so we can square the equation again and simplify to get higher powers into the expression:

[tex](t^2+\frac{1}{t^2})^2=49,[/tex]

[tex]t^4+(2 \cdot t^2 \cdot \frac{1}{t^2}) + \frac{1}{t^4}=49,[/tex]

[tex]t^4+2+ \frac{1}{t^4}=49,[/tex]

[tex]t^4+\frac{1}{t^4}=47.[/tex]

Multiplying this expression by [tex]t+\frac{1}{t}[/tex] to try and get a fifth power gives

[tex](t^4+\frac{1}{t^4})(t+\frac{1}{t})=t^5+t^3+\frac{1}{t^3}+\frac{1}{t^5}.[/tex]

The only thing left we need is [tex]t^3+\frac{1}{t^3}[/tex] to subtract from this; we know everything else. Since [tex]t^3+\frac{1}{t^3}[/tex] can be written as [tex](t+\frac{1}{t})(t^2-1+\frac{1}{t^2}),[/tex] we can simply plug in the values we know for [tex]t+\frac{1}{t}[/tex] and [tex]t^2+\frac{1}{t^2}:[/tex]

[tex]t^3+\frac{1}{t^3}=(3)(7-1)=18.[/tex]

All that is left is to plug it in our equation here:

[tex](t^4+\frac{1}{t^4})(t+\frac{1}{t})=t^5+t^3+\frac{1}{t^3}+\frac{1}{t^5},[/tex]

[tex](47)(3)=t^5+\frac{1}{t^5}+18,[/tex]

Multiplying and rearranging gives:

[tex]t^5+\frac{1}{t^5}=123.[/tex]

Find the slope of the line that passes through (-41, 87) and (-42, 41).

Answers

Answer:

slope is 46

Step-by-step explanation:

picture

4a to the power of 2 + 18 = 118?

Answers

SOLUTION:

=) (4a)² + 18 = 118

=) 16a + 18 = 118

=) 16a = 118 - 18

=) a = 100/16

=) a = 6.25

Answer:

2.5

Step-by-step explanation:

(4a)^2 + 18 = 118

16a^2 = 100

a^2 = 100/16

a^2 = 25/4

a = 5/2 = 2.5

The Gomez family ordered $39.50 worth of
pizza and subs. They gave the delivery person
a 20% tip. What was the total cost of the food
and tip? Roun to the nearest cent?

Answers

Step-by-step explanation:

To find the cost of the tip, we need to find 120% of 39.50.

120% = 100% (order) + 20% (tip)

Let's use fractions. 39.50 can be put over 1, and 120 can be put over 100.

Equation:

[tex]\frac{39.50}{1} \times \frac{120}{100} =?[/tex]

Multiply:

[tex]\frac{39.50}{1} \times \frac{120}{100} =\frac{4740}{100}[/tex]

Divide 4740 and 100 by 100:

[tex]\frac{4740 \div 100}{100 \div 100} = \frac{47.4}{1}[/tex]

The total cost of the food is $47.40.

WILL CHOOSE BRAINLIEST as long as it LOOKS correct

Mai and Tyler work on the equation 2 5 b + 1 = - 11 together. Mai's solution is b = - 25 and Tyler's is b = - 28 . Here is their work:


Mai:

2 5 b + 1 = - 11

2 5 b = - 10

b = - 10 ⋅ 5 2

b = - 25


Tyler:

2 5 b + 1 = - 11

2 b + 1 = - 55

2 b = - 56

b = - 28


Do you agree with their solutions? Explain or show your reasoning.

Answers

Answer:

I do not agree with the solutions, b=-30, reasoning below.

Step-by-step explanation:

Mai made an error between the first and second line, she added one to the right when she should have subtracted one:

2/5b+1=-11

2/5b=-12

She then multiplied by 5/2 which was correct, however she multiplied it by -10 when it should have been -12:

b=-12*5/2

b=-30

Tyler made an error between the first and second line when he did not multiply the 1 on the left by 5 also:

2/5b+1=-11

2b+5=-55

He did the next steps correctly, however he had the incorrect value, it should look like this:

2b=-60

b=-30

What is 2 + 2. Express answer as a fraction

Answers

2+2 = 4 therefore four as a fraction would just be four wholes —-> 4/1

Answer:

well i search "what is 2 in a fraction" answer is 1/50

It would, i think 1/50 + 1/50 = 0.04

( i used the calculater) ;-;''

hope it helped   ':^

I think it's the same answer but take out the zero and decimal point

= 4

Suppose f(x) = x2 - 5. Find the graph of
f(4x).
1
2.
Click on the correct answer.
3
4
A
Click on each graph to enlarge it.
graph 1
graph 2
graph 3
graph 4

Answers

Answer:

I think its 4 because the y intercept should be at -5 and it looks like oits going t a slope of 2. SO i think 4 is correct

Step-by-step explanation:

We know line segment BD is parallel to line segment AE. Which of the following statements must also be true (select two choices)​

Answers

The statement that must be true about the two similar triangles based on the triangle similarity theorem is: option 2 and option 3.

