The percentage is 26%, so the number is 26.
How to find the percenage?Here we know that the x% of the number 800,000 is equal to 208,000.
Remember that the x% of a number N, is given by the product:
(x%/100%)*N
So in this case we can solve the equation:
(x%/100%)*800,000 = 208,000
Solving that equation for the percentage, we will get:
x% = 100%*(208,000/800,000)
x% = 26%
That is the missing number.
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uck onto the tin has a height of 8 cm. 2.1 Calculate the area of sheet metal needed to make a soup tin. 2.2 Calculate the total surface area of the label. Use the formula: TSA = 2 × x radius x height where π = 3,142 2.3 Tins of butternut soup are tightly packed into boxes, with 4 tins fitting in the width of the box, and 5 tins fitting in the length of the box as shown in the diagrams. What are the dimensions (length and breadth) of the box? 7 4 1f thin box
The dimensions (length and breadth) of the box are 10r x 8r.
We are given that;
π = 3,142
Number of tins=4,5
Now,
To calculate the area of sheet metal needed to make a soup tin, we can use the formula for surface area of a cylinder which is given by:
Surface Area = 2πrh + 2πr^2
where r is the radius of the cylinder and h is the height of the cylinder.
Using the given values, we can calculate the surface area of the soup tin as follows:
Surface Area = 2π(4.5)(8) + 2π(4.5)^2 Surface Area = 226.08 cm^2
To calculate the total surface area of the label, we can use the formula for surface area of a cylinder which is given by:
Surface Area = 2πrh
where r is the radius of the cylinder and h is the height of the cylinder.
Using the given values, we can calculate the surface area of the label as follows:
Surface Area = 2π(4.5)(8) Surface Area = 226.08 cm^2
To find out the dimensions (length and breadth) of the box in which tins are packed, we can use the given information that 4 tins fit in the width of the box and 5 tins fit in the length of the box. Let’s assume that each tin has a diameter of d cm.
4d = width of box 5d = length of box
We know that diameter (d) = 2r where r is radius.
So, width of box = 4d = 8r length of box = 5d = 10r
Therefore, by the area the answer will be 10r x 8r.
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how do you solve this
Answer:
Θ ≈ 103°
Step-by-step explanation:
using the Cosine rule in Δ ABC
cosB = [tex]\frac{a^2+c^2-b^2}{2ac}[/tex]
where a is the side opposite ∠ A , b the side opposite ∠ B and c the side opposite ∠ C
here a = 42 , b = 78 and c = 57 , then
cos B = [tex]\frac{42^2+57^2-78^2}{2(42)(57)}[/tex]
= [tex]\frac{1764+3249-6084}{4788}[/tex]
= [tex]\frac{5013-6084}{4788}[/tex]
= [tex]\frac{-1071}{4788}[/tex] , then
B = Θ = [tex]cos^{-1}[/tex] ( - [tex]\frac{1071}{4788}[/tex] ) ≈ 103° ( to the nearest degree )
The difference of the same side interior angles of two parallel lines is 50 degrees. Find all angles
If the difference between the same side interior angles of two parallel lines is 50 degrees, we know that those angles must sum up to 180 degrees (because they are opposite each other).are supplementary angles. As a result, each of the four angles is 65 degrees, 115 degrees, 65 degrees, and 115 degrees..
Let's call one of the angles "x". Then, the other angle must be (x+50).
Now, let's look at the angles formed by a transversal intersecting those two parallel lines. There are eight angles in total, but we only need to find four of them since the other four are congruent (due to alternate interior angles being congruent).
The angles we need to find are:
1. x (one of the same side interior angles)
2. (x+50) (the other same side interior angle)
3. the corresponding angle to x (opposite x, on the other side of the transversal)
4. the corresponding angle to (x+50) (opposite (x+50), on the other side of the transversal)
Since corresponding angles are congruent when two parallel lines are intersected by a transversal, we know that angles 3 and 4 are equal to angles 1 and 2, respectively.
To determine all four angles, we just solve for x:
x + (x+50) = 180
2x + 50 = 180
2x = 130
x = 65
Therefore, our four angles are:
1. x = 65 degrees
2. (x+50) = 115 degrees
3. the angle corresponding to x = 65 degrees
4. the corresponding angle to (x+50) = 115 degrees
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What's the circumference
of a
circle with a diameter of 20
inches? Use 3.14 for .
C = [?] inches
Round to the nearest hundredth, if necessary.
