If cos 0 = 3/radical 22 and angle 0 is in Quadrant I, what is the exact value of tan 20 in
simplest radical form?
Answers
Answer:
[tex] \tan2\theta =-\dfrac{3\sqrt{13}}{2} [/tex]Step-by-step explanation:
To find:-
The value of [tex]\tan2\theta[/tex] .Answer:-
We are here given that the value of,
[tex]\longrightarrow \cos\theta=\dfrac{3}{\sqrt{22}} \\[/tex]
And we know that cosine is the ratio of base and hypotenuse. Therefore,
[tex]\longrightarrow \cos\theta =\dfrac{b}{h} \\[/tex]
So we can also say that,
[tex]\longrightarrow \cos\theta = \dfrac{b}{h}=\dfrac{3}{\sqrt{22}}\\[/tex]
Let us take the given ratio to be 3x:√22x . Now we may find out the value of perpendicular using Pythagoras theorem . The Pythagoras theorem is ,
Pythagoras theorem:-
In a right angled triangle the sum of squares of perpendicular and base is equal to the square of hypotenuse.Mathematically,
[tex]\longrightarrow \boxed{ \boldsymbol{p^2+b^2=h^2}} \\[/tex]
where the symbols have their usual meaning.
On substituting the respective values, we have;
[tex]\longrightarrow p^2+(3x)^2=(\sqrt{22}x)^2 \\[/tex]
[tex]\longrightarrow p^2 = 22x^2-9x^2\\[/tex]
[tex]\longrightarrow p^2=13x^2 \\[/tex]
[tex]\longrightarrow \boldsymbol{ p = \sqrt{13}x} \\[/tex]
Now again , we know that, tangent is defined as the ratio of perpendicular and base. Therefore,
[tex]\longrightarrow \tan\theta = \dfrac{p}{b} \\[/tex]
[tex]\longrightarrow \tan\theta = \dfrac{\sqrt{13}x}{3x}\\[/tex]
[tex]\longrightarrow \boldsymbol{ \tan\theta = \dfrac{\sqrt{13}}{3}}\\[/tex]
Now we may use a identity which is ,
[tex]\longrightarrow\boxed{ \boldsymbol{ \tan (2x)= \dfrac{2\tan x}{1-\tan^2 x}}}\\[/tex]
On substituting the respective values, we have;
[tex]\longrightarrow \tan2\theta = \dfrac{ 2\tan\theta}{1- \tan^2\theta}\\[/tex]
[tex]\longrightarrow \tan2\theta = \dfrac{2\bigg(\dfrac{\sqrt{13}}{3}\bigg)}{1-\bigg(\dfrac{\sqrt{13}}{3}\bigg)^2 } \\[/tex]
[tex]\longrightarrow \tan2\theta = \dfrac{\dfrac{2\sqrt{13}}{3}}{1-\dfrac{13}{9}} \\[/tex]
[tex]\longrightarrow \tan2\theta = \dfrac{\dfrac{2\sqrt{13}}{3}}{\dfrac{9-13}{9}} \\[/tex]
[tex]\longrightarrow \tan2\theta = \dfrac{\dfrac{2\sqrt{13}}{3}}{\dfrac{-4}{9}} \\[/tex]
[tex]\longrightarrow \tan2\theta = -\dfrac{2\sqrt{13}\cdot 9}{3\cdot 4 } \\[/tex]
[tex]\longrightarrow \boxed{\boldsymbol{ \tan2\theta = -\dfrac{3\sqrt{13}}{2}}} \\[/tex]
This is the required answer .
Related Questions
A baseball glove for $280 but it’s on sale for 55% off. Find the discount and the sale price.
Answers
Answer: The answer is 126 because if we minus 280 - 55% the answer is 126
$126
HOPE THIS HELPS
GIVING BRAINY AND EXTRA PTS NO LINKS GIVE EVIDENCE
Answers
Answer:
60
Step-by-step explanation:
I think that is the best choice sorry if i got it wrong.
