Answers
[tex]\text{Given that,}\\\\[/tex]
[tex]~~~~~~~\cos \theta = \dfrac 89\\\\\\\implies 2\cos^2 \left(\dfrac{\theta}2 \right) -1 = \dfrac 89~~~~~~;\left[1+ \cos 2\theta = 2\cos^2 \theta \right]\\\\\\\implies 2 \cos^2 \left(\dfrac{\theta}2 \right)= \dfrac 89 +1\\\\\\\implies 2 \cos^2 \left(\dfrac{\theta}2 \right)=\dfrac{17}9\\\\\\\implies \cos^2 \left(\dfrac{\theta}2 \right) = \dfrac{17}{18}\\\\\\\implies \cos \left(\dfrac{\theta}2 \right)=\sqrt{\dfrac{17}{18}}~~~~~~~~~~~;\left[\text{Positive value of} ~\cos \left(\dfrac{\theta}2\right) \right][/tex]
[tex]\implies \cos \left(\dfrac{\theta} 2 \right) =\dfrac{\sqrt{17}}{\sqrt{9 \times 2}}\\\\\\\implies \cos \left(\dfrac{\theta} 2 \right)=\dfrac{\sqrt{17}}{3\sqrt 2}\\\\\\\implies \cos \left(\dfrac{\theta} 2 \right)=\dfrac{\sqrt{17} \cdot \sqrt 2}{3\cdot 2}\\\\\\\implies \cos \left(\dfrac{\theta} 2 \right)=\dfrac{\sqrt{34}}{6 }[/tex]
Related Questions
Find the slope of the line that is parallel and perpendicular to the following equation.
y + 4 = -3(x +1)
Answers
Answer:
Parallel: -3
Perpendicular: 1/3
Step-by-step explanation:
First I would convert the equation into slope-intercept form to more easily identify the slope:
[tex]y+4=-3x-3\\ y=-3x-7[/tex]
Slope-intercept form is defined as y=mx+b where m is the slope and b is the y-intercept so we can identify the slope of this line as -3.
When a line is parallel to another line, this means that they have the same slope, therefore the slope of the line parallel to the equation is -3.
Perpendicular lines will have slopes that are negative reciprocals of each other, the negative reciprocal of -3 is 1/3; therefore, the slope of the line perpindicular to the equation is 1/3.
Answer:
parallel slope = -3
perpendicular slope: [tex]\sf \bold{\frac{1}{3} }[/tex]
Explanation:
y + 4 = -3(x +1)y + 4 = -3(x) - 3y = -3(x) - 3 - 4y = -3x - 7comparing with y = m(x) + b [ "m" is the slope, "b" is the y-intercept ]
slope: -3y-intercept: -7Parallel/Tangent slope:
m₁ = m₂ (same)
Perpendicular/Normal slope:
m₁ * m₂ = -1 (negatively reciprocal)
⇒ Here parallel slope:
m = -3⇒ Here perpendicular slope:
-3 * m₂ = -1m₂ = -1/-3m₂ = 1/3Solve:
n x 3.6 when n = 0.72
Answers
Answer:
Substitute n to that 0.72 and multiply it from 3.6
answer would be 2.592
Step-by-step explanation:
HELP ASAP!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
0.36
Step-by-step explanation:
0.67 - 0.31 = B
B = 0.36
I hope this helps!
PLS HELP WILL MARK YOU BRAINLIEST! NO FAKE ANSWERS!
Answers
Answer:
A.
Mean-103.0625
Median- 8, 9
Mode- 8, 1
B.
They should use the shoe size 6, because it has the most women waering it.
Your Welcome!
Step-by-step explanation:
Mean:-
5+5.5+6+6.5+7+7.5+8+8.5/854/86.9Median:-
Total terms 8
Median =n/2th term +(n/2+1)th term
Median=6.5 and 7Mode:-
No modes
PLS HELP ASAPPPPP!!!!!
Answers
Answer:
first you write number 4,second the frequency you write number 5...for this data
How do I solve this hmm
Answers
Answer:
put the numbers that are x into the equation. you always try to find y in this problem
Step-by-step explanation:
y=x+8
the first x is 0 so we do
y= 0+8
y=8
and you keep repeating this where x=1 and x= 2
Find the surface area. HELP PLEASE!!!!