Hint: C = πd
Enter
Answer:
C=62.8
Step-by-step explanation:
1) In the formula C=πd, d represents the diameter, which is 20 inches. All you need to do is apply 20 into the equation and you get C=π20.
2) They said to use 3.14 instead of pi, so we are going to multiply 20*3.14, which is 62.8.
What is the answer pls
Multiply: −6ab3(a5b2−2a4b−10ab−7).
Answer:
--6a^6b^5+12a^5b^4+60a^2b^4+42ab^3
Step-by-step explanation:
Find the area of a circle with radius,
r
= 46cm.
Give your answer rounded to 3 SF.
Answer:
6650 cm³
Step-by-step explanation:
area of a circle = π r², where r is the radius
area = π (46)²
= 2116 π
= 6650 cm³ to 3 significant figures
Describe the end behavior of the graph of the function f(x) equals minus 5 4X -2 for affinity type in the word infinity four minus infinity typing minus infinity -followed by the word infinity. Make sure that you type in the word infinity with a lowercase i
The end behavior of the graph of the function f(x) = -5(4x - 2) as x approaches infinity can be described as follows:
As x approaches infinity (or positive infinity), the value of 4x becomes infinitely large compared to the constant -2. Therefore, we can ignore the constant (-2) and simplify the function as f(x) = -5(4x) = -20x.
Since the coefficient of x is negative (-20), the graph of the function will decrease without bound as x approaches infinity. In other words, the function will approach negative infinity (or -∞) as x becomes infinitely large.
Similarly, as x approaches negative infinity, the value of 4x becomes infinitely large in the negative direction. Thus, we can simplify the function as f(x) = -5(4x) = -20x.
Since the coefficient of x is negative (-20), the graph of the function will also decrease without bound as x approaches negative infinity. Therefore, the function will approach negative infinity (or -∞) as x becomes infinitely negative.
Which of the following statements is true?
The measure of arc XYL + measure of arc VUL + measure of arc VIX = 360°. Therefore, the correct answer is option D.
The arc length is defined as the interspace between the two points along a section of a curve. An arc of a circle is any part of the circumference.
From the given circle, measure of arc XYL + measure of arc VUL + measure of arc VIX = 360° (Complete angle)
Therefore, the correct answer is option D.
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Please help urgent thank you so much
Answer: 4, 14
Step-by-step explanation:
Bring everything over to other side that is not in the absolute value:
3 |x - 9| + 5 = 20 >Subtract 5 from both sides
3 |x - 9| = 15 >Divide both sides by 3
|x - 9| = 5 >Create a positive and negative version to
drop the absolute value
x - 9 = 5 x - 9 = -5
x= 14 x = 4
Linda wants to save $900 to buy a TV. She saves $18 each week. The amount, A (in dollars), that she still needs after w weeks is given by the following function. If Linda still needs $576 , how many weeks has she been saving? How much money does Linda still need after 7 weeks?
A) first multiply 18 x 7 = 116, then subtract 500 - 116 = 384, so the answer is 384
B) first divide 384 from 18 which should give you 18, so the answer is 18
Winona has two jobs; one pays $10.00 per hour and the other pays $9.25 per hour plus an average of 70% of the hourly pay in tips and bonuses. Each pay
period, 20% of her total pay goes to taxes.
Part 1 of 2
(a) Write and simplify an equation that describes Winona's total take-home pay, P, in terms of the number of hours, x, worked at the first job and the
number of hours, y, worked at the second.
The total take-home pay from Winona's two jobs can be found using the equation
P=
Part 2 of 2
X
3
(b) If Winona is committed to work 30 hours per week at the first job, how many hours per week would she need to work at the second job if she needs
her biweekly take-home pay to be $800? Round the answer to one decimal place.
In order for her biweekly take-home pay to be $800, Winona needs to work
hours per week at her second job.
Answer:
76.5 hours
(If you like this answer i would appreciate if u give brainliest but otherwise, i hope this helped ^^)
Step-by-step explanation:
Part 1 of 2:
(a) The equation that describes Winona's total take-home pay, P, in terms of the number of hours, x, worked at the first job and the number of hours, y, worked at the second job can be written as:
P = (10x) + (9.25y + 0.7 * 9.25y) - 0.2[(10x) + (9.25y + 0.7 * 9.25y)]
Simplifying the equation:
P = 10x + 9.25y + 0.7 * 9.25y - 0.2(10x + 9.25y + 0.7 * 9.25y)
Part 2 of 2:
(b) If Winona is committed to working 30 hours per week at the first job, let's assume x = 30. We need to find the number of hours per week, y, she would need to work at the second job to reach a biweekly take-home pay of $800.
