solving sin ( 4x ) = √3 / 2 , the value of x is 15°
What is trigonometry?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. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
For angle of 30° and 60°
sin 30° = 1/2
cos 60° = √3/2
tan60° = √3
for angle 60 °
sin60° = √3/2
cos 60° = 1/2
tan60° = 1/√3
since sin(4x) = √3/2
and sin 60° = √3/2
sin60° = sin(4x)
this means 60° = 4x
divide both sides 4
x = 60/4
x = 15°
therefore the value of x is 15°
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Sergio purchased 4 items for $1.50 each. Sales tax was 8.25%. What was the total price?
please explain if you can, thxs!
Answer:
6.495.Step-by-step explanation:
The total cost of the items before tax was $1.50 * 4 = $<<1.54=6>>6.
The sales tax was $6 * 8.25% = $<<68.25*.01=0.495>>0.495.
So the total price was $6 + $0.495 = $<<6+0.495=6.495>>6.495.
√≈≈≈≈≈Which of the following is a one-to-one function? y = [[2x]], y = x^2, f(x) = { 4x + 1;x < -2
The one-to-one function is obtained as f(x) = 4x + 1 which is a linear function.
What is a function?A function y = f(x) is defined as a one to one relation between sets X and Y. The set X is called the domain while Y is called the range of f(x).
A function can either have one-to-one or many-to-one mapping.
One-to-one mapping implies unique element in the domain for each element in the range while for many-to-one mapping there are many elements in the domain for one element in the range.
The given functions are y = [2x] , y = x² and f(x) = 4x + 1 respectively.
They can be examined one by one as follows,
(a) y = [2x]
It is a greatest integer function.
At x = 1.1, y = [2 × 1.1] = [2.2] = 2
And, for x = 1.2, y = [2 × 1.2] = [2.4] = 2
It implies for different values of x, the function has same value.
Thus, it is not one-to-one function.
(b) y = x²
Find values of the function at two different x as,
x = -2, f(x) = (-2)² = 4
And, for x = 2, f(x) = 2² = 4.
It implies for different values of x, the function has same value.
Thus, it is not one-to-one function.
(c) f(x) = 4x + 1
It is a equation of a straight line.
Which implies it has different values for different values of x.
Thus, it is a one-to-one function.
Hence, out of the given functions only f(x) = 4x + 1 is one-to-one.
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write an equation in pint-slope form, slope-intercept, and standard form
Slope: -5 (-3,-7)
(-6,10), (-4,18)
(-4,9), (1,14)
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
to get the equation of any straight line, we simply need two points off of it, let's use (-6,10), (-4,18)
[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{18}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{18}-\stackrel{y1}{10}}}{\underset{\textit{\large run}} {\underset{x_2}{-4}-\underset{x_1}{(-6)}}} \implies \cfrac{8}{-4 +6} \implies \cfrac{ 8 }{ 2 } \implies 4[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{10}=\stackrel{m}{ 4}(x-\stackrel{x_1}{(-6)}) \implies {\large \begin{array}{llll} y -10 = 4 ( x +6) \end{array}} \\\\\\ y-10=4x+24\implies -4x+y=34\implies \stackrel{standard~form}{{\Large \begin{array}{llll} 4x-y=-34 \end{array}}}[/tex]
forty children from an after-school club went to the field trip . this is 25% of the children in the club. how many children are in the club?
Answer: 25% of 40 is 40 times 25 divided by 100 which is 10 (number of children in the club)
there:)
Answer: 160 children
Step-by-step explanation: 25% times 4 is 100%. So, you'd multiply 40 by 4.
Please its due today
a) The domain and the range of the function are given as follows:
Domain: [-4,5).Range: [0,9].b) The zero of the function is given as follows: (3,0).
c) The behaviors are given by these following intervals:
Increasing: (-4,0) U (3,5).Decreasing: (0,3).Constant: DNE.d) The extremas are given as follows:
Relative minimum: (3,0).Relative maximum: (0,9).e) The function is neither even nor odd.
What are the features of the function?The domain of a function is the set that contains all the input values for the function, hence in the graph it is given by the values of x.
The range of a function is the set that contains all the output values for the function, hence in the graph it is given by the values of y.
The zeros are the points of the function at which it either crosses or touches the x-axis.
The function is increasing when the graph is moving up, and decreasing it the graph is moving down.
The extremas are given as follows:
Relative minimum: function changes from decreasing to increasing.Relative maximum: function changes from increasing to decreasing.The function is classified as even, odd or neither as follows:
Even: f(x) = f(-x) for all values of x.Odd: f(-x) = -f(x) for all values of x.Neither: none of the two above statements are true.More can be learned about functions at https://brainly.com/question/24808124
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How do you verify that a dilation is a similarity transformation?
