2sin(2x+π÷3)≥√3
[tex]2 \sin(2x + \frac{\pi}{3} ) \geqslant \sqrt{3} [/tex]
with steps
![2sin(2x+3)3[tex]2 \sin(2x + \frac{\pi}{3} ) \geqslant \sqrt{3} [/tex]with Steps](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/lBwjtFX4EXWRzoENVPDC6IUZcvhh76oM.jpeg)
Answers
The solution to the inequality 2sin(2x+π/3)≥√3 is:
x ∈ [-π/6, π/3]
What is inequality?
An inequality is a mathematical statement that compares two values or expressions using symbols such as < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), or ≠ (not equal to). Inequalities are used to express relationships between quantities that are not necessarily equal.
To solve the inequality 2sin(2x+π/3)≥√3, we can follow these steps:
Step 1: Subtract π/3 from both sides to get rid of the constant term on the right-hand side:
2sin(2x+π/3) - π/3 ≥ √3 - π/3
Step 2: Divide both sides by 2 to isolate sin(2x+π/3):
sin(2x+π/3) ≥ (√3 - π/3)/2
Step 3: Use the fact that sin(x) is positive in the first and second quadrants of the unit circle to find the interval of x that satisfies the inequality. To do this, we need to find the angles α and β such that sin(α) = (√3 - π/3)/2 and sin(β) = - (√3 + π/3)/2. Then, the solution interval will be:
α/2 - π/6 ≤ x ≤ β/2 + π/6
To find α and β, we can use the inverse sine function on a calculator or look them up in a table. We get:
α ≈ 0.4636 radians
β ≈ 2.6779 radians
Substituting these values into the solution interval, we get:
0.2318 - π/6 ≤ x ≤ 1.3389 + π/6
Simplifying, we get:
-π/6 ≤ x ≤ π/3
Therefore, the solution to the inequality 2sin(2x+π/3)≥√3 is:
x ∈ [-π/6, π/3]
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Related Questions
help pls
1. Renae has been playing Tower of Hanoi and has noticed that the minimum number of moves it takes to defeat the game is related to the number of disks she must move. She has recorded her observations below. Write an equation that describes this pattern.
2. Use a proof by mathematical induction to show that your equation from question 1 applies to the minimum number of moves required to defeat the Tower of Hanoi game, based on the number of disks you must move. Think about the process of the game; and describe how your equation applies to it.
Answers
The minimum number of moves required to complete the Tower of Hanoi game is related to the number of disks, and can be described by the equation m = [tex]2^n - 1[/tex].
Let n be the number of disks and m be the minimum number of moves required to complete the Tower of Hanoi game. Renae's observations suggest that the equation m = [tex]2^n - 1[/tex] describes this pattern.
When n=1, the minimum number of moves required to complete the game is m=1. Plugging this value into the equation m=[tex]2^n-1[/tex]gives m=[tex]2^1-1[/tex]=1. Therefore, the equation holds true for n=1.
Assume that the equation holds true for n=k. That is, m=[tex]2^k-1[/tex] is the minimum number of moves required to complete the game with k disks.
Now, consider the case where n=k+1. This requires a minimum of m=[tex]2^k-1[/tex] moves, according to the equation. Then, the largest disk can be moved to the ending peg in one move. Finally, the k disks that were moved to the spare peg must be moved to the ending peg, which requires another minimum of m=[tex]2^k-1[/tex] moves.
Thus, the total minimum number of moves required to complete the game with k+1 disks is:
m = [tex]2(2^k-1) + 1[/tex]
m = [tex]2^(k+1) - 2 + 1[/tex]
m = [tex]2^(k+1) - 1[/tex]
This is the same as the equation we started with, but with k+1 in place of n. Therefore, the equation holds true for all positive integers n by mathematical induction.
