Answers
Hi there!
[tex]\large\boxed{cos(\frac{\theta}{2} )= \frac{3}{\sqrt{7}}}[/tex]
[tex]\large\boxed{tan(\frac{\theta}{2}) = \frac{\sqrt{5}}{3}}[/tex]
Begin by recalling that:
sin(θ) = O/H, so:
Opposite side = 3√5
Hypotenuse = 7
We can solve for the adjacent sign using the Pythagorean Theorem:
7² = (3√5)² + b²
49 = 45 + b²
b² = 4
b = 2.
Thus, cosθ = 2/ 7
Use the half angle identity to solve for cos(θ/2):
cos(θ/2) = √(1 + cosθ)
Plug in the value of cosθ:
= √(1 + 2/7) = √9/7, or 3 /√7
Thus:
[tex]cos(\frac{\theta}{2}) = \frac{3}{\sqrt{7}}[/tex]
Calculate tan(θ/2) using the same process but with a different formula:
tan(θ/2) = √(1 - cosθ / 1 + cosθ)
Substitute in the value of cosθ:
tan(θ/2) = √(1 - 2/7)/(1 + 2/7)
= √(5/7)/(9/7) = √5/9 = √5/3
Related Questions
A bear weighs 4,521 grams. How much does the bear weigh in kilograms
Answers
Answer:
A bear weighing 4,521 grams would weight 4.521 kilograms
A movie theater has a seating capacity of 329. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 2388, How many children, students, and adults attended?
___ children attended.
___students attended.
____adults attended.
Answers
Answer:
170 children
74 students
85 adults
Step-by-step explanation:
Given
Let:
[tex]C = Children; S = Students; A = Adults[/tex]
For the capacity, we have:
[tex]C + S + A = 329[/tex]
For the tickets sold, we have:
[tex]5C + 7S + 12A = 2388[/tex]
Half as many as adults are children implies that:
[tex]A = \frac{C}{2}[/tex]
Required
Solve for A, C and S
The equations to solve are:
[tex]C + S + A = 329[/tex] -- (1)
[tex]5C + 7S + 12A = 2388[/tex] -- (2)
[tex]A = \frac{C}{2}[/tex] -- (3)
Make C the subject in (3)
[tex]C = 2A[/tex]
Substitute [tex]C = 2A[/tex] in (1) and (2)
[tex]C + S + A = 329[/tex] -- (1)
[tex]2A + S + A = 329[/tex]
[tex]3A + S = 329[/tex]
Make S the subject
[tex]S = 329 - 3A[/tex]
[tex]5C + 7S + 12A = 2388[/tex] -- (2)
[tex]5*2A + 7S + 12A = 2388[/tex]
[tex]10A + 7S + 12A = 2388[/tex]
[tex]7S + 22A = 2388[/tex]
Substitute [tex]S = 329 - 3A[/tex]
[tex]7(329 - 3A) + 22A = 2388[/tex]
[tex]2303 - 21A + 22A = 2388[/tex]
[tex]2303 +A = 2388[/tex]
Solve for A
[tex]A = 2388 - 2303[/tex]
[tex]A = 85[/tex]
Recall that: [tex]C = 2A[/tex]
[tex]C = 2 * 85[/tex]
[tex]C = 170[/tex]
Recall that: [tex]S = 329 - 3A[/tex]
[tex]S = 329 - 3 * 85[/tex]
[tex]S = 329 - 255[/tex]
[tex]S = 74[/tex]
Hence, the result is:
[tex]C = 170[/tex]
[tex]S = 74[/tex]
[tex]A = 85[/tex]
Answer:
Down Below
Step-by-step explanation:
The answer is actually
162 children
86 students
81 adults
162x5=810
86x7=602
81x12=972
I found the original problem and the total ticket sale was $2384.
So I wrote the answers for the original problem just in case!
Ty for your time!
1 point
3. The dot plot shows the number of hours the students in Mrs. Ferro's
class volunteer each month. Which of the following statements is not
correct?
MRS. FERRO'S CLASS
+
11
+
12
4 5 6 7
10
8 9
HOURS
A. There are a total of 17 students in Mrs. Ferro's class.
B. Exactly 7 students volunteered for less than 7 hours.
C. Less than half of the students volunteer for 9 hours or more.
D. The range is data was 5 hours.
Answers
Answer:
B
Step-by-step explanation:
its not A cause theres 17 kids
its not D
its not c cause less than half of the students volunteer for 9 hours or more
the only one it can be is B because it's not correct theres exactly 6 students less than 7 hours not 6
What is the value of the expression below when x equals 4? 13 + 13x
Answers
Answer:
the answer is 50
Step-by-step explanation:
13+52
65
hope this helps
Multiply 15 by 9 then divide by 2 fraction
Answers
Answer:
15x9 is 130 but, what u mean by divided by 2 fraction?