A transformation that alters the size of a figure is called a dilation (similarity transformation). It needs a scale factor of k and a central point. Depending on the value of k, the dilatation is either an enlargement or a decrease. The dilation is an enlargement if |k|>1.
If two figures have the same shape but different sizes, they are said to be comparable. A stiff motion combined with a rescaling constitutes a similarity transformation. In other words, a similarity transformation can change shape without changing location or size.
A dilation is a transformation that yields a different-sized picture with the same general shape as the original. Enlargements are dilations that result in a bigger picture. Reduction is the name for a dilatation that shrinks the picture. The initial figure is stretched or contracted by a dilatation.
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A company has two manufacturing plants with daily production levels of 5x +14 items and 3x - 5 items, respectively. The first plant produces how many more items daily than the second plant?
Answer:
21x
Step-by-step explanation:
5x+14=19x
3x-5=-2x
-2x-19x=21x
(25 points for the answer)
If John save 1/5 of his paycheck how much money would it take him to get to 14,500$ for his holiday trip? He earns $9062.5 each paycheck. (Unrealistic question unless you are under paid severely)
Use multiplication or division ONLY!
The amount of john would save 2900 rs
14500*1/5=2900
How much he earns on paycheck?A paycheck, also spelled paycheque, pay check or pay cheque, is traditionally a paper document issued by an employer to pay an employee for services rendered.a check used to pay an employee the amount of money the employee has earned.A paycheck can be an actual piece of paper (a check) that a person can take to the bank to deposit to their account or exchange for cash. Alternatively, a paycheck can be money a company electronically deposits directly into the employee's bank account.Take a look at how each common payroll interval works: Weekly: Once a week (52 paychecks per year) Biweekly: Once every other week (26 paychecks per year) Semimonthly: Twice per month (24 paychecks per yearTo learn more about paycheck refers to:
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which is the functions for increases 8.3%
Answer:
The US Consumer Price Index (CPI) increased 8.3% in the 12 months through August, with rent, food and healthcare accounting for the rise Excluding volatile food and gas prices, inflation climbed 6.3% year-on-year in July and 8.2% in September. US inflation ticked back up in August despite plunging gas prices.
citations: https://nypost.com/2022/10/13/inflation-hits-8-2-in-september-as-core-prices-surge/Step-by-step explanation:
The right triangle represents a sketch of a wheelchair ramp that meets safety requirements. What is the horizontal distance required for the ramp? Round your answer the nearest tenth
The horizontal distance required for the ramp is 143.5 inches
Consider the following figure.
In right triangle ACB, CB is the horizontal distance,
hypotenuse AB = 144 in.
and the vertical distance AC = 12 in.
We need to find the measure of side CB
Let m be the measure of the horizontal distance CB
Using Pythagoras theorem for right triangle ACB,
(AB)² = (AC)² + (CB)²
Substitute given values in above equation.
(144)² = (12)² + (m)²
20736 = 144 + m^2
20736 - 144 = 144 + m^2 - 144
20592 = m^2
m^2 = 20592
m = 143.5 in.
Therefore, the horizontal distance is 143.5 in.
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A newsletter publisher believes that more than 47% of their readers own a personal computer. Is there sufficient evidence at the 0.05 level to substantiate the publisher's claim?
There is no sufficient evidence that we can use in order to substantiate the claim of the publisher,
How to write the hypothesisThe null hypothesis H0: p = 0.47
The alternative hypothesis is H1: p > 0.47
The question requires us to test the fact that more than 47 percent of the readers have their own personal computer. This is therefore the claim that is to be tested here.
There is no sufficient evidence to substantiate the claim because of the lack of certain details that would have been used to carry out the hypothesis test.
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A pattern follows the rule "Starting with three, every consecutive line has 2 less than twice the previous line. "
1. How many marbles must be in the fifth line?
Therefore , the solution to the given problem of unitary method comes out to be 34 marbles are therefore on the sixth line.
Define the unitary method.The term unitary refers to a single or unique or variable unit. As a result, the purpose of this strategy is to construct values with regard to a single unit. For instance, if a car drives 44 kilometres on two litres of fuel, the unitary technique can be used to determine how many kilometers it will travel on one.
Here,
Every subsequent line, beginning with one, contains two less characters than the one before it.
This signifies that your starting line contains three marbles. The 3 marbles are multiplied by 2 to get 3x2=6, and the result is subtracted to get 6-2=4.
This implies that you will receive 4 marbles for the following line.