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what is the constant of proportionality in the table below
Answers
Answer: 3
Step-by-step explanation:
k = y/x
In Problem 3, determine the level of measurement of each variable. 1. Birth order among siblings in a family
2. Volume of water used by a household in a day
3. Highest degree conferred (high school, bachelor’s, and so on)
4. Ages of children: 4 years, 5 years, 6 years, 7 years, and 8 years
Answers
1) Birth order among siblings in a family: Nominal level of measurement
2) Volume of water used by a household in a day: Ratio level of measurement
3) Highest degree conferred (high school, bachelor's, and so on): Ordinal level of measurement
4) Ages of children: 4 years, 5 years, 6 years, 7 years, and 8 years: Interval level of measurement
1) Birth order among siblings in a family: This variable is measured at the nominal level of measurement, as there is no inherent order or ranking to the categories
2) Volume of water used by a household in a day: This variable is measured at the ratio level of measurement, as it has a true zero point (i.e., no water usage) and the values can be compared in terms of ratios
3) Highest degree conferred (high school, bachelor's, and so on): This variable is measured at the ordinal level of measurement, as the categories have an inherent order or ranking (e.g., a bachelor's degree is higher than a high school diploma, but it does not necessarily indicate that someone with a bachelor's degree is "twice as educated" as someone with a high school diploma).
4) Ages of children: 4 years, 5 years, 6 years, 7 years, and 8 years: This variable is measured at the interval level of measurement, as the values have a meaningful order and distance between them (i.e., the difference between 4 years and 5 years is the same as the difference between 7 years and 8 years). However, there is no true zero point, as "zero years old" is not a meaningful category in this context.
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While birdwatching, Vicki saw 7 red birds, 9 white birds, and 19 black birds. Johnny saw 9 red birds, 12 blue birds, and 29 brown birds. Estimate how many more birds Johnny saw by rounding all numbers to the nearest ten before adding and subtracting.
Answers
Answer:
10
Step-by-step explanation:
7 rounds to 10
9 rounds to 10
19 rounds to 20
so Vicki has 40 birds
9 rounds to 10
12 rounds to 10
29 rounds to 30
so johnny has 50 birds
now subtract 50-40=10
Each yoga mat measures 2.2 ft by 6.3 ft. What is the area in square feet of each yoga mat?
Answers
2.2 x 6.3 = 13.86 square feet
At a school of 550 children 80% walk to school
Answers
If at a school of 550 children 80% walk to school, the 110 children come to school by other means.
If 80% of the children walk to school, then the remaining 20% of children must arrive at school by other means (such as being driven by a parent, taking public transportation, etc.).
To find out how many children come to school by other means, we can use the following formula:
Number of children who come to school by other means = Total number of children x Percentage who don't walk to school
In this case, we have:
Number of children who come to school by other means = 550 x 20% = 110
Therefore, 110 children come to school by other means.
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The given question is incomplete, the complete question is:
At a school of 550 children 80% walk to school, how many comes in other way ?
pre-event tickets for a local theater fundraiser cost $35 and $40 for at-the-door tickets. organizers sell a total of 250 tickets and generate a total revenue of $9,375. how many pre-event and at-the-door tickets were sold?
Answers
This can be calculated by multiplying the number of tickets sold by their respective prices: 200 x $35 = $7,000 and 50 x $40 = $2,375.
The local theater fundraiser sold 200 pre-event tickets at $35 each and 50 at-the-door tickets at $40 each to generate a total revenue of $9,375. This can be calculated by multiplying the number of tickets sold by their respective prices: 200 x $35 = $7,000 and 50 x $40 = $2,375.