What is the Triangle Similarity Theorem?

The triangle similarity theorem states when a segment intersects the other two sides of a triangle, and the segment is parallel to the third side, then the two triangles formed are similar, and the corresponding sides are proportional to each other.

Given that line segment BD is parallel to line segment AE, therefore, triangles CBD and CAE are similar triangles, their corresponding angles are congruent, while their corresponding sides are proportional.

Therefore, the statement that must be true about the two similar triangles based on the triangle similarity theorem is: option 2 and option 3.

Learn more about triangle similarity theorem on:

https://brainly.com/question/8242716

The area of a rectangular window is 7614 cm^2.
If the width of the window is 81 cm, what is its length?

Answers

Answer:

94cm

Step-by-step explanation:

length= area/width

= 7614/81

= 94cm

Which expression is equivalent to

Answers

Answer: C is correct answer

Step-by-step explanation:

Advertising A bank manager wants to encourage new customers to open accounts with principals of at least $3,000. He decides to make a poster advertising a simple interest rate of 3%. What must the principal be if the bank manager also wants to advertise that one can earn $10 the first month? Can the poster correctly say, "Open an account of $3,000 and earn at least $10 interest in 1 month!"?​

Answers

Answer: I GOT YOU

Step-by-step explanation: The poster says, "Open an account of ​$3,500 and earn at least ​$10 interest in 1​ month!" is correct

He decides to make a poster advertising a simple interest rate of 4.8%.  

We have to find what must the principal be if the bank manager also wants to advertise that one can earn  $10 the first month

So, the statement is correct.

Hence, the amount to be invested is $2500 and the poster says correctly.

Answer: 4,000

Step-by-step explanation: Dont feel like explaining, just trust me.

Need help with #8 its solving logarithm

Answers

Answer:

The answer to the logarithm is 2 so inputting this into the equation it would now be 2 ( 4 + 6) - 2(4) = 4 now solving it would be 20 - 8 which is 12/3 which is 4 so the final answer will be 1/4.

Step-by-step explanation:

5a - 12 What are the number of terms?

Answers

Answer:

2

Step-by-step explanation:

There are 2 terms

Hope this helps!

help ill give 5 stars

Answers

Answer:

[tex]-1\frac{7}{9}[/tex]

Step-by-step explanation:

Rewriting our equation with parts separated

[tex]2+\frac{8}{9} -4+\frac{2}{3}[/tex]

Solving the whole number parts

[tex]2-4=-2[/tex]

Solving the fraction parts

[tex]\frac{8}{9} -\frac{2}{3} =?[/tex]

Find the LCD of 8/9 and 2/3 and rewrite to solve with the equivalent fractions.

LCD = 9

[tex]\frac{8}{9} -\frac{6}{9} =\frac{2}{9}[/tex]

Combining the whole and fraction parts

[tex]-2+\frac{2}{9} =-1\frac{7}{9}[/tex]

Hence, -1 7/9 is the correct Answer.

[RevyBreeze]

5. A girl walks north 750 m in 10 minutes. What is her velocity?

Answers

Answer:  75 meters per minute north

Explanation:

Divide the distance (750) over the time (10) to get the speed

750/10 = 75

The velocity is made up of the speed and the direction. Therefore, her velocity is 75 meters per minute north. For each minute, she moves another 75 meters north.

I need help fast……………

Answers



First, find the area of the circle.

A=(pi)*r^2

A=3.14*10^2

A=3.14*100

A=314


Next, find the area of the square

A=l*w

A=20*20

A=400

Finally, subtract the area of the circle from the area of the square

400 - 314 = 86

Step-by-step explanation:

it is the area of the square minus 4 quarter circles (which means 1 full circle) with radius of 10 ft (the half of a side of the square).

we know how to calculate the area of a square "As"

As = side²

we know how to calculate the area of a circle "Ac"

Ac = pi×radius²

so, the shaded area "Ashade"

Ashade = side² - pi×radius² = 20² - pi×10² =

= 400 - pi×100 = 85.84073464... ft²

I don't know, if you need to round the answer in some way.

if it is to e.g. 2 digits after the decimal point (hundredths), then it would be

85.84 ft²

200 people stand in a circle in order 1 to
200. No. 1 has a sword. He kills the next
person (i.e. No. 2) and gives the sword
to the next living person (i.e. No. 3). All
people do the same until only 1
survives, which number survives to the
end?