As a result, in order to determine the sixth line, you must first determine the fifth line by counting the number of marbles on the fourth line because your diagram does not include a fifth line.
(4) = ten marbles.
10×2=20
20-2=18
(5) line = (18)
18×2=36
36-2=34
Therefore , the solution to the given problem of unitary method comes out to be 34 marbles are therefore on the sixth line.
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1) state whether the dilation with the given scale factor would be a reduction or an enlargement
k=4
k=1/2
k= .75
k=5/2
Reducing the object's size by dilation is a change. The items are enlarged or shrunk through dilation.
How do you know if a dilation is an enlargement or reduction?Resizing an object is accomplished through a change called dilation. The objects can be enlarged or shrunk via dilation.
A diminution in the image occurs when the scale factor is between 0 and 1. An enlarged version of the image is shown if the scale factor is larger than 1.
An enlargement (imagine stretching) is a dilation that makes a larger image, whereas a reduction (think shrinking) is a dilation that creates a smaller image. A diminution in the image occurs when the scale factor is between 0 and 1. An enlarged version of the image is shown if the scale factor is larger than 1.
A transformation called a dilation (similarity transformation) alters the size of a figure. A center point and a scaling factor, k, are necessary. Which kind of dilation it is—an enlargement or a reduction—depends on the value of k. An enlargement results from a dilatation if |k|>1.
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Describe the distribution of the ages of the Best Actor Oscar winners [LINK]:
A) What is the BEST description of the SHAPE?
- The distribution is not skewed
- The distribution is skewed left.
- The distribution is skewed right.
The correct option is option (c)-"The distribution is skewed right."
The distribution of the ages of the Best Actor Oscar winners is slightly skewed to the right.
A histogram of the ages of the Best Actor Oscar winners shows that the majority of the ages are centered around the mean age, with a few ages on the higher end that extend the right tail of the distribution. This creates a small skewness to the right.
The distribution seems to be centered at around 42-43.
The age distribution ranges from about 30 to about 75, without taking into account an outlier.
It's worth noting that the distribution is not extremely skewed, and the majority of the ages are still grouped around the center of the distribution.
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4/5 + 3/4= asap PLEASEEE
Airport Auto Leasing has a ratio of cars to trucks that is 5 to 3. If each leasing center has 24 trucks, which auto leasing company has more cars? Main Street Auto Leasing has more cars since it has cars while Airport Auto Leasing has cars only
If the ratio of cars to truck in Main Street Auto Leasing Company is 9 to 4 and in the airport Auto Leasing Company is 5 to 3 , then the Main Street Auto Leasing Company has more number of cars .
The Ratio of cars to truck in Main Street Auto Leasing Company is = 9:4 ;
the ratio of cars to truck in Airport Auto Leasing Company is = 5:3 ;
the number of trucks in each Leasing Company is = 24 trucks ;
Case (i) : Main Street Auto Leasing Company ;
Since the ratio is = 9:4 ,
So , the number of cars is = 9x and
the number of trucks = 4x ;
That means , [tex]4x = 24[/tex] ;
[tex]x = 6[/tex] ;
the number of cars in Main Street company is = [tex]9 \times 6[/tex] = 54 cars .
Case (ii) : Airport Auto Leasing Company ;
the ratio is = 5:3 ;
So , the number of cars is = 5x and
the number of trucks = 3x ;
That means , [tex]3x = 24[/tex] ;
[tex]x = 8[/tex] ;
the number of cars in Airport Auto company is = [tex]5 \times 8[/tex] = 40 cars .
Therefore , the Main Street Auto Leasing Company has more number of Cars .
The given question is incomplete , the complete question is
Main Street Auto Leasing has a ratio of cars to trucks that is 9 to 4. Airport Auto Leasing has a ratio of cars to trucks that is 5 to 3. If each leasing center has 24 trucks, which auto leasing company has more cars ?
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Find the value x that makes the equation true . x + 4 = 12
x = 16
x=8
x=24
x=3
Answer:
x = 8
Step-by-step explanation:
x + 4 = 12
Subtract 4 from both sides
x = 8
Let's check
8 + 4 = 12
12 = 12
So, x = 8 is correct!
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How do you calculate seed multiplication ratio?
The number of seeds produced from a single seed when it is sown and harvested is referred to as the seed multiplication ratio.
What is Seed?A seed is an undeveloped plant embryo and food reserve that is encased in a protective outer covering in botany. More broadly, "seed" refers to anything that can be sown, which could include seed and husk or tuber.
Seeds are the result of a ripened ovule being fertilised by sperm from pollen, resulting in a zygote. The embryo within a seed develops from the zygote, forming a seed coat around the ovule and growing to a certain size within the mother plant before growth stops.