Step-by-step explanation:
135/ 2 this is correct unless you want a mixed fraction which is 67 and 1/2
Solve and explain please
Answers
Answer:
x = 14Step-by-step explanation:
7x + 9 = 9x - 19. [Corresponding Angles]
=> 9x - 19 = 7x + 9
=> 9x - 7x = 19 + 9
=> 2x = 28
[tex] = > x = \frac{28}{2} [/tex]
=> x = 14 (Ans)
The usual price of a clock was $60. At a sale, it was
sold at a discount of 20%.
a) How much was the discount?
b) Find the selling price of the clock.
Answers
Answer:
$12 off w discount
$48 selling price
Step-by-step explanation:
Answer:
a. 20%=$12.00 b. price was $48.00
Step-by-step explanation:
60*20%=12
60-12=48
9+7 porfis es para aorita ayudemme
Answers
Answer:
16
Step-by-step explanation:
x2+4x+3 solve for x.
Answers
Answer:
(x+1)(x+3)
Step-by-step explanation:
Let's factor x^2+4x+3
x^2+4x+3
The middle number is 4 and the last number is 3.
Factoring means we want something like
(x+_)(x+_)
Which numbers go in the blanks?
We need two numbers that...
Add together to get 4
Multiply together to get 3
Can you think of the two numbers?
Try 1 and 3:
1+3 = 4
1*3 = 3
Fill in the blanks in
(x+_)(x+_)
with 1 and 3 to get...
(x+1)(x+3)
Harry's mother is 64 inches tall, and his father is 6 feet tall. How many inches taller is Harry's father than his mother?
Help please
Answers
Answer:
Harry's father is 8 inches taller than his mother.
Step-by-step explanation:
1 foot=12 inches
12x6=72
72-64=8
Can I please have Brainliest?
The sum of two numbers is 24. Three times the smaller numbers is 3 less than twice the larger number. Find the numbers.
Answers
Answer:
9, 15
Step-by-step explanation:
x = smaller number
y = larger number
system of equations:
x + y = 24
3x = 2y - 3
substitution method:
x = 24 - y
3(24 - y) = 2y - 3
72 - 3y = 2y - 3
72 = 5y - 3
75 = 5y
y = 15
x + 15 = 24
x = 9
What is the solution to the equation shown on the number line?
Answers
Answer:
B
Step-by-step explanation:
x-4=18
+4 +4
x=22
Answer:
22
Step-by-step explanation:
X-4 =18
So now we have to find a number on the line which 4 is deducted from you can get 18 as the answer
So 22-4 = 18
What is the diameter of a hemisphere with a volume of 69292 in?, to the
nearest tenth of an inch?
Answers
Answer:
64.2 in
Step-by-step explanation:
From deltamath
Yeah
what is 0.065 rounded to the nearest tenths?
please help :)
Answers
Answer:
Step-by-step explanation:
0.1 ;-;
use the laws of sine and cosine to find the missing Dimension part 3
Find the f to the nearest whole number
Answers
9514 1404 393
Answer:
12 or 103
Step-by-step explanation:
The given angle is opposite the shorter side, so there will be two solutions.
In order to find f, we need to know angle F. We can find that by first finding angle E.
E = arcsin(e/d·sin(D)) = arcsin(71/62·sin(36°)) = 42.307° or 137.693°
F = 180° -D -E = 180° -36° -{42.307°, 137.693°} = {101.693°, 6.307°}
Then the measure of f is ...
f = sin(F)/sin(D)×d = 62/sin(36°)×sin({101.693°, 6.307°})
f = {103.29, 11.59}
Side f is either 12 or 103.
Answer:
103Step-by-step explanation:
Find ∠E
sin E / 71 = sin 36° / 62sin E = 71 (sin 36°) / 62sin E = 0.673m∠E = arcsin (0.673)m∠E = 42° (rounded)Find m∠F
m∠F = 180° - (36° + 42°) = 102Find f
sin 102° / f = sin 36° / 62f = (62 sin 102°) / (sin 36°) f = 103 (rounded)Statistics urgent
Use n=6 and p=0.85 to complete
Answers
Answer:
I cant see anything on that picture. Wish I could help bruv. I wish I could help. It's a shame innit.
ZA and B are complementary angles. If m_A = (x – 15)° and m ZB = (x + 3)º, then find the measure of ZB.
Answers
Answer:
ZB = 54
Step-by-step explanation:
Complementary angles add to 90 degrees
ZA + ZB = 90
x-15 + x+3 = 90
Combine like terms
2x-12 =90
Add 12 to each side
2x-12+12 = 90+12
2x = 102
Divide by 2
2x/2 = 102/2
x = 51
We want to find the measure of ZB
ZB = x+3
ZB = 51+3
ZB = 54
I
4. Two rectangular corrals are to be made from 100 yds. of fencing. If a rancher wants the
total area to be maximized, what should the dimensions of the coral be?