Answers

Number 1 does. He killed rhe person behind him and nobody ever killed him because they kill the people behind them.

Answer:

Number 1

Step-by-step explanation:

what are the roots of the equation x^2 +30x =1000?

Answers

Answer:

x=20  and  x=-50

Step-by-step explanation:

To find the roots, we need to simply solve for x. We do this by first moving all of the terms to the left and setting the right side equal to 0.

-1000

x^2+30x-1000=0

Now, factor it.

What adds up to 30 but multiplies to get -1000?

-10 and 40? No, because they multiply to get -400.

-20 and 50? Yes, because they add up to 30 and multiply to get -1000.

(x-20)(x+50)

x-20=0

x=20

x+50=0

x=-50

So, the roots are x=20 and x=-50

Given :-

x² + 30x = 1000 .

To Find :-

The roots of the equation .

Solution :-

As we know that if the quadratic equation is in standard form which is ,

[tex] ax^2+bx + c =0[/tex]

Then its roots are given by ,

[tex] x =\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

So on converting the equation in standard form ,

[tex] x^2+30x -1000=0[/tex]

With respect to the standard form ,

a = 1b = 30c = -1000

Substitute in the Quadratic formula ,

[tex] x =\dfrac{-30\pm \sqrt{(30)^2-4(1)(-1000)}}{2(1)}[/tex]

Simplify,

[tex] x =\dfrac{-30\pm\sqrt{900+4000}}{2}[/tex]

Add the numbers inside square root ,

[tex] x =\dfrac{-30\pm\sqrt{4900}}{2}[/tex]

Divide each term in numerator by 2,

[tex] x =\dfrac{-30}{2}\pm\dfrac{\sqrt{70^2}}{2}[/tex]

Simplify ,

[tex] x = -15 \pm 35 [/tex]

Separate the two solutions ,

[tex] x = -15 + 35 , -15 -35[/tex]

Simplify ,

[tex]x = 20 , -50 [/tex]

Hence the solution of the equation are 20 and -50 .

I hope this helps.

The Drama Club can spend no more than $120 for costumes. They already spent $79. How much more can they spend for costumes? HELP PLEASE!

Answers

An$41 dollars left to spend

Step-by-step explanation:

i bought 15 laptops for 150,000. if the selling price is the cost price divided by 2 and then multiplied 3.what is my selling price and my profit or loss

Answers

Answer:

225,000 (selling price) 75,000 (profit)

Step-by-step explanation:

x = (150,000 ÷ 2) x 3

x = 75,000 x 3

x = 225,000

225,000 (sell) - 150,000 (cost)

= 75,000 (profit)

The cost price is : 150000/15 which is 10,000
The selling price would then me (10,000/2) x 3 which is 15,000

Therefore the selling price is 15,000 and the profit is 5000

Which equations could you use to find the price of one tire patch? Select all that apply. 4x – 1.9 = 22.2 4x – 22.2 = 1.9 4x + 1.9 = 22.2 4x + 22.2 = –1.9 22.2 – 4x = 1.9

Answers

Answer:C & E the explanation is the explanation from the explanation

Find the equation of a line that passes through the points (-1,3) and (3,-5).
Leave your answer in the form y = mx + c

Answers

Answer:  y =  mx+cG =  A100​G =  A100​G =  A100​

Step-by-step explanation:  Solve for c

c=y−mx  

{

m=−

x

c−y

,

m∈R,

 

x

=0

y=c and x=0

Answer:

y= -2x+1

Step-by-step explanation:

The slope of the line is -4/2, which gets simplified to -2. Then, the line passes through y-intercept (0,1), which becomes +1 as the y-intercept in y=mx+b form. Therefore, the equation is y= -2x+1. I'm 100% sure this is right. Hope that helps :)

Someone please help offering 25 points

Answers

Answer:

Assuming those triangles are both right, the answer is 5.3

Hi Everyone! Please Help! I really need help! Please answer as any as you can and he ones I already answered please stop if thy are prefect and if not please at the correct answer. Thanks! I really appreciate all of your peoples help!!!!!!!!