The formation of the seed is a step in the reproduction process of seed plants (spermatophytes). Other plants, such as ferns, mosses, and liverworts, do not have seeds and must reproduce through water-based means.
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PLEASE HURRY!!
Find the value of x
Answer:
Step-by-step explanation:
3x=24
x=8
The rate of growth dP / dt of a population of bacteria is proportional to the square root of t, where P is the population size and t is the time in days (0 ? t ? 10) as shown below.
dP/dt=k \sqrt{t}
The initial size of the population is 300. After 1 day the population has grown to 600. Estimate the population after 8 days. (Round your answer to the nearest whole number.)
The population of bacteria after 8 days is 7088
Here, we have been given an equation for the rate of growth of a population of bacteria
dP/dt = k√t
where P is the population size
and t is the time in days (0 ≤ t ≤ 10)
We rewrite above equation as,
dP = k√t dt
Integrating both sides, we get,
P = (2/3) × kt^(3/2) + C
We find the value of C.
For t = 0, P = 300 as the initial size of the population is 300.
Substitute t = 0 in above equation.
300 = 0 + C
C = 300
So, the above equation becomes,
P = 300 + (2/3) × kt^(3/2) .......(1)
Now we find the value of k.
After 1 day the population has grown to 600.
substitute t = 1, P = 600 in equation (1)
600 = 300 + (2/3) × k
(2/3)k = 300
k = 900/2
k = 450
So, the equation of population of bacteria after time t is:
P = 300 + [(2/3) × 450 × t^(3/2)]
P = 300 + 300 × t^(3/2)
P = 300 (1 + t^(3/2))
To find the population after 8 days, substitute t = 8
P = 300 (1 + 8^(3/2))
P = 7088.22
P ≈ 7088
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Which of the following is correctly written in Standard Form?
Therefore , the solution to the given problem of equation comes out to be4x-3y = 6 as a standard equation in all the above options.
An equation's definitionAn equation is a representation of two identical variables in mathematics, one on either side of an equals sign. Common difficulties can be solved using equations. We frequently seek pre algebra help when faced with obstacles in real life. Lessons in pre-algebra cover the basics of mathematics.
Here,
Given : 4x-3y = 6
-4x + 2y =8
=> y = 4/5x + 4
=> 4/5x + 2y = 6
Thus ,
From the above following equations we get ,
4x-3y = 6
as a standard equation in all the above options.
Therefore , the solution to the given problem of equation comes out to be 4x-3y = 6 as a standard equation in all the above options.
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3. ) Mary is the director of the Washington Performing Arts Center. Her employer offers a pension. Mary’s employer uses a formula to calculate the pension. Marina is planning on retiring at the end of this year after 30 years of employment. A retiring employee receives 1. 6% of his or her average salary for the last 5 years of employment multiplied by the number of years worked. Mary would receive this amount each year until her death. Her salaries for the last 5 years are $80,900; $90,200; $95,000; $99,000; and $104,000. Calculate Marina’s pension
Marina's pension amount is calculated by multiplying 1.6% of her average salary for the last 5 years by the number of years she has worked, which is 30.
1.6% x $80,900 = $1,282.40
1.6% x $90,200 = $1,444.32
1.6% x $95,000 = $1,520.00
1.6% x $99,000 = $1,584.00
1.6% x $104,000 = $1,664.00
Total = $7,604.72
Pension amount = $7,604.72 x 30 years
= $228,141.60
Marina's pension amount is determined using a formula set by her employer, the Washington Performing Arts Center. This formula takes into account her average salary for the last five years, which is $469,100, and multiplies it by 1.6%, then by the number of years she has worked for the Center, which is 30. This results in a pension amount of $228,141.60. This amount will be paid each year until her death. This pension amount is calculated based on the salaries she has earned over the past five years, which include $80,900; $90,200; $95,000; $99,000; and $104,000.
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what is the rate of decay f(x)=(.8)^x
9th grade AP algebra
The provided function, f(x)=(.8)^x, has a 20% rate of decay.
What is the Rate of decay or growth?
A rise in the resultant quantity for a given quantity is referred to as exponential growth, and a decrease in the resultant quantity for a given quantity is referred to as exponential decay.
given, a function f(x)=(.8)^x. To calculate the decay rate of this function.
The exponential decay formula aids in determining the exponential drop, which is a rapid reduction over time. To calculate population decay, half-life, radioactivity decay, and other phenomena, one uses the exponential decay formula. F(x) = a (1 - r)x is the general form.
