Answers
The exact value of cos(θ/2) is:
\(cos(\frac{\theta }{2}) = \right-\sqrt{\frac{1}{122} }\)
How to find the exact value of cos (θ/2)?To find the exact value of cos(θ/2), we can use the half-angle formula for cosine:
\(cos(\frac{\theta }{2}) = \right\pm\sqrt{\frac{1+cos\theta}{2} }\)
First, let's find the value of cos(θ) using the given information about θ:
Given:
tan(θ) = 11/60
θ lies in the 3rd quadrant (π < θ < 3π/2)
In the 3rd quadrant, both sin(θ) and cos(θ) are negative.
tan(θ) = opposite/adjacent
Also, in the 3rd quadrant, both opposite and adjacent are negative.
Thus,
opposite = -11
adjacent = -60
hypotenuse = √[(-60)² + (-11)²] (Pythagoras theorem)
hypotenuse = 61
cos(θ) = adjacent/hypotenuse
cos(θ) = -60/61
Finally, we can substitute these values into the half-angle formula for cosine:
\(cos(\frac{\theta }{2}) = \right\pm\sqrt{\frac{1+(\frac{-60}{61})}{2} }\)
\(cos(\frac{\theta }{2}) = \right\pm\sqrt{\frac{\frac{1}{61} }{2} }\)
\(cos(\frac{\theta }{2}) = \right\pm\sqrt{\frac{1}{122} }\)
Since the cos(θ/2) is negative. Therefore, the exact value of cos(θ/2) is:
\(cos(\frac{\theta }{2}) = \right-\sqrt{\frac{1}{122} }\)
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Related Questions
Please help and thank you
Answers
Daniella: Were you thinking of perpendicular lines?
Ori: It seems like you've got the basic idea, but your definition could be more precise.
Kaori: Yes! Well done. Here, have a cookie. You've earned it.
The figure shows four box-and-whisker plots. These represent variation in travel time for four different types of transportation from the beginning to the end of one route.
Conrad is at one end of the route. He is trying to decide how to get to an appointment at the other end. His appointment is in 30 minutes. Which type of transportation is LEAST likely to take more than 30 minutes?
Select one:
a.
bus
b.
car
c.
subway
d.
train
Answers
Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.
How to Interpret a Box-and-whisker Plot?
In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.
The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.
Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.
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Help !!
centimeters and millimeters <3
Answers
1 cm = 10 mm. Length of book : 28 cm. Length of book = 280 mm. This shows that measurements in mm are the same but look to have a higher number .
How to compare centimeters and millimeters ?The conversion factor provided states that 1 cm is equal to 10 mm, which means that 1 cm is made up of 10 individual millimeters.
The length of my book in when measured in millimeters is 280 mm.
In centimeters, this is therefore:
= 280 mm / 10 cm /mm
= 28 cm
Although the numerical value appears higher when expressed in millimeters, it is important to note that the actual length of the book remains the same.
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The cost table shows the average cost, a(x), of
producing x number of earbuds.
When verifying that a function represented in another
table is the inverse of the given cost function, which
ordered pair can be expected?
2 20
a(x) 52
25 30
67.5 84
O (20, 20)
O (52, 20)
O (20,52)
O (52,52)
Answers
Reverse the numbers in the table to get:
(52,20) (67.5,25) and (64,30)
The answer would be (52,20)
The ordered pair can be expected will be (52, 20). Then the correct option is B.
What is the inverse function?Let the function f is given as
y = m(x + a) + c
Then the inverse function of the function f will be given by swapping x with y and y with x.
The cost table shows the average cost, a(x), of producing x number of earbuds. When verifying that a function represented in another table is the inverse of the given cost function.
(2, 20), (a(x), 52), (25, 30), (67.5, 84)
The ordered pair of the inverse function is given as,
(20, 2), (52, a(x)), (30, 25), (84, 67.5)
The ordered pair can be expected will be (52, 20). Then the correct option is B.
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Find the value of x in this case.
Answers
Answer:
x = 18
Step-by-step explanation:
B > = C >
2x = ?
2x + 8x = 180
10x = 180
----- = ----
10 10
x = 18
2(18) = 36
8(18) = 144
144 + 36 = 180
Nicholas put 1,012 baseball cards into boxes. He put 22 cards in each box. How many boxes did Nicholas need for these baseball cards?
Answers
Answer:
46 boxes
Step-by-step explanation:
1012 / 22 = 46
A Triangle has a height that is half of 28 yards and an area of 56 yards^2. What is the length of the base of the trangle?