Using the simplified equation from part (a), we substitute x = 30 and solve for y:
800 = (10 * 30) + (9.25y + 0.7 * 9.25y) - 0.2[(10 * 30) + (9.25y + 0.7 * 9.25y)]
800 = 300 + (9.25y + 0.7 * 9.25y) - 0.2(300 + (9.25y + 0.7 * 9.25y))
Now, we can solve for y:
800 = 300 + 9.25y + 0.7 * 9.25y - 0.2(300 + 9.25y + 0.7 * 9.25y)
Simplify the equation:
800 = 300 + 9.25y + 0.7 * 9.25y - 0.2 * 300 - 0.2 * 9.25y - 0.2 * 0.7 * 9.25y
Combine like terms:
800 = 300 - 60 + 9.25y - 1.85y - 0.1295y
800 = 240 + 7.32y
Subtract 240 from both sides:
560 = 7.32y
Divide both sides by 7.32:
y ≈ 76.5
Therefore, Winona would need to work approximately 76.5 hours per week at her second job to reach a biweekly take-home pay of $800.
Whats the surface area
The surface area of the prism is S = 36 feet²
Given data ,
Let the surface area of the prism be represented as S
Now , the base of the prism is B
where B = l x w
And , length of prism = l and width of prism is = w
The formula for the surface area of a prism is SA=2B+ph, where B, is the area of the base, p represents the perimeter of the base, and h stands for the height of the prism
Surface Area of the prism = 2B + ph
The area of the triangular prism is A = ph + ( 1/2 ) bh
S = 2 ( 1/2 ) ( 3 x 4 ) + ( 4 x 2 ) + ( 3 x 2 ) + ( 5 x 2 )
On simplifying , we get
S = 12 + 8 + 6 + 10
S = 36 feet²
Hence , the surface area is S = 36 feet²
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change 4+(6/10)+(7/100) to decimal
Hello!
4 + (6/10) + (7/100)
= 4 + 0.6 + 0.07
= 4.67
In the early stages of building the Hoover Dam diversion tunnels were built to divert the flow of water away from the main construction site. Each diversion tunnel was cylindrical with a radius of 56 feet and a length of 4,000 feet. Find the volume and surface area of a diversion tunnel.
Answer:
Therefore, the volume of the diversion tunnel is approximately 9,839,916,800 cubic feet and the surface area is approximately 1,000,530.9 square feet.
Step-by-step explanation:
To find the volume and surface area of a diversion tunnel, we can use the formulas for the volume and lateral surface area of a cylinder.
The volume of a cylinder is given by the formula:
V = πr^2h
Where:
V is the volume,
π is a mathematical constant approximately equal to 3.14159,
r is the radius of the cylinder, and
h is the height (or length) of the cylinder.
Substituting the given values:
r = 56 feet
h = 4,000 feet
V = π(56^2)(4,000)
V ≈ 3.14159 * 56^2 * 4,000
Calculating the volume:
V ≈ 9,839,916,800 cubic feet
The surface area of the lateral (curved) part of a cylinder is given by the formula:
A = 2πrh
Where:
A is the surface area,
π is a mathematical constant approximately equal to 3.14159,
r is the radius of the cylinder, and
h is the height (or length) of the cylinder.
Substituting the given values:
r = 56 feet
h = 4,000 feet
A = 2π(56)(4,000)
A ≈ 2 * 3.14159 * 56 * 4,000
Calculating the surface area:
A ≈ 1,000,530.9 square feet
Therefore, the volume of the diversion tunnel is approximately 9,839,916,800 cubic feet and the surface area is approximately 1,000,530.9 square feet.
I NEED SELP ASAP PLEASEEEE 50 POINTS
Answer:
(x - 0)² + (y - 9)² = (√87.25)²
Step-by-step explanation:
equation of circle is (x - a)² + (y - b)² = r², where a and b are centre of the circle and r is the circle's radius.
