Find all solutions of the following equation in the interval [0, 2pi).2cos^2 x = 2- sin
Answers
Step 1: problem
[tex]2\cos ^2x\text{ = 2 - sinx}[/tex]Step 2: Concept
[tex]\text{cos}^2x=1-sin^2x[/tex]Step 3: Method
[tex]\begin{gathered} 2\cos ^2x\text{ = 2 - sinx} \\ 2(1-sin^2x)\text{ = 2 - sinx} \\ 2-2sin^2x\text{ = 2 - sinx} \\ 2-2=2sin^2x\text{ - sinx} \\ 2\sin ^2x\text{ - sinx = 0} \\ \sin x\text{ (2sinx - 1 ) = 0} \end{gathered}[/tex][tex]\begin{gathered} \sin x\text{ = 0 or 2sinx - 1 = 0} \\ x\text{ = }\sin ^{-1}0\text{ or 2sinx = 1} \\ \text{ x = 0 or sinx = }\frac{1}{2} \\ \text{ x = }\sin ^{-1}(\frac{1}{2})\text{ = 30} \end{gathered}[/tex][tex]x\text{ = 0, }\pi,\text{ }\frac{\pi}{6},\text{ }\frac{5\pi}{6}[/tex]Final answer
Related Questions
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T.28 Write an equation for a parallel or perpendicular line 5SH
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Line q has an equation of y = -x+ 2. Line r includes the point (9, -3) and is parallel to
line q. What is the equation of line r?
Skill plans
Write the equation in slope-intercept form. Write the numbers in the equation as simplified
proper fractions, improper fractions, or integers.
Answers
Answer:
y = - x + 6===========================
GivenLine q with equation of y = - x + 2,Line r with the point (9, - 3) and parallel to line q.To find Equation of line r.SolutionWe know parallel lines have equal slopes, so line r has the slope of - 1.
Line r is:
y = - x + b, where b- the y-interceptSubstitute the coordinates of the point into this equation and find the value of b:
- 3 = - 9 + bb = - 3 + 9b = 6The equation of line r is:
y = - x + 6can anyone help???????
Answers
Answer:
The sum of the angles is 180°.
We already know that one angle is 90°, and the other one is 38.
so: 180-(90+38)=52°
the exterior angle+52°= 180° (beacuse the form a flat angle)
so x=180-52
so: x=128°.
Answer:
128°
Step-by-step explanation:
We know that,
the exterior angle of a triangle is equal to the sum of the interior opposite angles of a triangle.
Accordingly,
38 + 90 = x
128° = x
your textbook authors suggest that if your population has fewer than 100 people you should group of answer choices use a stratified sampling method. use simple random selection. find a larger population test everyone in the population.
Answers
The proper sampling technique used when the number of samples is less than 100 is saturated sampling where the entire population will be the research sample.
What is saturated sampling ?
According to Arikunto if the population is less than 100 people so the researcher need to take all the samples namely saturated sampling.
What is stratified sampling ?
Stratified sampling is a sampling technique which used when we do a research on a heterogenous population. How to use this technique is to divide the population into several stratum and then take random samples from each stratum an then all the samples that have been taken are collected into one sample.
In conclusion, if the population has fewer than 100 people , the expert suggested to use saturated sampling.
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8. It takes Joe 12 minutes to ride a roller
coaster four times. Create a table to represent
the relationship between the total time, y, and
the number of rides, x.
Answers
The required table, which represents the relationship between the total time y and the number of rides x,
x y[min]
1 3
2 6
3 9
proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
Here,
Let,
Total time of ride a roller is directly proportional to the number of rides, x
y = kx
where k is the rate constant,
put y = 12 and x = 4
12 = 4k
k = 3
Now,
y = 3k
From the above expression, a table can be deduced.
Thus, the solution is given in the table as.
x y[min]
1 3
2 6
3 9
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Given the definitions of f(x) and g(x) below, find the value of (gof)(3).
f(x) = 2x² - x - 15
g(x) = -5x +9
Answers
Answer:
[tex] \huge{ \boxed{gof(3) = 9}}[/tex]
Step-by-step explanation:
In order to find gof(3), we first have to find gof(x). To find gof(x) substitute the f(x) into g(x). That is, for every x found in g(x) substitute it by f(x).