Answers
The length of the base of the triangle is 8 yards whose height is half of 28 yards.
What is triangle?A triangle is a two-dimensional geometric shape that is formed by three straight lines that connect three non-collinear points. These three lines are called the sides of the triangle, and the points where the sides meet are called the vertices of the triangle.
According to question:The following formula provides the area of a triangle:
Area = (1/2) x base x height
We are given that the height of the triangle is half of 28 yards, which is:
height = 1/2 x 28 = 14 yards
We are also given that the area of the triangle is 56 square yards. Substituting these values into the formula for the area, we get:
56 = (1/2) x base x 14
Simplifying this equation, we get:
56 = 7 x base
Dividing both sides by 7, we get:
base = 8
Therefore, the length of the base of the triangle is 8 yards.
The vertices are typically denoted by letters, such as A, B, and C. The three angles formed by the sides are also part of the triangle.
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(8.03 LC)
Aaron collects 54 rocks at the beach. He wants to give an equal number of rocks to 6 of
his friends. How many rocks did each of Aaron's friends get?
If r represents the number of rocks each friend will get, which equation could be used to
solve the problem?
Answers
Answer:
9, 54=6r
Step-by-step explanation:
54/6=9 rocks
54=6r
how much would $300 invested at 4% interest compounded monthly be worth after 8 years? round your answer to the nearest cent
Answers
Answer:
412.92
Step-by-step explanation:
\(A = P(1+\frac{r}{n} )^{nt}\)
A: Amount, P: Principal, r: interest, n: no.of times compounded yearly and t: time in years
We have P = 300
r = 4% = 0.04
n = 12 (compounded monthly)
t = 8
\(A = 300(1+\frac{0.04}{12} )^{12*8}\\\\300(\frac{12.04}{12} )^{96}\\\\= 412.92\)
An amount of Birr 500 is deposited in an account at the end of each six-month period with an interest computed at 6% compounded semi-annually. How many years does it take for the amount to reach Birr 56,398.43?
Answers
It would take approximately 17.12 years for the amount to reach Birr 56,398.43 with a deposit of Birr 500 at the end of each six-month period, compounded semi-annually at an interest rate of 6%.
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Final amount
P = Principal amount (initial deposit)
r = Annual interest rate (in decimal form)
n = Number of compounding periods per year
t = Number of years
In this case, the principal amount is Birr 500, the annual interest rate is 6% (or 0.06), and the interest is compounded semi-annually, so there are 2 compounding periods per year.
We need to find the number of years (t) it takes for the amount to reach Birr 56,398.43.
Let's substitute the given values into the formula and solve for t:
56,398.43 = 500(1 + 0.06/2)^(2t)
Divide both sides by 500:
112.79686 = (1 + 0.03)^(2t)
Take the natural logarithm of both sides to eliminate the exponent:
ln(112.79686) = ln(1.03)^(2t)
Using the property of logarithms, we can bring down the exponent:
ln(112.79686) = 2t * ln(1.03)
Now, divide both sides by 2 * ln(1.03):
t = ln(112.79686) / (2 * ln(1.03))
Using a calculator, we find t ≈ 17.12.
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Can you help me in this problem algebra
Answers
Answer:
2^4*2^5=2^(4+5)=2^9
Step-by-step explanation:
When dealing with operations with exponents and multiplication, the exponent operations always come first. So while the exponent 9 is correct for the answer, 4 is incorrect.
For example, if you were to solve each operation and eliminate every exponent, you would have
2^4*2^5=16*32=512 which is the same as 2^9=512.
As you can see, the exponent operation must come before the multiplication.
Michael makes $3.00 more an hour than Max. Together they make $45.00 an hour.how much does Max make per hour
Answers
Answer:
$21.00
Step-by-step explanation:
1(x+3)+x=45
x+3+x=45
x+x=42
2x=42
x=21
Find the amount (future value) of the ordinary annuity. (Round your answer to the nearest cent.)
$300/week for 9 1/2
years at 5.5%/year compounded weekly
Answers
Answer: $227,226.51
Step-by-step explanation:
First, we need to convert the period to weeks.
9 1/2 years = 9.5 years
1 year = 52 weeks
9.5 years = 494 weeks
Next, we can use the formula for the future value of an annuity:
FV = (PMT x (((1 + r/n)^(n*t)) - 1)) / (r/n)
where:
PMT = payment amount per period
r = annual interest rate
n = number of compounding periods per year
t = number of years
Plugging in the given values:
PMT = $300
r = 0.055 (5.5% expressed as a decimal)
n = 52 (compounded weekly)
t = 9.5 years = 494 weeks
FV = ($300 x (((1 + 0.055/52)^(52*494)) - 1)) / (0.055/52)
FV = $227,226.51
Therefore, the future value of the annuity is approximately $227,226.51.