(x - 0)² + (y - 9)² = r²
x² + (y² - 18y + 81) = r²
x² + y² - 18y + 81 = r²
at the point (7.5, 5):
(7.5)² + (5)² - 18(5) + 81
= 87.25
so r² = 87.25.
in standard form:
(x - 0)² + (y - 9)² = (√87.25)²
What numbers could go in the blanks so that this represents y as a function of x? {(2,7), (5,14), (x,y), (9,21)}
Every pair of values except (2, y different of 7), (5, y different of 14) and (9, y different of 21) can go in the blanks so that this represents y as a function of x.
When does a relation represents a function?A relation represents a function if each value of the input is mapped to only one value of the output, that is, one input cannot be mapped to multiple outputs.
For a point in the standard format (x,y), we have that:
x is the input.y is the output.The meaning is that the input given by the x-coordinate is mapped to the output given by the y-coordinate.Hence every point can go into the blank, except the ones that map the inputs 2, 5 and 9 to different outputs than the ones already given in this problem.
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100 POINTS
The numerator is 2 less than the denominator. If I add 3 both to the numerator and the denominator, the answer would be 5/6. what's the original fraction?
Answer:
[tex]\dfrac{7}{9}[/tex]
Step-by-step explanation:
Let x be the denominator.
If the numerator is 2 less than the denominator, then the expression for the numerator is (x - 2):
[tex]\dfrac{x-2}{x}[/tex]
If 3 is added to both the numerator and the denominator, and the answer is 5/6, then:
[tex]\dfrac{x-2+3}{x+3}=\dfrac{5}{6}[/tex]
Now we can solve the equation for x.
Simplify the numerator in the fraction on the left of the equation:
[tex]\dfrac{x+1}{x+3}=\dfrac{5}{6}[/tex]
Cross mutliply:
[tex]6(x+1)=5(x+3)[/tex]
Expand the brackets:
[tex]6 \cdot x +6 \cdot 1 = 5 \cdot x + 5 \cdot 3[/tex]
[tex]6x+6=5x+15[/tex]
Subtract 5x from both sides of the equation:
[tex]6x+6-5x=5x+15-5x[/tex]
[tex]x+6=15[/tex]
Subtract 6 from both sides of the equation:
[tex]x+6-6=15-6[/tex]
[tex]x=9[/tex]
Therefore, the value of x is 9.
Now substitute the found value of x into the original rational expression:
[tex]\dfrac{x-2}{x}=\dfrac{9-2}{9}=\dfrac{7}{9}[/tex]
Therefore, the original fraction is:
[tex]\boxed{\dfrac{7}{9}}[/tex]
HELP! FOR 100 POINTS
In a sale, all prices are reduced by 22%. A pair of trainers normally cost £80. What is the sale price of the pair of trainers?
Answer: $62.40
Step-by-step explanation:
Original price $80
22% of 80%
.22(80) = 17.60 >This is the discount
Sale price = Original price - discount
Sale price = 80 - 17.60
Sale price = $62.40
Answer:
[tex]\Huge \boxed{\text{\$62.40}}[/tex]
Step-by-step explanation:
In the sale, the prices decrease by 22%. This means that the sale price is 78% of the original price.
[tex]\Large \text{Sale price = (100 - 22)\% of old price}\\\text{Sale price = 78\% of \$80}\\\text{Sale price = 0.78 $\times$ 80}\\\text{Sale price = \$62.40}[/tex]
find the theoretical probability.
[tex]|\Omega|=8\\|\text{odd}|=4\\\\P(\text{odd})=\dfrac{4}{8}=\dfrac{1}{2}[/tex]
Answer:
4/8
or, 1/2
Step-by-step explanation:
odd numbers (O) = (1,3,5,7) = 4
total numbers (T) = 8
P(odd) = n(O)/n(T)
= 4/8
14. Simon earned 400sh as a for goods sold what Commission 15,000 worth so, 600 could be his varnings for a total sale of 7,000
His total earnings for a total sale of 7,000 could be 1450sh
How to determine his earnings for a total sale of 7,000.From the question, we have the following parameters that can be used in our computation:
Salary = 400
Commission = 15%
using the above as a guide, we have the following:
Total earnings = 400 + 15% * Total sales
So, we have
Total earnings = 400 + 15% * 7000
Evaluate
Total earnings = 1450
Hence, the total earnings is 1450
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Question
Simon earned 400sh weekly for goods sold and a commission of 15%
What could be his earnings for a total sale of 7,000.
Priya and Hadley, fans of this player, calculate the expected value of X is E(X) = 0.80. Priya says, "The probability that this player makes a free-throw is 0.80, on average." Hadley says, "This player will make 0.80 free-throws in his next set of 2." Whose statement is correct based on the expected value? Choose 1 answer: B Only Priya's Only Hadley's Both statements are correct. Neither statement is correct.
