We have verified the identity [tex]csc^2(x)cos^2(x) = csc^2(x) - 1.[/tex]
What is trigonometry?
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, as well as the functions derived from these relationships. The most common trigonometric functions are sine, cosine, and tangent, which are abbreviated as sin, cos, and tan, respectively. These functions are used to model periodic phenomena such as sound waves, ocean tides, and the motion of planets.
To verify the identity [tex]csc^2(x)cos^2(x) = csc^2(x) - 1[/tex], we will start with the left-hand side and manipulate it until we get the right-hand side. Here's the full work:
[tex]csc^2(x)cos^2(x)[/tex] (given)
[tex]= (1/sin^2(x))(cos^2(x))[/tex] (definition of csc)
[tex]= (cos^2(x))/sin^2(x)[/tex] (multiply by reciprocal)
[tex]= (cos^2(x))/(1 - cos^2(x))[/tex](Pythagorean identity)
[tex]= (cos^2(x))/(1 - cos^2(x)) * [(1 + cos^2(x))/(1 + cos^2(x))][/tex] (multiply by conjugate)
[tex]= (cos^2(x)(1+cos^2(x)))/((1 - cos^2(x))(1 + cos^2(x)))[/tex](multiply and simplify)
[tex]= cos^2(x) * (1 + cos^2(x)) / (1 - cos^4(x))[/tex] (expand denominator)
[tex]= cos^2(x) / (1 - cos^2(x))[/tex] (cancel common factor of [tex]1 + cos^2(x))[/tex]
[tex]= csc^2(x) - 1[/tex](definition of csc and simplify)
Therefore, we have verified the identity [tex]csc^2(x)cos^2(x) = csc^2(x) - 1.[/tex]
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Solve.
x−2/5=1/5
Responses
13
12
2
3
Answer:
Step-by-step explanation:
To solve for x in the equation:
x - 2/5 = 1/5
We can start by isolating x on one side of the equation. We can do this by adding 2/5 to both sides:
x - 2/5 + 2/5 = 1/5 + 2/5
Simplifying, we get:
x = 3/5
Therefore, the solution is:
x = 3/5
select the graph of y=2sin(pi/2x)-1
Answer:
The correct graph is D
There are 3 roles and they are assigned randomly to 3 people ( Alice, Bob and Charlie ): Truth teller ( Always tells the truth ) Liar ( Always lies ) Spy ( Can tell truths and lies ) - Alice says she is not the truth teller - Bob says he is not the spy - Charlie says he is not a liar Deduce who has what role?
In conclusion, it is not possible to determine with certainty who has what role.
Given by the solution:
Let's consider each statement one by one:
If Alice is the truth teller, then she is telling the truth, which means she can't be the truth teller, leading to a contradiction. So, Alice can't be the truth teller.
If Alice is the liar, then she is lying, which means she is the truth teller, leading to a contradiction. So, Alice can't be the liar.
If Alice is the spy, then she can either tell the truth or lie. If she tells the truth, then she can't be the truth teller, leading to a contradiction. If she lies, then she can't be the liar, leading to a contradiction. So, Alice can't be the spy.
Therefore, Alice can't have any of the roles.
Bob says he is not the spy.If Bob is the truth teller, then he is telling the truth, which means he can't be the spy, leading to a contradiction. So, Bob can't be the truth teller.
If Bob is the liar, then he is lying, which means he could be the spy. Therefore, Bob can be the liar or the spy.
Charlie says he is not a liar.If Charlie is the truth teller, then he is telling the truth, which means he can't be the liar, leading to a contradiction. So, Charlie can't be the truth teller.
If Charlie is the liar, then he is lying, which means he could be the truth teller or the spy. Therefore, Charlie can be the liar, the truth teller or the spy.
Combining the results from the above statements, we get the following possibilities:
Alice is the spy, Bob is the liar, and Charlie is the truth teller.Alice is the spy, Bob is the liar, and Charlie is the spy.Alice is the spy, Bob is the spy, and Charlie is the liar.In conclusion, it is not possible to determine with certainty who has what role.
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Tyler takes his friends out for pizza and wings. He pays the whole bill of $71.46. He wants to leave an 18% tip. How much does the bill and tip cost Tyler?
The total cost of the bill and tip for Tyler is $71.46. This means that Tyler paid $58.6 for the food and drinks, and an additional $12.86 as a tip for the service.
To calculate how much the bill and tip cost Tyler, we first need to calculate the amount of the tip. We can do this by multiplying the total bill by the percentage of the tip, which is 18% or 0.18 as a decimal.
Tip amount = $71.46 x 0.18 = $12.86
Once we know the tip amount, we can add it to the total bill to find the final cost.
Bill and tip cost = $71.46 - $12.86 = $58.6
Therefore, total bill is $84.32 with tip as $12.86 and bill as $58.6
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The graph below represents the prices, in dollars, of different numbers of pounds of regular bananas. The table below represents the prices, in dollars, of different numbers of pounds of organic bananas.
Which statement correctly compares the prices of regular bananas and organic bananas?
A. Organic bananas cost $0.50 more per pound.
B. Organic bananas cost $0.05 more per pound.
C. Regular bananas cost $0.08 more per pound.
D. Regular bananas cost $0.53 more per pound.
A quarterback completes of passes during the first three quarters of a football game. He completes e pass in the fourth quarter and of his passes for the entire game. How many passes does the quarterback throw in the fourth quarter?
Rounding up to the nearest whole number, the quarterback throws 3 passes in the fourth quarter to complete all of them.
Let's first find out how many passes the quarterback completed in the first three quarters:
18 passes completed out of 33 attempts in the first three quarters
= 18/33 = 0.545 (rounded to three decimal places)
We can then find the total number of passes attempted in the first three quarters by using the fact that the completion rate is the number of completions divided by the number of attempts:
0.545 = 18/x, where x is the total number of attempts in the first three quarters
Solving for x, we get:
x = 18/0.545 = 33
So the quarterback attempted 33 passes in the first three quarters.
Next, we can find the total number of passes attempted in the game by using the completion rate for the entire game:
0.625 = (18 + passes completed in the fourth quarter) / (33 + passes attempted in the fourth quarter)
Multiplying both sides by the denominator:
0.625 × (33 + passes attempted in the fourth quarter) = 18 + passes completed in the fourth quarter
20.625 + 0.625 × passes attempted in the fourth quarter = 18 + passes completed in the fourth quarter
Subtracting 18 and 0.625 × passes attempted in the fourth quarter from both sides, we get:
2.625 = passes completed in the fourth quarter - 0.625 × passes attempted in the fourth quarter
Adding 0.625 × passes attempted in the fourth quarter to both sides, we get:
passes completed in the fourth quarter = 2.625 + 0.625 × passes attempted in the fourth quarter
We don't know the exact number of passes attempted in the fourth quarter, but we can see that for every 1 pass attempted, the quarterback completes 0.625 - 0.545 = 0.08 more passes than in the first three quarters. So to complete all of his passes in the fourth quarter, he needs to attempt:
0.08 × x = 0.08 × 33 = 2.64
Question - A quarterback completes 18 of 33 passes during first three quarters of a football game. He completes every pass in the fourth quarter and 62.5% of his passes for the entire game. How many passes does the quarterback throw in fourth quarter?
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Are the two triangles similar ?
Yes or no?
How do you know ?
Find the length of CYT given that m/CAT=128° and CA =10 in Circle A.
3.14 in your calculation and round to the nearest tenth.
The length of arc CYT is solved to get
= 40.12
How to solve for length of arcLength of arc CYT is calculated using the formula for length of arc
= theta / 360 * 2πR
From the problem, we have that
theta = 360 - 128 = 230
R = radius = CA = 10
π = 3.14sds
plugging in the values we have
= 230 / 360 * 2 * 3.14 * 10
= 23/36 * 20 * 3.14
= 40.1222
= 40.12 (to the nearest tenth)
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What is the conversion of 3/4 to decimal ?
Answer: 0.75
Step-by-step explanation: .
The radius of a semicircle is 2 millimeters. What is the semicircle's perimeter?
Answer:
required perimeter is 12.57mm
6) a (m-2)-m+2=
(7) bc (x-y)+x-y =
Answer:
6) am - 2a - m + 2
7) bcx - bcy + x - y
Step-by-step explanation:
6) a(m - 2) - m + 2
am - 2a - m + 2
7) bc(x - y) + x - y
bcx - bcy + x - y
square root of 2w + 9 + square root of 4 - 3w = 0
As a result, the equation ((2w + 9) + ((4 - 3w) = 0) has no answer.
What in mathematics is the square root?The term "radical" is used to represent the square root or nth elements. Expression with a square base is referred to as a radical expression. Radicand: A value or phrase contained within the radical sign. Equation with radical formulas and factors as radicands is referred to as a radical equation.
√(2w + 9) + √(4 - 3w) = 0
We need to isolate the variable w.
First, we can move the second term to the other side of the equation by subtracting it from both sides:
√(2w + 9) = -√(4 - 3w)
Next, we can square both sides of the equation to eliminate the square roots:
(√(2w + 9))^2 = (-√(4 - 3w))^2
2w + 9 = 4 - 3w
Now, we can simplify and solve for w:
5w = -5
w = -1
In this case, when w = -1, both square roots are defined, and we can substitute this value back into the original equation to verify:
√(2(-1) + 9) + √(4 - 3(-1)) = √7 + √7 = 2√7
Since 2√7 is not equal to 0, our solution is not valid.
Therefore, there is no solution to the equation √(2w + 9) + √(4 - 3w) = 0.
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Caleb took 18 photos at the zoo. One sixth of his photos are of giraffes. How many of Caleb's photos are of giraffes?
The amount of photos that are giraffes is 3
1.) Caleb has 18 photos from going to the zoo.
2.) One sixth of them are giraffe pictures.
So basically, what you want to do is divide 18 by 6 = 3
The answer is : There are 3 giraffe photos out of the total 18 photos.
need help asap
Which ordered pair (from the table in part A) represents the initial value? What does the initial value represent in this problem? (1-2
sentences)
Part D:
What is the rate of change in this equation? What does the rate of change represent in this problem? (1-2 sentences)
Table from part A:
The table of values for y = -128x + 3840 is:
xy
0 3840
5 3200
8 2816
10 2560
30 0
C) The ordered pair that represents the initial value of the function is of (0,3840), meaning that the graph of the function crosses the y-axis at the value of y = 3840.
D) The rate of change of the equation is of -128, meaning that when x increases by one, y is decreased by 128.
How to define a linear function?The following is the definition of a linear function's slope and intercept:
y = mx + b.
In which:
m is the slope, representing the rate of change, that is, by how much y changes when x is increased by one.
The value of y at x=0 is represented by the intercept, b. Hence the ordered pair is of (0,b).
The function is defined as follows for this problem:
y = -128x + 3840.
The slope and intercept are therefore given as follow:
m = -128, b = 3840.
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what is left skewed histogram?
A left-skewed histogram is a frequency distribution in which the data is concentrated towards the right side of the histogram, with a tail stretching towards the left.
A left-skewed histogram is a kind of frequency distribution where the data is concentrated towards the right side of the histogram, with a tail extending towards the left. It is otherwise called a negatively skewed histogram or a left-tailed histogram. In a left-skewed histogram, the mean is not exactly in the middle, demonstrating that the information is slanted toward the lower end of the conveyance. This can happen when the information has a lower bound or a base worth, which makes the tail of the dispersion be pulled towards the left. Left-skewed histograms can be helpful in examining information that has a characteristic lower cutoff or floor, for example, response times, reaction rates, or pay levels.
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Two pools are being filled with water. To start, the first pool contains 915 Liters of water and the second pool is empty. Water is being added to the first pool at a rate of 15.25 liters per minute. Water is being added to the second pool at a rate of 45.75 Liters per minute. After how many minutes will the two pools have the same amount of water? How much water will be in each pool when they have the same amount?
a) 30 minutes are taken to have the same amount of water.
b) Both pools have an amount of 1372.5 liters when 30 minutes have passed.
What is Linear Function?A linear function is one that produces a straight line when plotted. Generally, it is a polynomial function with a maximum degree of 1 or 0.
Now in the given question ,
a) Physically speaking, the capacity (Q) of each pool, in liters, is equal to the product of flow rate , in liters per minute, and time (t), in minutes. Hence, we derive the following functions :
First pool,
[tex]Q_1=915+15.25t\\[/tex] ...... (1)
Second pool,
[tex]Q_2=45.75t[/tex] ....... (2)
The following expression can be used to calculate how long it will take to find two pools with the same amount of water:
[tex]Q_1=Q_2[/tex] ........ (3)
By putting value of (1) and (2) in (3),
915 + 15.25 t = 45.75 t
30.5 t = 915
t = 915 ÷ 30.5
t = 30 minutes
30 minutes are taken to have the same amount of water.
b) By (2) and knowing that t = 30 , then we have the corresponding amount:
[tex]Q_2=45.75t\\\\Q_2=45.75*30\\\\Q_2=1372.5L[/tex]
Both pools have an amount of 1372.5 liters when 30 minutes have passed.
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Determine whether if it is possible to form a triangle with the given side lenghts. AB = 2cm, BC = 8cm, AC = 5cm
Answer:
no because if one of the side is 2, if we calculate semi perimeter it will be 7.5 which is greater
what is 1 8 in decimal
1/8 in a decimal, divide the denominator by the numerator to get 1/8 as a decimal 1/8 is 0.125.
We divide the numerator by the denominator to convert a fraction to a decimal number. This results in a decimal value because, when dividing, we add the decimal place and then add the necessary number of zeros to finish the division.
1/8
1/2 x 1/2 x 1/2
0.5 x 0.5 x 0.5
0.125
To convert a fraction to a decimal, all you have to do is divide the numerator by the denominator. We position the number over its place value when converting a decimal to a fraction.
Just dividing the numerator by the denominator is all that is required to convert a fraction to a decimal.
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Find the value of x
73°
109°
Answer:
x = 88
Step-by-step explanation:
To find the value of x, we know that the sum of a quadrilateral's exterior angles are 360. We can use this information to create an algebraic expression and solve for x.
[tex]x+73+90+109=360[/tex]
Add like terms
[tex]x+272=360\\[/tex]
Subtract 272 on both sides
[tex]x=88[/tex]
To prove our work, we can add up all the angle measures and see if they add up to 360.
[tex]88+73+90+109=360[/tex]
So, our work is correct.
This year Boris watched 60 movies. He thought that 33 of them were very good. Of the movies he watched, what percentage did he rate as very good?
Answer:
55%
Step-by-step explanation:
To get 55 I just divided 33/60 and multiplied it buy 100
the options are
(- 3, 2)
(- 2, - 3)
(2, - 3)
(2, 3)
(-2,3)
(3, - 2)
(- 3, - 2)
Answer: the third and 5th option but I'm not sure if its right
I really need help with this question
Volume of a cone
1/4π ft³
To find the volume of the cone, we use the formula
volume = (1/3) × π × r² × h
From the question, we are given its height and radius
we substitute for these in the equation above. these will give us the answer. (note in terms of pi)
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on a car trip, jane ate some pretzels. after spilling and losing half of the pretzels, she at 14. her sister then ate on more than half the remaining pretzels, after which there was 3
The number of pretzels in the beginning was 44 pretzels solving the equation.
What is an Equation?An equation is a mathematical statement containing two expressions on either sides which are connected with an equal to sign.
Either sides of an equation is called as left hand side and right hand side.
Let the total number of pretzels = x
Pretzels has been spilled and lost half of the pretzels.
Remaining pretzels = x - x/2
Jane ate 14 pretzels.
Remaining pretzels = x - x/2 - 14
Her sister then ate one more than half the remaining pretzels.
Remaining pretzels = x - x/2 - 14 - [1/2 (x - x/2 - 14) + 1]
Remaining pretzels is 3.
So we get an equation,
x - x/2 - 14 - [1/2 (x - x/2 - 14) + 1] = 3
Solve for x.
x - x/2 - 14 - (x/2 - x/4 - 7 + 1) = 3
x - x/2 - x/2 + x/4 - 14 + 7 - 1 = 3
x/4 - 7 - 1 = 3
x/4 - 8 = 3
x/4 = 11
x = 44
Hence the total number of pretzels was 44.
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Your question is incomplete. The complete question is as follows.
On a car trip, Jane ate some pretzels. After spilling and losing half of the pretzels, she ate 14. Her sister then ate one more than half the remaining pretzels, after which there was 3 pretzels.
How many pretzels was there?
Alex and his father took a taxi cab that charges $2.60 per mile plus $3.00 for the two passengers, and they paid a total of $18.60. Alex wrote the equation 18.60=2.60b+3.00 for this situation and found b=6, where b represents the number of miles the taxi traveled. How could Alex correctly solve this problem without using the equation?
Answer:
Answer is explained Below
Step-by-step explanation:
He could subtract 3 from both sides of the equation first. Then he could divide both sides to get D alone. When you do the D=
PLEASE HELP WILL GIVE BRAINLIEST IF AT LEAST 3 ARE RIGHT
Answer:1. a+b/a-b
2. 8/x-y
3. 2q+p/pq^2
Don’t know how to do the last two sorry
Step-by-step explanation:
Witch is bigger 1/2 Tons or 1000 lb
Answer:
1/2 ton
Step-by-step explanation:
1/2 ton is 1102 pounds
What is a 8-sided shape called?
Answer:
Octagon.
Octa comes from the Greek word "okto", which means eight.
ok so write about the chapter 1- 12 travellers question and answer
where's the question tho
Answer:
without question how am i suppsed to answer..............
Jessica has $50 to buy a jacket and a hat in the store.A jacket cost 39.08 and a hat costs 12.55.Jessica says she stays with her budget.is she correct?Explain
how to convert 250 grams to pounds?
250 grams is approximately equal to 0.5511 pounds ( rounded to four decimal places )
The conversion factor to convert grams to pounds is 0.00220462
1 gram = 0.00220462 pounds
The conversion is the process of changing the unit of one quantity to another units
The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing
The mass in pounds = The mass in grams × conversion factor
Substitute the values in the equation
1 gram = 0.00220462 pounds
250 grams = 250 × 0.00220462
Multiply the numbers
= 0.5511 pounds ( rounded to four decimal places )
Therefore, 250 grams is 0.5511 pounds
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