Answers
Answer:
I think the answer is 792
Answer:
SA = 696cm^2
Step-by-step explanation:
First we need to identify the shapes
There are 3 rectangles and 2 triangles
Now the individual surface area for each shape
20 x 10 = 200 (1 rectangle)
1/2(12 x 8) = 48 (1 triangle)
Now we add them together
(200 x 3) + (48 x 2) = 696
What is the measure of the third angle in a triangle if the sum of the other two angle measures is 110°?
Answers
Step-by-step explanation:
the third angle in a triangle= 70
help me please please with all of them
Answers
Step-by-step explanation:
for question one the answer is the intial area of fire
2. is the decay factor
3. 38400
4. the initial population
P,Q and R are points on a circle, centre O, if angle OPQ=36 degree, what is the size of angle PRQ.
Answers
Answer:
18
Step-by-step explanation:
an angle subtended by a chord to the center is twice to that subtended by the same chord to the circumference
Is –12,365 − –110 positive or negative?
Answers
Answer:
Negative
Step-by-step explanation:
This is the same as saying -12,365 + 110
This equals -12,265
Hope that helps!
Answer:
Same sign - Positive
Different sign - Negative
only for some maths
How to find the base of a triangle if your height is 6 inches.
Answers
Answer:
Triangle Area = 1/2 x Base Length x Height Example:
(- 18) × (- 5) × (- 4) =
Answers
Answer:
−360
Step-by-step explanation:
Express as a fraction in the simplest form: 43.5%
a. 435/1000
b. 870/200
c. 87/200
Answers
Answer:
C
Step-by-step explanation:
43.5 x 10 = 435
435/1000 = 87/200 (simplified)
Which is a factor of both terms of the expression 6f−12?
Answers
Answer:
6(f-2)
Step-by-step explanation:
Answer:
Step-by-step explanation:
If you solve the highest common factor first, then you can look for other factors.
Solution
6 = 2 * 3
12 = 2*2*3
The highest common factor is one 2 and one 3 making 6.
Use the distributive property to show what the 2 factors look like when the common factor is taken out.
6( f - 2)
Other factors.
You could take out just 1 factor like 2 or 3
2(3f - 6)
3(2f - 4)
Answer
I would submit 6(f - 2)
find the measures of m and n
Answers
Answer:
m=3 n=6
Step-by-step explanation:
top diagonals are congruent
9 = 3m
solve for m
m = 3
bottom diagonals are congruent
m + 8 = 2n -1
plug in 3 for m
3 + 8 = 2n -1
solve for n
11 +1 = 2n
12 = 2n
n=6
Suppose a 8-year loan for principal amount
$8500
was taken out. Over the life of the loan
$3400
was paid. If interest did not compound, what was the interest rate per year?
Answers
Step-by-step explanation:
8500× 8
8500
× 8
52000
so,
I will complete your answer
you can any doubt please ask to me
the interest rate per year is = 52000 answer
Find the area of this circle. Use 3.14 for a 11 ft The area of the circle is about ft2. (Round to the nearest hundredth as needed.)
Answers
Answer:
Area of circle is 379.94 feet²Step-by-step explanation:
Given:
Radius of circle = 11 feetTo Find:
Area of circle.Solution:
Here given that radius of circle is 11 feet. Using the formula of area of circle we will get the required area of circle
Area of circle = πr²On substituting the required values:
Area = 3.14 × (11)²
Area = 3.14 × 121
Area = 379.94 feet²
Hence,
Area of circle is 379.94 feet²What is 8 1/3 - 3 1/2?
Answers
Answer:
4 5/6
Step-by-step explanation:
Turn both 8 1/3 and 3 1/2 into improper fractions (just to make it less complicated).
8 1/3 = 25/3
3 1/2 = 7/2
Then, try and make the denominators the same by finding the LCD (least common denominator).
The least common denominator of 3 and 2 is 6. Multiply both the denominators (3 and 2) to get 6, multiply the numerator with it as well (I can't explain this part properly, but the fractions will somehow explain).
[tex]\frac{25*2}{3*2}[/tex] = [tex]\frac{50}{6}[/tex]
[tex]\frac{7*3}{2*3}[/tex] = [tex]\frac{21}{6}[/tex]
So, then subtract (50/6 - 21/6).
50/6 - 21/6
= 29/6 = 4 5/6
So, 8 1/3 - 3 1/2 is 4 5/6.