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please need full answer asap
Answers
Answer:
Step-by-step explanation:
[tex](x+14)^2+x^2=22^2[/tex] (Pythagoras Theorem)
[tex](x^2+28x+196)+x^2=484[/tex]
[tex]2x^2+28x+196=484[/tex]
[tex]2x^2+28x-288=0[/tex]
[tex]x^2+14x-144=0[/tex]
Using quadratic formula,
[tex]x=\frac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex]
[tex]x=\frac{-14\pm \sqrt{(14^2-4\times1\times(-144)} }{2\times1}[/tex]
[tex]=\frac{-14\pm \sqrt{(196+576} }{2}[/tex]
[tex]=\frac{-14\pm 2\sqrt{193} }{2}[/tex]
[tex]=-7\pm\sqrt{193}[/tex]
[tex]=-7\pm13.89[/tex]
[tex]=6.89 ,-20.89[/tex] (-20.89 is not useful...cannot have a negative length for
radius)
Solution: radius is 6.89
Help please…… i need it
Answers
The sides of 15mm, 28mm and 11mm are the sides of a triangle.
What is the triangle inequality theorem?To determine if three given lengths can form a triangle, we can apply the Triangle Inequality Theorem, which states that the sum of any two sides of a triangle must be greater than the third side.
If we add the two shorter sides together, we get [tex]15 + 11 = 26[/tex] . This sum is greater than the longest side, which is [tex]28[/tex] . Similarly, if we add the two smaller sides to the longest side, we get [tex]11 + 28 = 39[/tex] and [tex]15 + 28 = 43[/tex] , which are both greater than the remaining side.
Therefore, the three given lengths satisfy the Triangle Inequality Theorem and can form a triangle.
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Which number is a perfect square
Responses
2
8
16
20
Answers
Answer:
16
Step-by-step explanation:
because it is a square number. The other numbers, if you square root them you won't get a whole number.
For breakfast each day, you plan to flip a coin to decide whether to have cereal or toast. When you flip heads, you will have cereal. When you flip tails, you will have toast. Your friend predicts that you will have cereal 15 times this month. Is your friend correct? Explain your reasoning.
Answers
Answer: yes
Step-by-step explanation:
there is a 50% chance of landing on heads which means that you are statistically likely to have cereals for half a month and toast for half a month. half a month is usually 15 days so your friend is correct
please mark brailiest
When K is small, x is also small.The "x is small" approximation only works when: the initial concentration of the reactant is relatively large and the equilibrium constant is small.The x is small approximation does not mean that x is zero. If that were the case, the reactant and product concentrations wouldn't change from their initial values. The x is small approximation just means that when x is added or subtracted to another number, it doesnt' change that number by very much.The x is small approximation must satisfy the <5% rule, whereby the x approximation divided by the number it was subtracted from is is less than 5% (or 0.05).The method of successive approximation is solving for x as if it were small, and then substituting the value obtained back into the equation (where x was initially neglected) to solve for x again. This can be repeated until the calculated value of x stops changing with each iteration, an indication that we have arrived at an acceptable value for x.
Answers
The "x is small" approximation only works when the initial concentration of the reactant is relatively large and the equilibrium constant is small.
What does the "x is small" approximation mean? The x is small approximation does not mean that x is zero. If that were the case, the reactant and product concentrations wouldn't change from their initial values. The x is small approximation just means that when x is added or subtracted to another number, it doesn't change that number by very much. When does the "x is small" approximation work? The "x is small" approximation only works when the initial concentration of the reactant is relatively large and the equilibrium constant is small. What is the <5% rule? The x is small approximation must satisfy the <5% rule, whereby the x approximation divided by the number it was subtracted from is less than 5% (or 0.05). What is the method of successive approximation? The method of successive approximation is solving for x as if it were small, and then substituting the value obtained back into the equation (where x was initially neglected) to solve for x again. This can be repeated until the calculated value of x stops changing with each iteration, an indication that we have arrived at an acceptable value for x.
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Which correlation coefficient reflects the strongest relationship?
a) +0.05
b) +0.25
c) +1.23
d) -0.33
Answers
The correlation coefficient that reflects the strongest relationship is +0.25, the correct option is b.
EXPLANATION:
The correlation coefficient ranges from -1 to +1.
The magnitude (absolute value) of the correlation coefficient indicates the strength of the relationship, with values closer to -1 or +1 indicating a stronger relationship.
Therefore, the correlation coefficient that reflects the strongest relationship is +1.23.