Answer:
60 degrees
Step-by-step explanation:
Angle 1 is already 55 degrees, if you move the y line 5 degrees clockwise then it equals 60 degrees. Angle 1 and 3 are vertical angles so they are equal, if angle 1 is 60 degrees after we move the line then angle 3 is also 60 degrees
Which point is located in Quadrant ll? (-4,5) (-4,-5) (4,-5) (4,5)
Answers
Answer:
(-4,5)
Step-by-step explanation:
that is the top left quadrant which means the x value has to be negative but the y value has to be positive
Please help me ASAP please
Answers
Answer:
217=31m; m=7, 7 miles per day
Step-by-step explanation:
217/31=m 217=31m, just divide the total number of miles by the number of days
Let X and Y be independent Bernoulli random variables with parameters 0.2 and 0.3, respectively. Find the distribution of X Y. List all possible values that X Y can take. Write your answer as a comma-separated list ordered from smallest to largest value. possible values: List the probabilities that X Y takes each of the values. Write your answer as a comma-separated list giving the probabilities in the same order as in (a)
Answers
Answer:
a) 0 , 1
b) 0.56 , 0.06
Step-by-step explanation:
X = 0.2
Y = 0.3
Find the distribution of X + Y
a) All the possible values of X + Y
The possible values of X + Y are ; 0,1
b) The probabilities that X + Y takes each of the values
P(X+Y=0 ) = ( 1-0.2 )*(1-0.3) = 0.56
P( X +Y = 1) = 0.2*0.3 = 0.06
A research analyst for a car rental agency found that the probability distribution function for the age of the rental car (in years) is a straight line. The line decreases from the point (0, h) to the point (10, 0). None of the rental cars are older than 10 years. Enter your answers as decimals. 7(a). What is the height for the line when the age of the car is zero?
Answers
Answer:
10 years
Step-by-step explanation:
Given
Decline from (0,h) to (10,0)
See attachment for graph
Required
Determine the age when height = 0
The function of the graph is represented as: (age, height)
So, we need to read from the graph the corresponding value of age (on the x-axis) when height = 0 (i.e. the y-axis)
From the attached graph;
[tex]age = 10[/tex] when [tex]height = 0[/tex]
Hence, the age of the car is 10 years
URGENT (WILL GIVE BRANLIEST) whats 1 + 1?
Answers
Answer:
2
Step-by-step explanation:
1 + 1 = 2
Have a nice day!
and can I maybe have brainliest?
Answer:
1+1=2
Step-by-step explanation:
hold up one finger then add another and it equals two: )
Hope this helps!
Have a great day!
- Hailey
Can anyone please help me with this question?
Answers
Answer:
d
Step-by-step explanation:
The Robotics Manufacturing Company operates an equipment repair business where emergency jobs arrive randomly at the rate of three jobs per 8-hour day. The company's repair facility is a single-server system operated by a repair technician. The service time varies, with a mean repair time of 2 hours and a standard deviation of 1.5 hours. The company's cost of the repair operation is $28 per hour. In the economic analysis of the waiting line system, Robotics uses $35 per hour cost for customers waiting during the repair process. What are the arrival rate and service rate in jobs per hour
Answers
Answer:
The correct answer is:
[tex]\lambda=0.375 \ jobs \ per \ hour[/tex][tex]\mu=0.5 \ jobs \ per \ hour[/tex]Step-by-step explanation:
The given values are:
Service time varies,
Repair time = 2 hours
Standard deviation = 1.5 hours
Robotics uses per hour cost,
= $35
Company's cost per hour,
= $28
(a)
⇒ Arrival rate = Jobs per hours
then,
= [tex]\frac{8 \ hours}{3 \ jobs}[/tex]
= [tex]2.666 \ hours \ per \ job[/tex]
The jobs per hour will be:
⇒ [tex]\lambda=\frac{1}{2.666}[/tex]
[tex]=0.375[/tex]
(b)
⇒ Service rate = jobs per hour
then,
μ = [tex]\frac{1 \ repair \ job}{2 \ hours}[/tex]
= [tex]0.5 \ jobs[/tex]
Please help me! NO sites or links please!
xoxo
Answers
first you change all the denominator to the same 1/8x2 = 2/16 and 5/16 no need to change and 3/8x2 = 6/16 . And then you add them all together and it will be the answer of D ( you don’t need to add the denominator)
The Wells family uses up a
1
2
-gallon jug of milk every 3 days. At what rate do they drink milk?