From the question
[tex]f(x) = 2 {x}^{2} - x - 15 \\ g(x) = - 5x + 9 \\ \\ gof(x) = - 5(2 {x}^{2} - x - 15) + 9 \\ gof(x) = - {10x}^{2} + 5x + 75 + 9 \\ \\ gof(x) = - {10x}^{2} + 5x + 84[/tex]
To find gof(3), substitute the value of x that is 3 into gof(x). For every x found in gof(x), replace it by 3 and solve.
[tex]gof(3) = - 10( {3})^{2} + 5(3) + 84 \\ \quad \: \: \: \: \: = - 10(9) + 15 + 84 \\ \: \: \: = - 90 + 15 + 84 \\ = 9[/tex]
We have the final answer as
gof(3) = 9How far can a family travelin 4 days if they travel 620 milesin two days? (at the same rateof speed)
Answers
Let x be the number of miles the family travel in 4 days
620 miles = 2 days
x = 4 days
cross-multiply
2x = 2480
Divide both-side of the equation by 2
x = 1240 miles
3. Which expressions are equivalent to the given one?
Select each that apply.
20/-4
a. 20 x
b. 20 x-1
c. 5
d. -5
Answers
Answer:
b, d
Step-by-step explanation:
20/-4 = -5
20 x (-1/4) = -5
A car can travel 100 km on five liters of gas. How many liters will be needed to travel 40 km?
Answers
Answer:
2
Step-by-step explanation:
40 x 5 ÷ 100
2 x 5 ÷ 5 = 2
• 100%XIsabel is thinking of two numbers. Their greatest common factor is 14. Their least common multiple is 168. One of the numbers is 56.What is the other number?O A. 84Ο Ο ΟOB. 42C. 28O D. 8O E. 7
Answers
GCF = 14
LCM = 168
let x and y be the numbers
if X = 56
The other number (y) can be obtained using the formula:
=> (GCF x LCM) / X
=> (14 X 168)/ 56
=> 2352/56
=>42
Option B is correct
What is the formula for the sequence
1, 6, 12, 19, 27 ?
Answers
Answer: the formula is 5,6,7,8,9,10 every step plus one
Step-by-step explanation:
1+5 =6
6+6=12
12+7=19
19+8=27
27+9=36
Mr Kennedy raised beef cattle. The stock tank near the windmill has a diameter of 3 meters. When it is full, the water is 1.5 meters deep. How many cubic meters of water are in the stock tank when it is full use 3.14 for pi.A 7.1 B 10.6 C 42.4 D 14.1
Answers
Answer: B 10.6
Explanation:
We would assume that the stock tank is cylindrical. We would calculate the volume by applying the formula,
Volume = πr^h
where
π = 3.14
r is the radius of the cylinder
h is the height of the cylinder
From the information given,
diameter = 3
radius = diameter/2 = 3/2
r = 1.5
h = 1.5
Volume = 3.14 x 1.5^2 x 1.5 = 10.5975 cubic meters
By rounding to the nearest tenth,
Volume = 10.6 cubic meters
Will mark As Brainliest pls answer the 5 questions
Answers
The required solution of the linear equation is x = 6.
What is linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Given [tex]\frac{3x}{2} - \frac{2x}{3}=5[/tex]
[tex]\frac{3x}{2} - \frac{2x}{3} = 5\\ \Rightarrow \frac{9x-4x}{6} = 5\\ \Rightarrow \frac{5x}{6} = 5\\\Rightarrow 5x = 30\\\Rightarrow x = 6[/tex]
Therefore, the required solution of the linear equation is x = 6.
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How do I solve this?
Answers
Answer:
12
Step-by-step explanation:
Rewrite 16 as 4 ^ 2...
[tex]\sqrt[3]{4^2}[/tex]
Pull terms out from under the radical, assuming positive real numbers...
3 x 4
Multiply 3 by 4...
12
Hope this helps! :)
help meeeeeeeeeeeeeee pleaseeeeeee
Answers
Answer: Width = 3.4 meters, Length = 6.4 meters
Step-by-step explanation:
If the width is [tex]w[/tex], then the length is [tex]w+3[/tex].