However, since this value is greater than +1, which is not possible, it seems to be an invalid value.
Among the given options,
The correlation coefficient that reflects the strongest relationship is b) +0.25.
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Select the correct answer. Simon used these steps to solve an equation: Step 1: -6(x + 7) = 2(x − 11) Step 2: -6x − 42 = 2x − 22 Step 3: -8x − 42 = -22 Step 4: -8x = 20 Which property did he use to get from step 3 to step 4? A. addition property of equality B. distributive property C. subtraction property of equality D. transitive property
Answers
Answer: A - addition property of equality
Explanation: because -8x - 42 = -22
+42 +42
____________
-8x = 20
__ __
-8 -8
x = -2.5
Please help I’ll give brainliest
Answers
The solutions to the equation [tex]15z^2 +6z -8 =4z[/tex] are z = 2/3 or z = -4/5.
To solve the quadratic equation [tex]15z^2 +6z -8 =4z[/tex], we first need to rearrange it into standard form:
[tex]15z^2 + 2z - 8 = 0[/tex]
Now we can apply the quadratic formula:
z = (-b ± √(b² - 4ac)) / 2a
where a = 15, b = 2, and c = -8.
Plugging in these values, we get:
z = (-2 ± √(2² - 4(15)(-8))) / (2(15))
z = (-2 ± √(4 + 480)) / 30
z = (-2 ± √484) / 30
z = (-2 ± 22) / 30
So z equals either (-2 + 22)/30 = 2/3 or (-2 - 22)/30 = -4/5.
Therefore, the solutions to the equation 15z² +6z -8 =4z are z = 2/3 or z = -4/5.
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Solve for x and y and how.
Answers
Answer:
The lines that go through all 3 sides of the triangle mean the angles are all equal. Since a triangle is 180 degrees, to find a single angle, we must divide by 3.
180 degrees / 3 = 60 degrees
Solve for X
60 = (2x + 10)
-10 from both sides:
50 = (2x)
x = 25
Solve for Y
60 = (3y + 3)
-3 from both sides:
57 = (3y)
y = 19
Hope that helps
what is an equivalent expression to 4x(2x-3)-5(3x-4)
Answers
Answer:4x + 3x + 2x - 4 - 3
Step-by-step explanation:Hope this helps
Justin wants to buy a new football that costs 22.99. He has a discount coupon of 12% off. If Justin has exactly $20, does he have enough money to buy the football with the coupon? How much more money does he need OR how much money does he get in change?
Answers
He needs an additional $0.23 to buy the football with the coupon after the discount coupon.
What is Discount?A discount is a reduction in the price of a product or service. It is often used as a marketing tool to attract customers and increase sales. Discounts can be expressed as a percentage or a dollar amount.
What is discounted price?The discounted price is the price of a product or service after a discount has been applied. The discount is usually expressed as a percentage or a dollar amount and is subtracted from the original price.
In the given question,
The discount Justin can get is 12% of the original price, which is:
0.12 x 22.99 = 2.76
So the discounted price of the football is:
22.99 - 2.76 = 20.23
Since Justin has exactly $20, he doesn't have enough money to buy the football with the coupon. He needs:
20.23 - 20 = 0.23
So he needs an additional $0.23 to buy the football with the coupon.
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Simplify: the sum of 6. 6 and 3. 2 all divided by 5 times the quantity of the squared difference of 2 minus 5 plus 6
Answers
The simplified form of the expression the sum of 6. 6 and 3. 2 all divided by 5 times the quantity of the squared difference of 2 minus 5 plus 6 is -0.3267
To simplify this expression, we'll work from the inside out, using the order of arithmetic operation
First, we'll evaluate the expression inside the parentheses:
(2 - 5 + 6) = 3
Next, we'll calculate the squared difference of 2 and 5:
(2 - 5)^2 = (-3)^2 = 9
Then, we'll subtract the result from step 2 from the result of step 1:
3 - 9 = -6
Next, we'll calculate the sum of 6.6 and 3.2:
6.6 + 3.2 = 9.8
Finally, we'll divide the result from step 4 by 5 times the result from step 3:
9.8 / (5 × -6) = 9.8 / -30
= -0.3267 (rounded to four decimal places)
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please I really need help by tmr!!