Simplify your answer and write it as a proper fraction, mixed number, or whole number
Answers
Answer:
4 gallons/1 day
Step-by-step explanation:
What is a rate? A rate is writing a ratio in fraction form. A ratio is the proportion of two things. (ex: for every 1 dog, there are two cats.)
Creating the ratio: For the ratio, there is no given amount of which one needs to come first, but because it is about the milk, I put that first. In the problem it says 12 gallons for 3 days so: 12/3
Simplifying: To simplify, think of the largest factor between the two numbers. If you can't immediately, think of one factor in common and keep simplifying. In this case, 4 is the greatest common factor between these. To simplify, divide both sides by four, and that is your answer: 4: 1
Given tan theta = -2 and pi/2 < theta < pi; find cos2theta.
a. - 4/3
b.- 4/5
c. 3/4
d. - 3/5
PLEASE HELP ASAP
Answers
Answer:
Cos 2theta = -3/5
Step-by-step explanation:
Given that;
tan theta = -2
tan theta = -2/1 = opp/adj
hyp^2 = (-2)^2+1^2
hyp = √4+1
hyp = √5
sin theta = opp/hyp
sin theta = -2/√5
Cos theta = adj/hyp
Cos theta = -2/√5
Cos 2theta = 1-2sin^2 theta
Cos 2theta = 1- 2(-2/√5)^2
Cos 2theta = 1- 2(4/5)
Cos 2theta = 1- 8/5
Cos 2theta = (5-8)/5
Cos 2theta = -3/5
hi guys what is and can u please do the method 4050 divided by 100
Answers
Answer:
40.5
Step-by-step explanation:
what i do is I divided first by 10. because 100 is 10x10.
so 4050 divided by 10 is 405.
405 divided by 10 is 40.5
4050 divided by 100 = 40.5
How many sides does a polygon have if the sum of the interior angles is 3420
Answers
Answer: 21 sides
Step-by-step explanation: (n-2)=3420 you should divide each side by 180
Katie needs 3/4 cup sugar to make cookies. She only has 1/3. How much more sugar does Katie need?
Answers
Answer:
I think it is 5/12 but might be wrong
Step-by-step explanation:
Subtracted 1/3 from 3/4
Forbes reports that women trust recommendations from Pinterest more than recommendations from any other social network platform (Forbes website, April 10, 2012). But, does trust in Pinterest differ by gender? The following sample data show the number of women and men who stated in a recent sample that they trust recommendations made on Pinterest. Women Men Sample 150 170 Trust Recommendations Made on Pinterest 117 102 a. What is the point estimate of the proportion of women who trust recommendations made on Pinterest (to 2 decimals)?
Answers
Answer:
The point estimate of the proportion of women who trust recommendations made on Pinterest is of 0.78.
Step-by-step explanation:
To find the point estimate of the proportion of women who trust recommendations made on Pinterest, we find the sample proportion.
In this question:
150 women
117 trust recommendations made on Pinterest.
Point estimate:
[tex]p = \frac{117}{150} = 0.78[/tex]
The point estimate of the proportion of women who trust recommendations made on Pinterest is of 0.78.
Found on __, genes determine which __ your cells will make.
(Which word belongs in the blanks?)
Variants, Organism, structure, function, mutations, proteins, genes.
Answers
Found on organism, genes determine which protein your cells will make.
What is genes?A gene is a fundamental unit of heredity that encodes the production of a gene product as a sequence of nucleotides in DNA.
Genes, which may be found on the organism, govern which protein your cells will produce.
Found on organism, genes determine which protein your cells will make.
Hence, organism,and protein are the correct answer.