Where
a = the initial amount
1-r is the decay factor
x = time span
from the given expression,
Decay factor = 0.8
That is also equal to 1 - r
1 - r = 0.8
r =0.2
Thus, rate of decay = r * 100%
rate of decay = 0.2 * 100 = 20%
therefore, The rate of the of the given function f(x)=(.8)^x is 20%.
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Let ABC be a triangle, and
M, N, and K represent the midpoints of sides AB, BC, and AC respectively.
If area of the triangle ABC is 6.0 square feet, then what is the area of the triangle MAK?
Step-by-step explanation:
please refer to the sketch
Mrs Anderson has 185 pieces of wood he sold 25 peacas of wood to his neighbor and distract the rest of the world into piles around his house each pile of wood contained 40 pieces of wood which equation can be used to find peat the number of piles of wood Mr. Anderson made?
Answer: Let x be the number of piles of wood that Mr. Anderson made.
We know that he sold 25 pieces of wood to his neighbor, and the rest of the pieces of wood were divided into piles around his house, with each pile containing 40 pieces of wood.
Therefore, we can set up the equation:
185 pieces - 25 pieces = x * 40 pieces
Simplifying the equation:
160 = x * 40
To find the value of x, we need to divide 160 by 40
160/40 = x
x = 4
Therefore, Mr. Anderson made 4 piles of wood after he sold 25 pieces of wood to his neighbor.
It's worth noting that this equation was used to find the number of piles of wood Mr. Anderson made after selling 25 pieces to his neighbor, and assuming that he didn't use the rest of the wood for anything else except for making the piles.
Step-by-step explanation:
Write the answer to 3^4 x 3^7
(i) in the form 3^x
(ii) as an integer
Answer:
I)3^4 x 3^7=3^4+7(b/c the base is similar)
3^4 x 3^7=3^11
Ii) first 3^4=3x3x3x3=81
3^7=2187
then 81 x 2187=177147
A neighbor of yours is getting ready to
plant a garden of flowers in his backyard.
He asks you for ideas on how to
conserve soil. You notice that his
backyard has a lot of hills. What do you
suggest?
In order to maintain soil fertility and productivity, soil must be protected from erosion and other forms of deterioration. Water use and watershed management are typically included.
What comes first in gardening?Eliminating the existing vegetation is the first step in making a garden bed. Weeds can be manually pulled. Just be certain to remove the roots to prevent regrowth. You might want to rent a gas-powered sod cutter to get rid of the grass if you're starting with a lawn.
What is an example of soil conservation?Better soil conservation techniques that affect both erosion and fertility include crop rotation, cover crops, conservation tillage, and installed windbreaks.
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Which of the following is the graph of y=-4 square root x
In the second graph, these points are located. As a result, the second graph is the function's correct graph.
what is function ?In mathematics, the term "linear function" refers to two different but related ideas. In calculus and related fields, a quadratic variable of grade 0 or 1 is a linear function if its graph is a direct line. A straight line on a reference system is a representation of a linear function. For instance, the linear function y = 3x - 2 is a straight line just on coordinate plane, hence it is a linear function. Since f(x) may be connected to y, the function can be represented by f(x) = 3x - 2.
given
The function provided is
This function is defined for any x values that are positive, including 0.
The radical expression x has a constant positive value. Given that is a function, it is always negative.
At x=0, = 0
At x=1, = -4
At x=4, = -8
This indicates that the graph of the specified function traveling through the points (0,0), (1,-4) and (4,-8).
In the second graph, these points are located. As a result, the second graph is the function's correct graph.
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Write an equation of the line that passes through (3,-4) and is perpendicular to y=1/2x+7.
What is the value of sin cos theta?
If sinθ⋅cosθ = 1/2, then the value of sinθ + cosθ = √2
We know that the trigonometric sine function is nothinng but the ratio of the length of the opposite side of angle to that of the hypotenuse in a right triangle.
And cosine function (cos function) is the ratio of the length of the adjacent side of angle to that of the hypotenuse.
Given that sinθ⋅cosθ = 1/2
2(sinθ⋅cosθ) = 1 .........(1)
We know that trigonometric identity,
sin(2θ) = 2 sinθ cosθ
so equation (1) becomes,
sin(2θ) = 1
We know that sin(π/2) = 1
Comparing with equation sin(2θ) = 1 we get,
2θ = π/2
θ = π/4
Using trigonometric table,
sin(π/4) = 1/√2
and cos(π/4) = 1/√2
The value of sinθ+cosθ would be,
sin(π/4) + cos(π/4)
= (1/√2) + (1/√2)
= 2/√2
= √2
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The complete question is:
If sinθ⋅cosθ=1/2 find the value of sinθ+cosθ