How many intersections are there between the graphs of f(x) = 0.8x and g(x) = \lfloor x \rfloor?
Answers
The answer is one intersection.
What is a function?
A function is a relationship or expression involving one or more variables. It has a set of input and outputs.
The graph of the function f(x) = 0.8x is a straight line with slope 0.8 passing through the origin (0, 0). The graph of the function g(x) = ⌊x⌋ is the collection of all points (x, y) where y is the greatest integer less than or equal to x. This function is not continuous and has a discontinuity at each integer.
To find the intersections between the two graphs, we need to determine where the values of f(x) and g(x) are equal.
we need to find the integer values of x where 0.8x and x are equal.
0.8x = x
0.2x = 0
x = 0
Thus, the two graphs intersect at the point (0, 0). There are no other intersections between the two graphs, since they have different slopes and one is continuous while the other is not. Therefore, the answer is one intersection.
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Shaila is riding on a rollercoaster when her phone falls out of her pocket. The phone followed the equation y=−16t2+400
where y
gives the height of the phone after t
seconds. How long did it take her phone to hit the ground?
The phone hit the ground after seconds.
Answers
Answer:
5 seconds
Step-by-step explanation:
when the phone hits the ground then y = 0 , that is
- 16t² + 400 = 0 ( subtract 400 from both sides )
- 16t² = - 400 ( divide both sides by - 16 )
t² = 25 ( take square root of both sides )
t = [tex]\sqrt{25}[/tex] = 5
the phone hits the ground after 5 seconds
Answer:
5 seconds
Step-by-step explanation:
y = [tex]-16t^{2} + 400 \\[/tex]
Make t the subject:
[tex]16t^{2} = -400\\t^{2} = \frac{400}{16} = 25\\ t = \sqrt{25} = 5[/tex]
Therefore the answer is 5 seconds
What is the volume of the cone expressed in terms of pi?
Answers
H= 9 in
Cone formula:
V = 1/3 π r ^ 2 h
V = 1/3 π (4)^2 (9)
V= 48 π
Solution:
48 π in^3
what is the probability of getting all tails? express your answer as a simplified fraction or a decimal rounded to four decimal places.
Answers
The probability of getting all tails when flipping a coin three times can be calculated using the multiplication rule of probability. For each flip of the coin, there are two possible outcomes: heads or tails.
Assuming the coin is fair, both outcomes are equally likely, so the probability of getting tails on any one flip is 1/2.
To calculate the probability of getting all tails in three flips, we need to multiply the probabilities of getting tails on each individual flip. Since the flips are independent events (i.e. the outcome of one flip does not affect the outcome of another flip), we can simply multiply the probabilities together:P(all tails) = P(tails on first flip) x P(tails on second flip) x P(tails on third flip)
= (1/2) x (1/2) x (1/2)
= 1/8
Therefore, the probability of getting all tails when flipping a coin three times is 1/8 or 0.125 when expressed as a decimal rounded to four decimal places.
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Tolosa sold 540 eggs if these are 35% of total eggs,then how many eggs are not sold?
Answers
The total number of eggs is 1542.
To find the total number of eggs, we can use the fact that the 540 eggs sold represent 35% of the total eggs. We can start by setting up a proportion:
35/100 = 540/x
where x is the total number of eggs. To solve for x, we can cross-multiply and simplify:
35x = 54000
x = 54000/35
x = 1542.86
Therefore, the total number of eggs is approximately 1542.86. Since we can't have a fraction of an egg, we can assume that the total number of eggs is 1542.
To find the number of eggs that are not sold, we can subtract the number of eggs sold from the total number of eggs:
1542 - 540 = 1002
Find out more about The total number of eggs is 1542.