Find the area of this parallelogram.
A) 20 B) 24 C) 40 D) 60
Answers
\(\underline{\clubsuit{\bf{Given-}}}\)
Height of the Parallelogram = 4cmi.e, H = 4cm
Breadth of the Parallelogram = 10cmi.e, B = 10cm
Measure a side of the Parallelogram = 6cm.PS - Neglecting this because it is given just to puzzle us nothing else.
\(\underline{\clubsuit{\bf{To\:find-}}}\)
the area of the Parallelogram.\(\underline{\clubsuit{\bf{Concept-}}}\)
— Area of Parallelogram Formula
A parallelogram's area is defined as the space enclosed by two pairs of parallel lines. Since a rectangle and a parallelogram have identical properties, the area of a parallelogram equals the area of a rectangle.
— What's the procedure to find?
To find the area of the parallelogram, we have to multiply the base (denoted by B) of the perpendicular by its height (denoted by H). We should keep in mind that the base and the height of the parallelogram are perpendicular to each other, whereas the lateral side of the parallelogram is not perpendicular to the base. Thus, a dotted line is drawn to represent the height.
— Formula
Area of Parallelogram = Breadth (B) × Height (H)
\(\underline{\clubsuit{\bf{Solution-}}}\)
Applying the formula and putting the values stated above,
\(\rightarrow{\sf{Area=10\times4}}\)
\(\rightarrow{\boxed{\bf{Area=40cm^2}}}\)
Hence, the area of the Parallelogram is 40cm².
Is (1, 2) solution for this system of inequalities ?
Answers
Answer:
MAYBE
Step-by-step explanation:
Calculate the area of a circle with a radius of 5 meters
Answers
Ans: pi (5)^2 = 78.5( cor. to 3 sig. fig)/ 25 pi
g(x) = -3x2 - 4x + 12, find g(-4).
Answers
Answer:
Your answer is -20
Hope that this is helpful. Vote and like it
Answer:
11
Step-by-step explanation:
Josh pays 7.59$ for 2.2 pounds of ground Turkey. what is the price per pound of turkey
Answers
Answer:
$3.45 per pound of turkey.
Step-by-step explanation:
$7.59 for 2.2[0] pounds of turkey
x = 1 pound of turkey.
Divide 7.59 ÷ 2.20
$3.45 is your answer.
You could also use a ratio table, but with lots of trial and error!
Hope this helps :)
Answer:
the ans is 3.45$... good luck
Brady started to fill the box shown with some unit cubes.
Enter the total number of unit cubes needed to completely fill the box.Include the unit cubes already shown in your total.
Answers
Answer:
210
Step-by-step explanation:
Step 1: 6 rows and 6 columns each side so 6*6=36
Step 2: we have 6 sides so 36*6=216 cubes
Step 3: substract 6 cubes from the total since each row and column shares the same cube 216-6=210 cubes
The total number of unit cubes is A = 210 cubes and volume is V = 216 units³
What is the Volume of a Rectangle?The volume of the rectangle is given by the product of the length of the rectangle and the width of the rectangle and the height of the rectangle
Volume of Rectangle = Length x Width x Height
Volume of Rectangle = Area of Rectangle x Height
Given data ,
Let the height of the rectangle be = 6 units
Let the length of the rectangle be = 5 units
And , let the width be = 7 units
So , Volume of Rectangle = Length x Width x Height
V = 6 x 5 x 7
V = 210 units³
Hence , the number of unit cubes is A = 210
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What is 12 1/2 expressed as a fraction?
3/25
1/8
6/25
1/4
Answers
Answer:
1/8
Step-by-step explanation:
Answer:
25/2
Step-by-step explanation:
see if we break it down
12 1/2
(12x2+1)/2
25/2
we cant break it down so leave it like that
I want a way to solve this question
Answers
Answer:
log xy3 the perimeter of the length in it multiply it 3 times you will get the answer. and try multiplying 6.1cm to 5kg
Solve for v.
2(4v-9)=14
Answers
Answer:
v=4
Step-by-step explanation:
2(4v-9)=14
2*4v 2*9
8v-18=14
+18 +18
8v 32
v=4
sorry if that looks confusing
Pam is a wedding planner She is setting up a room to seat at least 100 guests. She has some tables that seat 10 people and some tables that seat 5 people. She only has 10 of the tables that seat 5.