Answers
The dimensions of the coral if the area is maximized will be 50/3 yards by 25yards.
Measurement is a branch of mathematics used in determining the area and volume of an object.
From the question,
Let the length of the two rectangular corrals be x
Let the length of the three fence section be y
Note that the area of the rectangle A = length * width
A = xy .....1
Also, since the rectangular corrals are to be made from 100 yd, then;
3x + 2y = 100 ..... 2
Divide through by 2
3x/2 + 2y/2 = 100/2
1.5x + y = 50
y = 50 - 1.5x .... 3
Substitute equation 3 into 1 to have:
A = x(50-1.5x)
A = 50x - 1.5x²
Since the total area is to b maximized, this means that:
dA/dx = 0
dA/dx = 50 - 3.0x
0 = 50 - 3x
3x = 50
x = 50/3 yards
Substitute the value of x into equation 3:
y = 50 - 1.5x
y = 50 - 1.5(50/3)
y = 50 - 25
y = 25yards
Hence the dimensions of the coral if the area is maximized will be 50/3 yards by 25yards.
Learn more here: https://brainly.com/question/10369514
HURRY
Which function does this graph represent?
Answers
Answer:
B
Step-by-step explanation:
Hope this helps!
Answer:
the answer is B
Step-by-step explanation:
the answer is B
Six less than two times a number is 20
Answers
Answer:
2x - 6 = 20
2x - 6 + 6 = 20 + 6
2x = 26
x = 13
The number should be 13
Step-by-step explanation:
A tool set is on sale fro $424.15. The original price of the set was $499.00. What percent of the original price is the sales price. (find percent)
Answers
Answer:
499-424.15=74.85
499:100=4.99
74.85:4.99=15 is the percent of the discount
100-15=85 is the percent of the original price that you pay
Step-by-step explanation:
Find the mean of the data in the dot plot below.
Answers
Answer:
the mean is 83.6
Step-by-step explanation:
Answer:
The mean is 83.6 cm
Step-by-step explanation:
81 + 83 +84 + 85 + 85 = 416
416 divided by 5 = 83.6
Find the slope of a line that passes through the points (-7, 3) and (5, 6).
Answers
Answer:
the formula to find slope is m=∆y/∆y
this means m=y2-y1/x2-x1
using this formula
m=5-3/6-(-7)
m=2/13
Answer:
The slope is 0.25
Step-by-step explanation:
You and your friend are selling magazine subscriptions. You sell 8 fewer magazine subscriptions than your friend. Together you sell 42 magazine subscriptions. a. Write a system of linear equations that represent the situation.
b. How many magazine subscriptions did you sell?
c. How many magazine subscriptions did your friend sell.
Answers
Answer:
b. you sold 17
c. your friend sold 25
Step-by-step explanation:
you=y your friend=x
y=x-8
42=x +y
42=x+(x-8)
42=x+x-8
42=2x-8
50=2x
25=x
Use x to solve for y...
y=25-8
y=17
What is the surface area of a storage box that measures 19 centimeters by 16 centimeters by 14 centimeters
Answers
Answer:
surface area = 2(length× breadth) +2(length ×height) +2(height×breadth
I really need help please help
Answers
Answer: tan^-1(5/8) = 32 degrees from horizontal line
Step-by-step explanation: tan (Alfa) = 2000 / 3200 because
Angle from horizontal line. 2000/3200 = 20/32 = 5/8
someone please help me answer this!!
Answers
Zoe supplies customs to a number of theatre companies she recently provided 20 different hats including 44 doors considering this data how many of the 15 has requested from Zoes inventory should you expect to be fedoras
Answers
Answer:
I was searching for the same answer but no one has it smh
Step-by-step explanation:
Need help like right now please
Answers
Answer:
X= 12√3
y=12
Step-by-step explanation:
To find x
Cos30°=x/24
√3/2=x/24
x=12√3
To find y
Sin30°=y/24
1/2=y/24
y=12
hope it helps
have a great day!!
Find x:
sin 60 degrees= opp/hyp
Sin 60 deg = x/ 24
Times 24 both sides
X = 20.78
Find y:
Cos 60 deg= y/ 24
Times both sides 24
y = 12
A 20 ft. beam leans against a wall. The beam
reaches the wall 13.9 ft. above the ground.
What is the measure of the angle formed by the
beam and the ground?
Answers
Answer:
a 44°
Step-by-step explanation:
Think of the right triangle formed by the beam, the ground, and the wall.
The beam is the hypotenuse. For the angle between the ground and the beam, call it angle A, the 13.9 ft side is the opposite leg. The trig ratio that relates the opposite leg and the hypotenuse is the sine.
sin A = opp/hyp
sin A = 13.9/20
sin A = 0.695
A = sin^-1 0.695
A = 44°