Answers

Answer:

12. B

13. B

14. C

15. C

16. D

17. C

18. C

19. C

20. D

21. B

Step-by-step explanation:

12.

16/8 = 2

13.

12 - 4 = 8

12 - 6 = 6

(8 + 6)/2 = 7

15. 2000 x 1000 = 2,000,000

16. 999 + 9999 = 10,998

17.

24/4 = 6

6 x 5 = 30

18.

6 x 3 = 18

19. July 18th

20.

728 cannot divide evenly by 72

21.

1111 x 1111 = 1,234,321

biggest odd number is 3

Determine whether the relation is a function. Explain why or why not.


{(3, 7), (3, 8), (3, –2), (3, 4), (3, 1)}

Answers

Answer:

the relation is a function ..this the domains are the 3s and the co-domain are (7, 8, –2, 4,1) so here it's a function it does not matter if the domain are the same but if the co-domain is the same them it's not a function but here they're different

Wayne Gretzky holds the NHL record for the most points scored in a career. He scored 2857 points in 1487 games.

a) Calculate his average points per game.

b) At this rate, how many more points would he have scored if he had played 79 more games.

Answers

Answer:

1999 The most points scored in an NHL career is 2,857, achieved by Wayne Gretzky (Canada) while playing for the Edmonton Oilers (Canada), Los Angeles Kings, St Louis Blues and New York Rangers (all USA) from 1979 to 1999. The points total comprises 894 goals and 1,963 assists in 1,487 games.

Step-by-step explanation:

a) Wayne Gretzky's average points per game is approximately 1.9202.

b) Wayne Gretzky would have scored approximately 151.5438 more points if he had played 79 more games.

a) To calculate Wayne Gretzky's average points per game, we divide the total points scored (2857) by the total number of games played (1487):

Average points per game = Total points scored / Total games played

Average points per game = 2857 / 1487 ≈ 1.9202

Wayne Gretzky's average points per game is approximately 1.9202.

b) To find out how many more points Wayne Gretzky would have scored if he had played 79 more games, we can use the average points per game calculated in part (a).

We know that his average points per game is approximately 1.9202. So, to find the additional points in 79 games, we can multiply the average points per game by the number of additional games:

Additional points = Average points per game * Additional games

Additional points = 1.9202 * 79 ≈ 151.5438

Wayne Gretzky would have scored approximately 151.5438 more points if he had played 79 more games.

To know more about average points:

https://brainly.com/question/16699422

#SPJ2

solve system of equations:

-2x + y = 5
-4x + 3y = 7

Answers

answer:

(x,y)=( -4, -3)

Answer:

{x,y}={-4,-3}

Step-by-step explanation:

// Solve equation [1] for the variable  y

 [1]    y = 2x + 5

// Plug this in for variable  y  in equation [2]

  [2]    -4x + 3•(2x+5) = 7

  [2]    2x = -8

// Solve equation [2] for the variable  x

  [2]    2x = - 8

  [2]    x = - 4

// By now we know this much :

   x = -4

   y = 2x+5

// Use the  x  value to solve for  y

   y = 2(-4)+5 = -3

Solution :

{x,y} = {-4,-3}

pls, mark me as brainiest!

The design is rotated about the line x=1 to produce the shape of the urn. Finish the potter's design by drawing a picture
of what the urn looks like. In your picture, include a properly labeled coordinate plane and the line x= 1.
Upload your drawing below.
Sign out

Answers

When the urn is reflected over x = 1, the new urn becomes a mirror of the old diagram.

How to draw the new poster design

From the question, we understand that the new poster design is to be drawn by reflecting the urn (i.e. the red figure) across the line x = 1

The line x = 1 is a vertical line that passes through the x-axis at x = 1.

To reflect the urn across x = 1, we simply flip the urn over the line.

See attachment for the diagram

Read more about reflection at:

https://brainly.com/question/4289712

When the urn is reflected over x = 1, the new urn becomes a mirror of the old diagram.

The new poster design is to be drawn by reflecting the urn (i.e. the red figure) across the line x = 1

The line x = 1 is a vertical line that passes through the x-axis at x = 1.

To reflect the urn across x = 1, we simply flip the urn over the line.

_______|________

\              |              /

 \            |            /

 /            |            \

/______|_______\

             |

(copy and paste for the people that have to "draw" this out on odyssey ware <3) p.p.s just copy the thing. it won't paste correctly.

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