1. Let x = the number of 10-person tables, and y = the number of 5-person tables. Write an inequality to describe the number of tables Pam could set up for the wedding.
2. Write a second inequality based on the fact that there are only 10 tables that seat 5.
Answers
Answer:
1. 10x + 5y ≥ 100
2. y ≤ 10
If pand q vary inversely and pis 28 when Q is 29. determine q when p is equal to 14.
Answers
9514 1404 393
Answer:
q = 58
Step-by-step explanation:
If the variation is inverse, when p is multiplied by 1/2, q will be multiplied by the inverse (reciprocal) of 1/2, which is 2/1 = 2.
When p = (1/2)(28), q = (2)(29) = 59
q = 58
Jordan has a part-time job which pays $75 a week. He has already saved $55 toward the purchase of a $400
could use to find the minimum number of weeks Jordan must work to have enough money to buy the iPhone
Answers
Answer:
5 weeks
Step-by-step explanation:
The amount of money he has to earn in order to buy the phone is: 400-55 = 345( dollars)
He gets 345 dollars in: 345÷75= 4 weeks and remains 45 dollars
So he needs to work for 1 more week to have enough money to buy the phone
So he needs to work at least 5 weeks
I need help ASAP pleasee
Answers
Answer:
The answer is 4 1/2
Step-by-step explanation:
Because A to C is 2 1/4 so all you have to do add 2 1/4 + 2 1/4 which will equal 4 1/2
1)if the equations 2x +y=7 and x-y= 2 are solved simultaneously, then y =
(a)1 (b)-2 (c)-1 (d)+2 (e)3
2)Find the H.C.F of 12, 15 and 18.
(a) 2 (b)6 (c) 4 (d)5 (e)3
3)Express 100011two as a decimal number.
(a) 32 (b) 33 (c) 34 (d) 35 (e) 36
Answers
Answer:
Step-by-step explanation:
1) 2x + y =7 -------------(I)
x - y = 2 -----------(II)
2x + y = 7
x - y = 2 {Now add both the equations. 'y will be cancelled}
3x = 9
x = 9/3
x = 3
Plugin x = 3 in equation (I)
2*3 + y = 7
6+ y = 7
y = 7 - 6 = 1
Answer: a) y = 1
2) Prime factorize 12 , 15 and 18
12 = 2 * 2 * 3
15 = 3 * 5
18 = 2 * 3 * 3
HCF = 3
e) 3
Answer:
one ×=y-7/2
two y=x-2
number 2 3
I didn't find any decimals
Danica made $319 babysitting last month. In the that month, She babysat for a total of 29 hours. How much money did Dianica make per hour?
Answers
Answer:
$11/hr
Step-by-step explanation:
$319 divided by 29 hours she worked= getting paid 11/hr
Nelson lands 4650 on 2% interest rate. He plans to pay this after 2 months. What will the total principal and interest payment be?
Answers
The total principal and interest payment that Nelson will have to pay after 2 months is $4665.50.
To calculate the total principal and interest payment, we need to determine the interest amount and add it to the principal.
First, let's find the interest amount:
Interest = Principal x Interest Rate x Time
Given:
Principal = $4650
Interest Rate = 2% per year
Time = 2 months
Since the interest rate is given on an annual basis, we need to convert the time from months to years. There are 12 months in a year, so 2 months is equivalent to 2/12 = 1/6 years.
Interest = $4650 x 0.02 x (1/6) = $15.50
Now, we can calculate the total principal and interest payment:
Total Payment = Principal + Interest
Total Payment = $4650 + $15.50 = $4665.50
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Determine the shaded areas part 2
Answers
9514 1404 393
Answer:
(a) cannot be determined
(b) 44 cm^2
(c) 87 m^2
(d) 180 m^2
(e) 132 m^2
Step-by-step explanation:
(a) missing a horizontal dimension
__
(b) The difference between the bounding rectangle and the lower-left cutout is ...
(8 cm)(7 cm) -(3 cm)(4 cm) = (56 -12) cm^2 = 44 cm^2
__
(c) The difference between the bounding rectangle and the center cutout is ...
(13 m)(7 m) -(4 m)(1 m) = (91 -4) m^2 = 87 m^2
__
(d) The difference between the bounding rectangle and the two cutouts is ...
(20 m)(25 m) -(16 m)(20 m) = (20 m)(25 -16) m = (20 m)(9 m) = 180 m^2
__
(e) The difference between the bounding rectangle and the two cutouts is ...
(14 m)(12 m) -(12 m)(3 m) = (12 m)(14 -3) m = (12 m)(11 m) = 132 m^2