Only Priya's statement is correct based on the expected value. The expected value of X represents the average or mean number of successful free-throws that the player makes. Therefore, it is correct to say that the probability of making a free-throw is 0.80 on average. Hadley's statement about the next set of 2 free-throws is incorrect because the expected value does not tell us exactly how many free-throws the player will make in a given set, but rather what the average or expected number of successful free-throws will be over a series of trials.
Solve for x:
A: 3x - 7 = -19; x =
B: 2x + 3 = -11; x =
C: -3 + 1 = -26; x =
D: 6x + 3 = -15; x =
E: -9 + 7x = 33; x =
F: -2x + 8 = 4; x =
( URGENT PLEASE SOLVE !!! )
Estudios de caso con características cualitativas y cuantitativas
De acuerdo con la información, el tipo de estudio de caso descrito es estudios de caso mixtos debido a que son aquellos que combinan características cualitativas y cuantitativas.
¿Qué son los estudios de caso mixtos?Los estudios de caso mixtos se caracterizan por combinar características cualitativas y cuantitativas en la recopilación y análisis de datos. Estos estudios buscan obtener una comprensión más completa y profunda del fenómeno estudiado.
Los datos cualitativos se obtienen a través de entrevistas, observaciones o análisis de contenido, brindando una comprensión rica de los contextos y perspectivas. Los datos cuantitativos se recopilan mediante encuestas, cuestionarios o análisis estadísticos, permitiendo obtener información objetiva y generalizable.ENGLISH VERSION
According to the information, the type of case study described is mixed case studies because they are those that combine qualitative and quantitative characteristics.
The mixed case studies are characterized by combining qualitative and quantitative characteristics in the compilation and analysis of data. These studies seek to obtain a more complete and profound understanding of the phenomenon studied.
The qualitative data are obtained through interviews, observations or analysis of content, bringing an understanding of contexts and perspectives.The quantitative data are compiled through surveys, questionnaires or statistical analysis, allowing to obtain objectivable and generalizable information.Learn more about case study in: https://brainly.com/question/24259426
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12 4 8 16 3'9' 27' 81' 243 a. yes, b. yes. 2 233 119 C. d. yes. 6 not geometric
Option A is correct, the sequence is a geometric and common ratio is 2/3.
To determine whether the given sequence is geometric, we need to check if there is a common ratio between consecutive terms.
Let's examine the given sequence:
1/3, 2/9, 4/27, 8/81, 16/243...
To find the ratio between consecutive terms, we can divide each term by its preceding term:
(2/9)/(1/3) = 2/9 × 3/1 = 2/3
(4/27)/(2/9) = 4/27 × 9/2 = 4/6 = 2/3
(8/81)/(4/27) = 8/81 × 27/4 = 2/3
(16/243)/(8/81) = 16/243 × 81/8 = 2/3
As we can see, there is a common ratio of 2/3 between consecutive terms.
Therefore, the given sequence is indeed geometric.
Hence, the sequence is a geometric and common ration is 2/3, Option A is correct.
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2. The area of a figure is 207 m². If the
dimensions are multiplied by what will
3'
be the area of the new figure?
Answer:
Step-by-step explanation:
If the dimensions of a figure are multiplied by 1/3, then the area of the new figure will be 1/9 of the original area.
Therefore, if the area of the original figure is 207 m², then the area of the new figure will be 23 m² (207 m² * 1/9).
I hope this helps!
Answer:
23 m^2
Step-by-step explanation:
As all of the dimensions have been multiplied by a constant, the two figures are similar to one another.
The ratio between the areas of two similar figures is given by the ratio of similarity (= the ratio between two similar sides between the two figures) squared.
In our case, the ratio of similarity is 1/3.
Therefore, the ratio between the two areas is (1/3)^2 = 1/9.
[tex]207 \times \frac19 = 23 \left[\text{m}^2\right][/tex]
Find the difference by subtracting the second polynomial from the first.(11m^(2)n^(5)-3m^(2)n^(3)+5mn-n ) and (-6m^(2)n^(5)+3m^(2)n^(5)+m+2n )
The difference between the two polynomials is 5m^(2)n^(5) - 3m^(2)n^(3) + 5mn + m + n.