[tex]w(w+3)=22\\\\w^2 +3w=22\\\\w^2 +3w-22=0\\ \\ w=\frac{-3 \pm \sqrt{3^2 -4(1)(-22)}}{2(1)}\\\\w \approx 3.4 \text{ } (w > 0)\\\\\implies w+3 \approx 6.4[/tex]
Three friends go grocery shopping together, and each buys the same kind of oranges. LaMar buys 2 pounds (lb) and pays $7.00. Enrico buys 5 pounds and pays $17.50. Anna buys 3 pounds and pays $10.50. Identify the graph and unit price that represent the orange costs.
Answers
The unit price of the oranges bought by the three friends is $3.50 per pound.
Lamar bought 2 pounds for $7 , unit price = 7 / 2 = $ 3.5 per pound
Enrico bought 5 pounds for $17.50 , unit price = 17.50 / 5 = $ 3.5 per pound
Anna bought 3 pounds for $10.50 , unit price = 10.5/ 2 = $3.5 per pound
Hence we can see that the unit price rate for the oranges is $3.50 .
The average price of a product is calculated by dividing the total sales income by the number of units sold. Managers must supply "similar" units when a single product is given in many variations, such as different bottle sizes.
By weighting different unit selling prices higher by unit sales mix (%) for each single variant, the determination of average pricing is made practicable. We obtain pricing per statistical unit when we employ a standard rather than a genuine range of sizes and product types.
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Mike bought 4 basketballs for $62. What was the price per basketball?
Answers
Answer: The answer would be $15.50 per basketball
Step-by-step explanation:
If mike bought 4 basketball for 62 dollars you have to divide 62 and 4. Which equals 15.5 so in dollars it would be 15 dollars and 50 cents or $15.50.
Use the table below to answer question 9.
x -3 0 1 3
f(x) 12 0 0 6
g(x) 39 3 7 39
h(x) -14 1 -2 -20
2*f(3)-3*g(1)+h(3)=
Answers
answer:
-29
step-by-step explanation:
you need a graphing calculator.
so, let's start by setting up a table (for my sake because that text is confusing)
x f(x) g(x) h(x)
-3 12 39 -14
0 0 3 1
1 0 7 -2
3 6 39 -20
okay, that's out of the way. now, your equation is 2 * f(3) - 3 * g(1) + h(3).
for f(3), we look at the chart to see which f(x) value matches x=3.
f(3) = 6
same with g(1) and h(3)
g(1) = 7
h(3) = -20
now, replacing the functions(x) with their numbers is the next step.
2 * 6 - 3 *7 + (-20)
(2*6) - (3*7) - 20
(12) - (21) - 20 = -29
At the beginning of a baking session, there were 2.26 kilograms of flour in the bag. By the end if the baking session, there was 0.98 kilograms of flour in the bag. What is the percent of decrease, rounded to the nearest tenth, for the amount of flour?
Answers
The percent of decrease, for the amount of flour, is 56.63%.
What is percentage?A percentage is a number that tells us how much out of 100.
Given that, at the beginning of a baking session, there were 2.26 kilograms of flour in the bag, by the end if the baking session, there was 0.98 kilograms of flour in the bag
The amount percentage left = (2.26 - 0.98)/2.26*100 = 56.63%
Hence, The percent of decrease, for the amount of flour, is 56.63%.
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Need help with homework
Answers
we have the expression
[tex]10-4+2(4)^2[/tex]step 1
squared 4 before multiplying
[tex]\begin{gathered} 10-4+2(16) \\ 10-4+32 \end{gathered}[/tex]therefore
step 1 is incorrect
Justine's work is incorrect
the answer is option N 1If four people equally share a 1/2 page to 3/4page.what fraction of the page in the photograph
Answers
Step-by-step explanation:
fraction of page of photograph is 3/32
(1/2÷4)*3/4
1/2*1/4*3/4
1/8*3/4
=3/32
Which is a better estimate for the weight of a winter coat?