To learn more about the genes, refer:
https://brainly.com/question/8832859
#SPJ2
The graph of y = f(x) is shown below. Find all values of x for which f(x) > 0.
Answers
Answer:
from 2 to 6
or x [2,6]
I hope it's right
if you have 10 gums and then you take out 5 how much will you have left
Answers
Answer:
10, cos gums can't be removed
Answer:
5
Step-by-step explanation:
this is a standard subtraction problem:
10 - 5 = 5
So you have 5 gums left
You are asked to draw a triangle with side lengths of 10 inches and 13 inches. What is the longest whole number length that your third side can be?
Answers
Answer:
22
Step-by-step explanation:
10 plus 13 equals 23, so if it is more than that than the lines wont be able to connect. if it is 23 exactly, the triangle will be a stright line, not a triangle, so it is 22.
Answer:
22
Step-by-step explanation:
triangle inequality theorem:
10 + 13 > x
x < 23
10 + x > 13
x > 3
third side: 3 < x < 23
may someone please help? thank you!
Answers
Answer:
[tex]6\sqrt2\\OR\\8.48528137[/tex]
Step-by-step explanation:
The area of a sector of a circle is found by:
[tex]A = \frac{\theta*r^2}{2}[/tex]
The question asks for the radius so the equation above can be repurposed
[tex]r = \sqrt\frac{2A}{\theta}[/tex]
A = 3pi
angle = pi/12
[tex]\frac{6\pi}{\pi/12} = \frac{72\pi}{\pi} = 72[/tex]
[tex]\sqrt{72} = 6\sqrt2 = 8.48528137[/tex]
What is the total surface area ?
Answers
Answer:
The answer is 126.
Step-by-step explanation:
If you multiply 2*9 first, you get 18. Then multiply 18 by 7. The answer will be 126. I hope this helps.
Algebra 2
L.3 Multiply polynomials BGN
Answers
Answer:
x² + 4x
Step-by-step explanation:
Area of the rectangle = length × width
length = x + 4
width = x
Therefore,
Area = x(x + 4)
Area = x*x + x*4
x² + 4x
I WILL GIVE YOU BRAINERLEST AND A LIKE
The area of a triangle is 20 square feet.
What are the height and base of the
triangle?
Answers
What is { 1 + 7 - 6 + 99 }
Answers
1 + 7 - 6 + 99 = 101
Step-by-step explanation:
7 + 1 = 8
8 - 6 = 2
99 + 2 = 101
Hope to be brainliest! #SpreadTheKnowledge
Answer:
101
that was easy:D
mark me as brainliest plz
Solve 3≥y−2. Graph the solution. The solution is
Answers
Answer:
y ≤ 5
Step-by-step explanation:
too lazy to explain :/
Which of the following best describes the correlation coefficient of r = -0.09 ?
Answers
convert 0.5t5kg5hg to kilogram
Answers
Answer:
505.5kg
Step-by-step explanation:
To convert 0.5t5kg5hg to kilogram, first we need to convert 0.5t and 0.5hg to kg as shown;
1t = 1000kg
0.5t = 0.5 *1000
0.5t = 500kg
Similarly
1hg = 0.1kg
5hg = 5 * 0.1
5hg = 0.5kg
Adding up;
0.5t5kg5hg = 500kg+5kg+0.5kg
0.5t5kg5hg = 505.5kg
Hence the conversion to kg is 505.5kg
How many solutions does this system of equations have?
Answers
Answer:
this equation will have 2 solutions
Find lateral surface
area of the play tent.
h = 4 in
14 in
5 in
5 in
W
6 in
Answers
Answer:
224 in.²
Step-by-step explanation:
The tent has a shape of a triangular prism. So, we are looking for the Lateral surface area of a triangular prism.
Lateral surface area of a triangular prism = Perimeter of base × height of prism
Perimeter of base = 5 + 6 + 5 = 16 in.
Height of prism = 14 in.
Plug in the values
Lateral Surface Area = 16 × 14 = 224 in.²