To subtract the second polynomial from the first polynomial, we need to perform term-wise subtraction. Let's break down the process step by step:
The first polynomial is: 11m^(2)n^(5) - 3m^(2)n^(3) + 5mn - n.
The second polynomial is: -6m^(2)n^(5) + 3m^(2)n^(5) + m + 2n.
To subtract the second polynomial from the first, we need to change the signs of all terms in the second polynomial and then combine like terms.
First, let's change the signs of the terms in the second polynomial:
-(-6m^(2)n^(5) + 3m^(2)n^(5) + m + 2n) = 6m^(2)n^(5) - 3m^(2)n^(5) - m - 2n.
Now, we can combine like terms by adding or subtracting coefficients of similar monomials:
(11m^(2)n^(5) - 3m^(2)n^(3) + 5mn - n) - (6m^(2)n^(5) - 3m^(2)n^(5) - m - 2n)
= 11m^(2)n^(5) - 3m^(2)n^(3) + 5mn - n - 6m^(2)n^(5) + 3m^(2)n^(5) + m + 2n
= (11m^(2)n^(5) - 6m^(2)n^(5)) + (-3m^(2)n^(3) + 3m^(2)n^(5)) + (5mn + m) + (-n + 2n)
= 5m^(2)n^(5) - 3m^(2)n^(3) + 5mn + m + n.
Therefore, the difference between the two polynomials is 5m^(2)n^(5) - 3m^(2)n^(3) + 5mn + m + n.
In summary, to find the difference, we changed the signs of all terms in the second polynomial and then combined like terms with the first polynomial. The resulting polynomial is the difference between the two original polynomials.
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If the triangle on the grid below is translated by using the rule (x,y) →(x+5.y-2), what will be the coordinates of gº?
Answer:
Step-by-step explanation:
Thanks to social media, the happiest creature on earth, an always smiling Australian marsupial called a quokka, has become well known. Suppose that the weights of quokkas can be described by the Normal model N(12,2.9 ). Complete parts a through c. a) What percent of quokkas weigh over 16.8 pounds? b) What percent of quokkas weigh under 13.8 pounds? c) What percent of quokkas weigh between 13.8 and 16.8 pounds?
The percentages are given as follows:
a) Over 16.8 pounds: 4.85%.
b) Under 13.8 pounds: 73.24%.
c) Between 13.8 and 16.8 pounds: 21.91%.
How to obtain probabilities using the normal distribution?We first must use the z-score formula, as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
In which:
X is the measure.[tex]\mu[/tex] is the population mean.[tex]\sigma[/tex] is the population standard deviation.The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, and can be positive(above the mean) or negative(below the mean).
The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure represented by X in the distribution.
The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 12, \sigma = 2.9[/tex]
Item a:
The proportion is one subtracted by the p-value of Z when X = 16.8, hence:
Z = (16.8 - 12)/2.9
Z = 1.66.
Z = 1.66 has a p-value of 0.9515.
1 - 0.9515 = 0.0485, hence the percentage is of 4.85%.
Item b:
The proportion is the p-value of Z when X = 13.8, hence:
Z = (13.8 - 12)/2.9
Z = 0.62.
Z = 0.62 has a p-value of 0.7324.
Item c:
The proportion is the subtraction of the p-values, hence:
0.9515 - 0.7324 = 0.2191 = 21.91%.
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Use the given information about to find the exact value of cos
The exact value of cos(2θ) given the information and using trigonometric identity is 1519.
Understanding Trigonometric IdentityTo find the exact value of cos(2θ), we can use the double-angle formula for cosine:
cos(2θ) = cos²(θ) - sin²(θ)
First, let's find the values of sin(θ) and cos(θ) using the given information about θ:
Given:
tan(θ) = 9/40
θ : lies in the fourth quadrant (3π/2 < θ < 2π).
In the fourth quadrant, both sin(θ) and cos(θ) are negative.
Since:
tan(θ) = sin(θ)/cos(θ),
we can write:
9/40 = sin(θ)/cos(θ)
Using the properties of trigonometric functions, we can rewrite this as:
sin(θ) = -9
cos(θ) = -40
Now, let's calculate cos²(θ) and sin²(θ):
cos²(θ) = (-40)² = 1600
sin²(θ) = (-9)² = 81
Finally, we can substitute these values into the double-angle formula for cosine:
cos(2θ) = cos²(θ) - sin²(θ)
= 1600 - 81
= 1519
Therefore, the exact value of cos(2θ) is 1519.
Learn more about trig identity here:
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