X - y = -2 7x + 2y = -5
Élimination method
Answers
Answer:
x = -1, y = 1
Step-by-step explanation:
Multiply the top equation by 2:
[tex]2x - 2y = - 4[/tex]
Leaving the bottom equation unchanged, add the two resulting equations to eliminate y, obtaining:
[tex]9x = - 9[/tex]
Solve this for x, and then substitute this value of x into the bottom equation. Finally, solve for y.
[tex]x = - 1[/tex]
[tex]7( - 1) + 2y = - 5[/tex]
[tex] - 7 + 2y = - 5[/tex]
[tex]2y = 2[/tex]
[tex]y = 1[/tex]
This shows how to copy the triangle, cut the copy into pieces, and form a rectangle.
What is the area of the rectangle?
( ) square millimeters
What is the area of the triangle?
( )square millimeters
Answers
The area of the rectangle and triangle are 48 mm² and 24 mm² respectively.
What is an area?The area is the amount of space occupied by a two dimensional shape or object.
Area of rectangle = length * width = 6 mm * 8 mm = 48 mm²
Area of triangle = (1/2) * base * height = 0.5 * 6 * 8 = 24 mm²
The area of the rectangle and triangle are 48 mm² and 24 mm² respectively.
Find out more on area at: https://brainly.com/question/25292087
Which of the following equations represents the problem "The sum of two consecutive integers is -17"?
2x + 2
2x + 1 = -17
2x = -17
Answers
Answer:
2x + 1 = -17
Step-by-step explanation:
consecutive integers would be
x and x+1
when you add them together its
2x+1
Trying to finish khan academy. I need to simplify. How do I do it?
Answers
Answer:
-5+5k-8k-20
-3k-25
-(3k+25)
Answer:
Step-by-step explanation:
(-5 - -25k) - (8k + 20) =
-(18k - 15)
Sage borrowed $4500 from her parents to buy her a new car. So far she has repaid $2740 How much money does save still owe her parents?
Answers
Answer:1760
Step-by-step explanation:you get the money given by the parents minus the money given back to the parents
A right rectangular prisim has a length of 2 1/2 feet a width of 3 feet and a height of 1 1/2 feet. Unit cubes with side lengths of 1/2 foot are added to completely fill the prisim with no space remaining. What is the volume in cubic feet of the right rectangular prisim?
Answers
Can anyone please answer the attachment
Answers
Answer:
•SEE BELOW•1) NAME OF CIRCLE : CIRCLE ABDE
2) CHORD : SEGMENT DE
3)DIAMETER: SEG DB
4)TANGENT LINE : RAY E
5) SECANT LINE : SEGMENT AB
HOPE IT HELPS!
MARK AS BRAINLIAST.
You took a test and got 12 points on it. The next week, you retook it and got 25% more points than before. How many points did you get when you retook it?
Answers
Answer:
15 points
Step-by-step explanation:
12 divied by .25 =3
so there for it would be 15 points
Answer:
The answer is 15 points. Have a great day:)
Which of the following are identities? Check all that apply.
A. sin(x+y)+ sin(x - y) = 2cos x siny
B. cos(x + y) + cos(x- y) = 2cos x cosy
C. tan(x - 2) = tan x
D. COS(x + y) - cos(x - y) = 2 cos xcosy
Answers
Answer:
B. cos(x+y) + cos(x-y)= 2cosx.cosy
Step-by-step explanation:
cos(x+y) + cos(x-y)
= cosx.cosy - sinx.siny + cosx.cosy + sinx.siny
=cosx.cosy + cosx.cosy
=2cosx.cosy
how do you slove this question i know the answer but don't know how to get it ;A quart of milk costs $0.35. A case of 12 quarts cost $4.08. How much is saved per quart buying the case?
Answers
Answer:
$0.01 or 1 cent.
Step-by-step explanation:
Case: 12 quarts = $4.08
1 quart for case= $0.34
A quart normal= $0.35
0.35-0.34=$0.01
HELP ME: Lee works at a job where her pay varies directly with the number of hours she works. Her pay for 6.5 hours is $49.40. Write a direct variation equation relating Lee’s pay x to the hours worked y. Then find her pay if she works 25 hours in a week. y = 7.6x; $190
Answers
Answer: 90$
Step-by-step explanation:
