Find the exact value of cos (2theta), given tan A = -8/15, and theta lies in Quadrant II.
Please show steps and thank you in advance!
Answers
The value of cos (2tetha) is 161/289
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
sin(tetha) = opp/hyp
cos(tetha) = adj/hyp
tan(tetha) = opp/adj
Therefore if tan(tetha) = -8/15, therefore opposite is 8 and adj is 15
hyp = √8²+15²
= √ 64+225
= √ 289
= 17
therefore cos (tetha) = 8/17 and since theta is in second quadrant, cos tetha will be negative
cos (tetha) = -15/17
cos²(tetha) = 225/289
sin(tetha) = 8/17
sin²(tetha) = 64/289
cos(2tetha) = cos²(tetha) -sin²(tetha)
= 225/289 - 64/289
= 161/289
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Related Questions
Which of the following numbers is a factor of
63
6363?
Choose 1 answer:
Choose 1 answer:
(Choice A)
6
66
A
6
66
(Choice B)
3
33
B
3
33
(Choice C)
8
88
C
8
88
(Choice D)
2
22
D
2
2
Answers
The only number that is a factor of 63 and 6363 is option B: 3, while the other options are not factors
What is the scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
According to the given information:To determine which of the given numbers is a factor of 63 or 6363, we need to check if they divide the given numbers without leaving any remainder.
Option A: 6
63 ÷ 6 = 10 remainder 3
6363 ÷ 6 = 1060 remainder 3
Since both calculations leave a remainder of 3, 6 is not a factor of 63 or 6363.
Option B: 3
63 ÷ 3 = 21
6363 ÷ 3 = 2121
Since both calculations give a whole number without any remainder, 3 is a factor of 63 and 6363.
Option C: 8
63 ÷ 8 = 7 remainder 7
6363 ÷ 8 = 795 remainder 3
Since both calculations leave a remainder, 8 is not a factor of 63 or 6363.
Option D: 2
63 ÷ 2 = 31.5
6363 ÷ 2 = 3181.5
Since both calculations give a non-integer result, 2 is not a factor of 63 or 6363.
Therefore, the only number that is a factor of 63 and 6363 is option B: 3, while the other options are not factors
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In 1995, 57. 5% of students at Gardiner university graduated in 4 or fewer years of study. In 2009, that number had fallen to 52. 8%. What was the rate of change for percent of students graduating within 4 years from 1995 to 2009.
Answers
The percent rate of change of students graduating within 4 years from 1995 to 2009 = 8.17%
Here, the percent of studenst graduated in 1995 = 57. 5%
and the percent of studenst graduated in 2009 = 52. 8%
First we find the relative change.
Let a represents the initial value and b represents the findal value
a = 57.5 and b = 52.8
so, the relative rate of change of students would be,
r = (b - a)/a
r = |(52.8 - 57.5)| / 57.5
r = 0.0817
And the percent rate of change of students graduating within 4 years from 1995 to 2009 would be,
p = r × 100
p = 0.0817 × 100
p = 8.17%
Therefore, the required percent is 8.17%
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What is the most common type of employee benefit?
O retirement
O disability insurance
O life insurance
O healthcare
Answers
Answer:
life insurance is the most common type of employee benefit
Carol was packing up some of her old stuff into a box. A box can hold 2 pounds, but she only filled it up 1/2 full How much weight was in the box?
Answers
Answer:
1 pound
Step-by-step explanation:
If a box can hold 2 pounds but is only filled up 1/2 full, then there is only 1 pound of weight in the box.
To see why, consider that if the box was completely full, it would hold 2 pounds. But if it is only half full, it can only hold half of that amount, or 1 pound. Thus, the weight in the box is 1 pound.
I will be giving brainliest plis help me!!!??!!?!??
Answers
Answer:sine
Step-by-step explanation:
SOMEONE PLS HELP ASAP
Answers
Answer:
10.12
Step-by-step explanation:
440=(x)(4x+3)
=10.11979...
A(n) method is like a blueprint, or template, for all the objects within a class. true or false?
Answers
The statement " A(n) method is like a blueprint, or template, for all the objects within a class" is true because methods define the behavior or operations that an object can perform and are defined within a class, acting as a blueprint or template for creating objects in object-oriented programming.
A method in object-oriented programming is a set of instructions that defines the behavior or operations that an object can perform. It is a part of a class, which acts as a blueprint or template for creating objects. When an object is created from a class, it can access and use the methods defined within that class.
Methods can be used to perform tasks, manipulate data, or interact with other objects. They are an essential aspect of encapsulation in object-oriented programming, as they allow for data to be accessed and manipulated in a controlled manner. Overall, methods are a crucial tool for developers to create robust and scalable applications.
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Animal Pens
The animal shelter is building new animal playpens. They
use fencing to enclose an area shaped like a rectangle.
The design for one of the playpens is shown below. What
other playpens could be made with the same amount of
fencing?
8 ft
10 ft
80
10 ft
2. Be Efficient How much fencing is used for
the playpen design shown above? How do
you know? 20.2.2. MAI
Ion
3. Explain Leah says that a square playpen with sides that are 9 feet uses
the same amount of fencing. Is Leah's statement correct? Explain your thinking. 2022
4. Make Sense Describe one other playpen that could be made.
Answers
The total fencing used is 36 ft and the playpen would look like a square rather than a rectangle.
1) The given design uses 36 feet of fencing. Other playpens that could be made with the same amount of fencing are:
A square playpen with sides of length 9 feet (since 4 x 9 = 36)
A rectangular playpen with length 12 feet and width 6 feet (since 2 x (12 + 6) = 36)
2) The fencing used for the given design is the sum of the lengths of all four sides. From the diagram, we can see that the two shorter sides have a length of 8 feet each, and the two longer sides have a length of 10 feet each. Therefore, the total fencing used is:
2(8 ft) + 2(10 ft) = 16 ft + 20 ft = 36 ft
3) Leah's statement is not correct. A square playpen with sides of length 9 feet would require a perimeter of 4 x 9 = 36 feet, which is the same amount of fencing used for the given design. However, the shape of the playpen would be different, since the sides would all be equal in length. The playpen would look like a square rather than a rectangle.
4) Another playpen that could be made with the same amount of fencing is a rectangular playpen with length 18 feet and width 0 feet (i.e., a straight line). The perimeter would be:
2(18 ft) + 2(0 ft) = 36 ft
This playpen may not be practical for animals, but it satisfies the requirement of using 36 feet of fencing.
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Rewrite the expression as a product of four linear factors:
(12x² – 19x)² – 13(12x² – 19x) – 90
Answers
Answer:
(4x - 9)(3x + 2)(4x - 5)(3x - 1).
Step-by-step explanation:
Let's substitute y = (12x² - 19x):
So we have y² - 13y - 90, which can be factored as:
y² - 13y - 90 = (y - 18)(y + 5)
Substituting y back:
(12x² - 19x)² - 13(12x² - 19x) - 90 = [(12x² - 19x) - 18][(12x² - 19x) + 5]
= (12x² - 19x - 18)(12x² - 19x + 5)
= (4x - 9)(3x + 2)(4x - 5)(3x - 1)
If a sphere has a volume of 36π cubic inches, what is its radius?
radius = ___ inches
Answers
The radius of the sphere is approximately 3.634 inches.
We have,
The formula for the volume of a sphere is:
V = (4/3)πr³
where V is the volume of the sphere and r is its radius.
We know that the volume of the sphere is 36π cubic inches.
Substituting this value into the formula, we get:
36π = (4/3)πr³
Multiplying both sides by 3/4π, we get:
r³ = (36π)/(3/4π) = 48
Taking the cube root of both sides.
r = (48)^(1/3)
r = 3.634 inches (rounded to three decimal places)
Therefore,
The radius of the sphere is approximately 3.634 inches.
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What do (180 degrees)/pi and pi/(180 degrees) equal?
Answers
Pi/(180 degrees) equals 1 degree in radians.
What is radian?Radians are a unit of measurement for angles, just like degrees. The radian is defined as the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle.
To visualize this, imagine taking a circle with a radius of r and drawing an arc on the circle that is the same length as the radius. The angle subtended by this arc at the center of the circle is one radian. Since the circumference of a circle is 2pir, there are always 2*pi b in a full circle.
(180 degrees)/pi is equivalent to the value of 180 degrees in radians. To convert from degrees to radians, we multiply the degree value by (pi/180). So:
(180 degrees)/pi = (180 degrees) * (pi/180) = pi radians
Therefore, (180 degrees)/pi equals pi in radians.
On the other hand, pi/(180 degrees) is equivalent to the value of 1 degree in radians. To convert from radians to degrees, we multiply the radian value by (180/pi). So:
pi/(180 degrees) = pi * (180/pi) = 180 degrees
Therefore, pi/(180 degrees) equals 1 degree in radians.
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What are 2 questions that would require an interpretation of the table?
Answers
1. What is the relationship between education level and income in this population? 2. How does the popularity of different music genres vary across different age groups?
What do you mean by an interpretation?An interpretation is a way of understanding or explaining something. Interpretation often involves making connections between different elements or pieces of information to create a coherent understanding. It can also involve applying theories, frameworks, or methods to analyze or explain a particular subject. Ultimately, interpretations are subjective and may vary based on individual experiences and perspectives, making it important to consider multiple interpretations when analyzing a particular subject.
Here is two example questions:
1. What is the relationship between education level and income in this population?
Interpretation: To answer this question, you would need to examine a table that includes columns for education level and income, such as a cross-tabulation or a summary statistics table. You could look for patterns or trends in the data, such as higher incomes being associated with higher levels of education. You might also look for any outliers or anomalies in the data that could be affecting the overall relationship between education level and income.
2. How does the popularity of different music genres vary across different age groups?
Interpretation: To answer this question, you would need to examine a table that includes rows for different age groups and columns for different music genres, such as a frequency table or a bar chart. You could look for patterns or trends in the data, such as certain music genres being more popular among younger age groups or older age groups. You might also look for any outliers or anomalies in the data that could be affecting the overall relationship between age and music genre popularity.
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Find the surface area of the composite solid.
Answers
The surface area of the figure is derived to be equal to 656.4 square meters.
How to evaluate the surface area of a cylinderThe top of the figure is a triangular prism, the bottom is a triangle, and the sides are 3 same size rectangles, so the surface area is calculated as follows:
area of one top triangle face = 1/2 × 12 m × 5 m = 30 m²
area of top triangular prism = 3 × 30 m² = 90 m².
area of bottom triangle = 1/2 × 12 m × 10.4 m = 62.4 m²
area of one rectangle side = 14 m × 12 m = 168 m²
area of the three rectangle sides = 3 × 168 m² = 504 m²
surface area of the figure = 90 m² + 62.4 m² + 504 m²
surface area of the figure = 656.4 m².
Therefore, the surface area of the figure is derived to be equal to 656.4 square meters.
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since critical values of t vary by sample size, before using the t table we must first calculate
Answers
Critical values of t, which are used for hypothesis testing and confidence interval calculations, vary depending on the sample size and the degrees of freedom.
b) degrees of freedom.
Degrees of freedom (df) are calculated based on the sample size and represent the number of independent pieces of information available in the data. It is an important parameter in determining the appropriate critical value to use from the t-distribution table. Therefore, before using the t-table, it is essential to calculate the degrees of freedom of the data set in question.
Options a, c, and d are not correct answers as they do not pertain to the calculation needed before using the t-table.
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Complete Question
Since critical values of t vary by sample size, before using the t table we must first calculate:
a) the Z score.
b) degrees of freedom.
c) the population standard deviation.
d) the sample size.
The degrees of freedom will then determine the critical values of t that should be used in calculating confidence intervals or conducting hypothesis tests. Therefore, it is important to consider the sample size when working with t statistics and using the t table.
To answer your question, before using the t-table, you must first calculate the degrees of freedom. The degrees of freedom are important as they determine the critical values of t based on your sample size. Here's a step-by-step explanation:
1. Obtain your sample data.
2. Determine the sample size (n) by counting the number of data points in your sample.
3. Calculate the degrees of freedom (df) by subtracting 1 from the sample size: df = n - 1.
4. Refer to the t-table with the calculated degrees of freedom to find the critical values of t for your desired level of confidence or significance.
By following these steps, you'll be able to find the appropriate critical values of t based on your sample size before using the t-table.
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7. Julie had a balance of $1,189.17 in her checking account. She wrote checks for $62.41, $224.14, $12.92, and $357.16. Her deposits were $197.34 and $879.13. What was Julie's new bank balance?
Answers
According to the given information, Julie's new bank balance was $1,609.01
To calculate Julie's new bank balance, we need to subtract the total amount of checks she wrote from her initial balance, and then add the total amount of deposits she made.
Total amount of checks = $62.41 + $224.14 + $12.92 + $357.16 = $656.63
Total amount of deposits = $197.34 + $879.13 = $1,076.47
New bank balance = Initial balance - Total amount of checks + Total amount of deposits
New bank balance = $1,189.17 - $656.63 + $1,076.47
New bank balance = $1,609.01
Therefore, Julie's new bank balance was $1,609.01.
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the population of a town is 1,800 and is decreasing at a rate of 3.8% per year what will their population be after 6 years
Answers
Step-by-step explanation:
DECREASING 3.8% means 96.2 % is left each year ( .962 in decimal)
1800 (.962) ^6 =~ 1427 population
Answer:
1389.6
explamation
1500 of 3.8% is 68.4
68.4*6=410.4
1800-410.4=139.6
Suppose there is a regular polygon that can be decomposed into 46
triangles. The measure of one of its interior angles is (9.5x+26.2)
.
What is the value of x
?
Answers
The value of x in the regular polygon is 15.4.
What is the value of x?The value of x is calculated as follows;
The sum of the interior angles of a polygon with n sides is given by the formula;
(n-2) x 180
Since the regular polygon in question can be decomposed into 46 triangles, it has 46 x 3 = 138 sides.
The value of each interior angle is calculated as;
= (n - 2) x 180 / n
= (138 - 2) x 180 / 138
= 169.6⁰
9.5x + 26.2 = 169.6
9.5x = 143.4
x = 15.1
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What is 6w-w to the cube root when w=288
Answers
6w - w = 6 * 288 - 288
Next, we simplify the expression inside the parentheses:
6 * 288 - 288 = 1728 - 288
Then, we subtract the two values to get the result:
1728 - 288 = 1440
Finally, we take the cube root of the result:
∛1440 ≈ 11.09 (rounded to two decimal places)
So, 6w - w to the cube root when w=288 is approximately equal to 11.09.
Simplify the expression.
−7+11+ (−3) + 9 =
Answers
Answer:
10
Step-by-step explanation:
Answer: Simple. The answer is 10.
What is the radius of the circle if it has a circumference of 153. 86153. 86153, point, 86 units
Answers
If the circumference of the circle is 153.86 units, then the radius of that circle is 24.5 units.
The "Circum-ference" of circle is defined as "total-length" of boundary of the circle. The formula for circumference is = 2 × π × Radius,
The "Radius" of circle is the distance from center of circle to its outer edge. It is half of "diameter" of circle, and it is a measure of size of circle.
We know that, circumference of circle is 153.86 units,
So, the circumference equation becomes,
⇒ 2 × 3.14 × Radius = 153.86,
⇒ 153.86/(2 × 3.14) = Radius,
⇒ Radius ≈ 24.5
So, the radius of the circle is approximately 24.5 units.
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The given question is incomplete, the complete question is
What is the radius of the circle if it has a circumference of 153.86 units?
Choose the graph that correctly represents the equation 3x + 9y = −18
Answers
It is recommended that a ramp have at least 5 feet of horizontal distance for every 1 foot of horizontal rise along an incline. The ramp shown has a vertical rise of 3 feet. Does the ramp shown match the recommended specifications? Explain.
Answers
Yes ,inclination in between 4in / 15 in < 4in / 18 in
What is incline?An inclined plane, also known as a ramp, is a flat supporting surface that is tilted at an angle from the vertical direction with one end higher than the other. It can be used to lift or lower a load.
What is horizontal and vertical?The horizontal line in coordinate geometry is the line perpendicular to the x-axis, and the vertical line is the line perpendicular to the y-axis. Horizontal lines and vertical lines will be parallel to the x-axis and the y-axis, respectively. As a result, lines that share at least one point are perpendicular to one another when they are drawn.
6 feet of horizontal distance for every 1 foot,
ramp shown has a vertical rise of 5 feet.
Therefore
M ≤ 1foot / 6 feet
Converting both to a single units of ( inches )
M ≤ 12 inches / 72 inches
Dividing by 4
M ≤ 4 inches / 18 inches
Where 5 feet = 60 inches
12 inches / 60 inches
= 4 inches / 15 inches
Therefore:
4in / 15 in < 4inch / 18 inch
The condition states the ramp has to be at least 6feet, what this means is it has to be between 0-6 so since it is lesser. Yes it meets the recommendations.
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Yes, inclination in between 4in / 15 in < 4in / 18 in
What is incline?A flat supporting surface that is inclined at an angle from the vertical direction with one end higher than the other is referred to as an inclined plane or a ramp. A load may be raised or lowered using it.
What is horizontal and vertical?In coordinate geometry, the horizontal line is the line parallel to the x-axis, while the vertical line is the line parallel to the y-axis. Vertical and horizontal lines will be perpendicular to the x- and y-axes, respectively. As a result, when lines are drawn, they are perpendicular to one another if they share at least one point.
6 feet of horizontal distance for every 1 foot,
ramp shown has a vertical rise of 5 feet.
Therefore
M ≤ 1foot / 6 feet
Converting both to a single units of ( inches )
M ≤ 12 inches / 72 inches
Dividing by 4
M ≤ 4 inches / 18 inches
Where 5 feet = 60 inches
12 inches / 60 inches
= 4 inches / 15 inches
Therefore:
4in / 15 in < 4inch / 18 inch
The condition states the ramp has to be at least 6 feet, what this means is it has to be between 0-6 so since it is lesser. Yes it meets the recommendations.
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Can someone help with this question????
Answers
Answer:
besides this pic nothing else can be done
Solve for the value of X 130 degrees X+134
Answers
Answer:
-4. my answers need to be 20 characters+ soooo
Select THREE expressions that are equivalent
to 15x + 9y.
A. 15(x + 9y)
B. 3(5x + 3y)
C. 5(3x + 3y)
D. 9(15x + y)
E. 5x + 5x + 5x + 5y + 4y
F. x + 3x + 6x + 5x + y + 6y + y + y
Answers
ADF
Thats not the answer those are just my favorite letters
A laptop computer sells for $2,149.99 and has a mail-in rebate for $200. What is
the cost after the rebate if an envelope costs 15¢ and a stamp costs 39¢?
Answers
The cost of the envelope and stamp may vary depending on the location and the method of delivery. In this example, we assumed that the cost of the envelope is $0.15 and the cost of the stamp is $0.39, but these values may change based on the specific circumstances.
What is cost?
Cost" is the amount of money or resources that are required to produce, acquire, or obtain something. In other words, cost refers to the expenses that are incurred in the process of acquiring or producing a good or service.
For example, the cost of producing a product may include the cost of raw materials, labor, overhead expenses, and other related costs. Similarly, the cost of acquiring a product may include the purchase price, taxes, shipping costs, and any other fees or expenses associated with the purchase. Overall, cost is a crucial factor in business and economics, as it determines the profitability of a venture and helps to make informed decisions regarding investments and pricing strategies
To find the cost of the laptop after the mail-in rebate and the cost of the envelope and stamp, we can follow these steps:
Subtract the mail-in rebate from the original price of the laptop:
$2,149.99 - $200 = $1,949.99
Add the cost of the envelope and stamp to the cost of the laptop after the mail-in rebate:
$1,949.99 + $0.15 + $0.39 = $2,090.53
Therefore, the cost of the laptop after the mail-in rebate and the cost of the envelope and stamp is $2,090.53.
To explain this calculation, we first subtract the mail-in rebate of $200 from the original price of the laptop, which gives us the price of the laptop after the rebate. Then, we add the cost of the envelope and the stamp to this price to get the total cost of the laptop after the rebate and the cost of the envelope and stamp.
Therefore, The cost of the envelope and stamp may vary depending on the location and the method of delivery. In this example, we assumed that the cost of the envelope is $0.15 and the cost of the stamp is $0.39, but these values may change based on the specific circumstances.
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There are 56 people at the party. Only 14
of them are wearing red. What percent of
people are NOT wearing red?
Answers
Answer: 75%
have a good day/night and crush that homework/class!! you are loved
brainliest??
Answer: 75%
Step-by-step explanation: 56 - 14 = 42. So, 42 people are not wearing red. 42/56 is .75, which is the decimal form for 75%. Also, if you simplify 42/56, you get 3/4 which is also 75%
The weight of 4 hummingbirds is recorded below. The weight of each hummingbird has been rounded to the nearest 1 /2 1 dot above two and one-half; 1 dot above three; 1 dot above four and one-half, and 1 dot above five. A line plot labeled weights of birds in grams shows, moving left to right, labeled tick marks at two, two and one-half, three, three and one-half, four, four and one-half, and five. Dots are plotted as follows: 1 dot above two and one-half; 1 dot above three; 1 dot above four and one-half, and 1 dot above five. What is the weight of all 4 hummingbirds combined? grams
Answers
Answer:
5
Step-by-step explanation:
Answer:
15 grams
Step-by-step explanation:
Based on the information provided, the weight of each hummingbird is 2.5 grams, 3 grams, 4.5 grams, and 5 grams. To find the total weight of all 4 hummingbirds combined, we can add up their individual weights: 2.5 + 3 + 4.5 + 5 = 15 grams. So, the total weight of all 4 hummingbirds combined is 15 grams.
A textbook store sold a combined total of 300 physics and biology textbooks in a week. The number of physics textbooks sold was 72 more than the number of biology textbooks sold. How many textbooks of each type were sold?
Answers
Hence, 186 physics textbooks and 114 biology textbooks were sold as it states that 300 textbooks were sold in total.
what is equation ?The formulas 2x + 3 and 7, for instance, are identical when written as 2x + 3 = 7, where x has been the variable. The x-value that fulfils the equality can be found by solving this equation. In this instance, we can take 3 out of both sides to get 2x = 4, and thereafter divide each sides by 2 to get x = 2. To describe relationships amongst quantities and to solve issues, equations are used widely in mathematics as well as in chemistry, chemistry, economics, and other sciences. They are also utilised in daily life, such as in financial computations and the solution of time, distance, and speed-related issues.
given
Assume that x biology textbooks were sold in total.
The issue states that there were 72 more physics textbooks sold than there were biology textbooks. Hence, x + 72 is the total number of physics textbooks sold.
It states that 300 textbooks were sold in total. Thus, we can create the following equation:
[tex]x + (x + 72) = 300[/tex]
When we simplify and find x, we obtain:
[tex]2x + 72 = 300\\2x = 300 - 72[/tex]
2x = 228
x = 114
Hence, 114 biology textbooks were sold.
The quantity of sold physics textbooks is given by x + 72, or 114 + 72 = 186.
Hence, 186 physics textbooks and 114 biology textbooks were sold as it states that 300 textbooks were sold in total.
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each unit square of a $3\times 3$ grid of unit squares is to be colored either blue or red. for each square, either color is equally likely to be used. find the probability of obtaining a grid that does not have a $2\times 2$ red square.
Answers
The probability of obtaining a grid that does not have a 2 × 2 red square is 127/128 and the value of (p + q + 1) / 310 is 0.82.
Total number of outcomes = [tex]2^9[/tex] = 512
We will subtract the outcomes of obtaining a grid that does not have a
2 × 2 red squares from the total outcomes.
Favorable outcomes = Total outcomes - outcomes having [tex]2[/tex] × [tex]2[/tex] red squares
= [tex]2 ^3 - 4[/tex]
= 508
So favorable outcomes are 508.
Probability calculates the chances of experiments occurring. It is obtained by the ratio between favorable outcomes and total outcomes. It is basically how likely something is to happen.
Probability = Favorable outcomes / Total no. of outcomes
= 508 / 512
= p/q
= 127/128
So, the probability of obtaining a grid that does not have a 2 × 2 red square is 127/128.
Now, the value of (p + q + 1)/310
= (127 + 128 + 1)/310
= 256/310
= 0.82
Therefore, the value of (p + q + 1) / 310 is 0.82.
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The complete question is -
"Each unit square of a 3 * 3 square grid is to be colored either blue or red for each square, either color is equally likely. The probability of obtaining a grid that does not have a 2 * 2 red square is CHCF(p,q) is 1). Find this probability and then find the value of (p + q + 1) / 310 ?"