2 tons
2 pounds
Answers
Answer:
2 pounds is the correct answer because 2 tons would be to much for any human to hold / wear
what 82 x 82 x 82 x 82
Answers
Answer:45212176
Step-by-step explanation:calculator
Answer:
82x82x82x82, or 82 squared to the 4th power, is 45212176.
Rita started playing a video game at 9:10 A.M. It took her 1 hour and 45 minutes to beat the first level and 1 hour and 25 minutes to beat the second level. Rita played the final level for 1 hour and 10 minutes and finished the game. What time was it when Rita stopped playing the game?
Answers
Answer: it would be about 1:30pm
Step-by-step explanation:
Determine whether the given numbers represent the lengths of sides of a right triangle.15,11,4Do the given numbers represent the lengths of the sides of a right triangle?No or Yes
Answers
Answer:
No
Explanation:
To determine if the lengths form the side of a right triangle, use the Pythagorean Theorem:
[tex]\begin{gathered} c^2=a^2+b^2 \\ Where\; c\text{ is the hypotenuse, the longest side} \end{gathered}[/tex]Substitute 15,11 and 4 into the formula:
[tex]\begin{gathered} 15^2=225 \\ 11^2+4^2=121+16=137 \\ \text{Therefore:} \\ 15^2\ne11^2+4^2 \end{gathered}[/tex]Since the Pythagorean Theorem does not hold, the side lengths(15,11,4) do not represent the lengths of the sides of a right triangle.
−1,51.27,−1,0,12,57,7677,√2,√8,5
Answers
Given the following question:
[tex]-1,5,\frac{1}{2},\frac{5}{7},0,\sqrt[]{2},\sqrt[]{8},-1.27,\frac{76}{77}[/tex]Natural numbers are positive integers.
5 is a natural number
Whole numbers are integers, neither fraction or decimals just integers.
5, and 0 are whole numbers
Integers are a set of numbers that can be expressed without being a fraction/decimal.
-1, 5, and 0 are integers.
Rational numbers are a set of numbers that can be written as fractions.
-1, 5, 1/2, 5/7, 0, 76/77, 1.27 are all rational numbers they can all be expressed as a fraction.
(zero is also rational)
Irrational numbers cannot be expressed as a fraction
√2, √8,
Real numbers are numbers that include rational and irrational numbers.
-1, 5, 1/2, 5/7, 0, 76/77, -1.27, √2, √8
Which function has the greatest y-intercept?
f(x)
h(x)
g(x)
Answers
Answer:
h(x)
Step-by-step explanation:
y-intercept is shorthand for ' y - axis intercept'
the graph which intercepts the y-axis the highest is h(x)
Transform the given general equation to standard equation
x2 + y2 - 4x + 4y - 4 = 0
please answer my question, thank you!
Answers
Answer:12
Step-by-step explanation:
1) Frank walks to school 35% of the time. If there are 180 days in a school year, how many days did he walk to school?
Answers
Answer:
63 days
Explanation:
Given the total number of days in a yesr = 180 days
Percent of the time he walks to school = 35 %
Number of days he walks to school = 35% of 180
Number of days he walks to school = 0.35 * 180
Number of days he walks to school = 63 days
Hence the number of days he walked to schools is 63 days
22 more than a number divided by 4
Answers
Answer:
X / 4 + 22
Step-by-step explanation:
22 more means we add 22. Then, we take x as our variable, in this case, it is "a number". We divide x by 4, and then we add 22. x / 4 + 22.
Hi please help me in this onei don't know how to solve itfind the value of x
Answers
EXPLANATION
If the measure of ∠2= x+78 and the other ∠=40 degrees, by definition we know that sum of interior angles of a triangle is equal to 180 degrees.
Furthermore, we have two congruent legs, so this is an Isosceles triangle with two congruent angles (with the same measure).
Thus,
180 = 40 + 2* m∠2
Substituting m∠2 by the equation as follows:
180 = 40 + 2(x + 78)
Subtracting -40 to both sides:
180 - 40 = 2(x+78)
Simplifying:
140 = 2(x+78)
Dividing both sides by 2:
140/2 = x + 78
Simplifying:
70 = x + 78
Subtracting -78 to both sides:
70 - 78 = x
Simplifying:
-8 = x
Switching:
x = -8
Answer: The value of x is -8.