To find the total number of eggs, we can use the fact that the 540 eggs sold represent 35% of the total eggs. We can start by setting up a proportion:
35/100 = 540/x
where x is the total number of eggs. To solve for x, we can cross-multiply and simplify:
35x = 54000
x = 54000/35
x = 1542.86
Therefore, the total number of eggs is approximately 1542.86. Since we can't have a fraction of an egg, we can assume that the total number of eggs is 1542.
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(BRAINLIEST) A baker sells cupcakes and bases her prices on the number of cupcakes purchased.
The graph shows a piecewise function with one piece increasing from the point 0 comma 0 through the point 12 comma 18 to the endpoint 24 comma 36 and another piece going from the point 24 comma 36 through the point 48 comma 60 and increasing to the right.
Based on the graph, what is the pricing the baker uses for her sales?
The first 24 cupcakes cost $1.50 each, and all cupcakes after that cost $1 each.
The first 24 cupcakes cost $1 each, and all cupcakes after that cost $1.50 each.
The first 36 cupcakes cost $1.50 each, and all cupcakes after that cost $1 each.
The first 36 cupcakes cost $1 each, and all cupcakes after that cost $1.50 each.
Answers
Answer: The first 24 cupcakes cost $1.50 each, and all cupcakes after that cost $1 each.
Step-by-step explanation:
The graph shows two pieces of the function, with one increasing from the point (0, 0) through the point (12, 18) to the endpoint (24, 36) and the other increasing from the point (24, 36) through the point (48, 60) to the right.
This means that the first 24 cupcakes cost $1.50 each and all cupcakes after that cost $1 each, as shown by the first piece of the function. The second piece of the function shows that the price per cupcake does not increase after 36 cupcakes, so option 3 and option 4 can be eliminated.
Therefore, the correct answer is: The first 24 cupcakes cost $1.50 each, and all cupcakes after that cost $1 each.
Odero sold a suit for 960 making a loss of 20% for how much would he have sold it to make a profit of 20%
Answers
From the given information provided, Odero would have had to sell the suit for 1224 to make a profit of 20%.
If Odero sold a suit for 960 and made a loss of 20%, it means his selling price was only 80% of the cost price. We can use this information to find his cost price:
Cost price = Selling price / (1 - Loss%)
Cost price = 960 / (1 - 0.20)
Cost price = 960 / 0.80
Cost price = 1200
Therefore, Odero's cost price for the suit was 1200.
Now, we need to find the selling price that would give him a profit of 20%. Let's call this selling price S:
Profit% = (Selling price - Cost price) / Cost price × 100
20% = (S - 1200) / 1200 × 100
2 = (S - 1200) / 12
S - 1200 = 24
S = 1224
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A. 1/2 + 1/4
B. 5/6 + 5/12
C. 13/14 + 5/7
D. 3/4 + 5/24
Please
Answers
B. 5/6 + 5/12 = 10/12 + 5/12 = 15/12 or 1 3/12 or 1 1/4
C. 13/14 + 5/7 = 13/14 + 10/14 = 23/14 or 1 9/14
D. 3/4 + 5/24 = 18/24 + 5/24 = 13/24
Please Help! I don't understand this question!
Answers
Answer:
all you gotta do is mirror that half u and make it a full u
and since the points it intersects at is (1,-1) plot the other half on (1,1)
jamal throws a ball up in the air. The graph below shows the height of the ball h in feet after t seconds. after how many seconds does the ball hit the ground? (1,16) (2,0) area amd projectile motion
Answers
Answer:
Step-by-step explanation:
maple has 4 identical loaves of bread that weigh a total of 6.6 pounds how much does 1 loaf of bread weigh
Answers
Answer:
1.65 pounds
Step-by-step explanation:
6.6 ÷ 4 = 1.65
Answer:
1.65
Step-by-step explanation:
since all together it weighs 6.6 pounds then 1 = x then you cross multiply after cross multiplying you divide 4 by 6.6. Then x = 1.65