What is the solution to the trigonometric inequality 2sin(x)+3>sin^2(x) over the interval 0<=x<=2pi radians?
Answers
2 sin(x) + 3 > sin²(x)
can be rewritten as
sin²(x) - 2 sin(x) - 3 < 0
(sin(x) - 3) (sin(x) + 1) < 0
The left side is equal to zero when either
sin(x) - 3 = 0 or sin(x) + 1 = 0
sin(x) = 3 or sin(x) = -1
The first case can never happen for real x, since |sin(x)| ≤ 1. From the second case, we get one zero in the interval 0 ≤ x ≤ 2π at x = 3π/2.
Now, split up the solution domain into two intervals, and check the sign of the left side of the inequality at some point in the interval. If the inequality holds up, that interval will belong to the solution set for the inequality.
• From 0 ≤ x < 3π/2, take x = 0. Then
sin²(0) - 2 sin(0) - 3 = 0² - 0 - 3 < 0
is true.
• From 3π/2 < x ≤ 2π, take x = 2π. Then
sin²(2π) - 2 sin(2π) - 3 = 0² - 0 - 3 = -3 < 0
is also true.
This means both intervals 0 ≤ x < 3π/2 and 3π/2 < x ≤ 2π satisfy the inequality.
Answer:
C
Step-by-step explanation:
EDGE 2022
Related Questions
What is the 20% of 40% of 1250?
can you let me know how pls
Answers
Step-by-step explanation:
First, 40 percent of 1250 = 750
20 percent of 750 = 600
I don't know if this is correct I just did what my mind said sooo
Please will give brainliest and thanks for the problems
Answers
What is 104 1/6 simplified pls help me
Answers
Answer:
104
Step-by-step explanation:
If is wrong i'm sorry
There are 135 people in a sport centre.
77 people use the gym.
62 people use the swimming pool.
65 people use the track.
27 people use the gym and the pool.
23 people use the pool and the track.
31 people use the gym and the track.
4 people use all three facilities.
How many people use at least two
facilities?
Answers
Answer:
he total number of people who use at least two facilities is 4 + 45 = 49
Step-by-step explanation:
To find the number of people who use at least two facilities, we can find the number of people who use all three facilities and add the number of people who use only two facilities.
The number of people who use all three facilities is 4, and the number of people who use only two facilities is 27 + 23 + 31 - 3 * 4 = 45.
Therefore, the total number of people who use at least two facilities is 4 + 45 = 49.
Using the slope formula, find the slope of the line through the given points.
(2,6) and (6,2)
Answers
Answer:
m=(y2-y1)/(x2-x1)
=(2-6)/(6-2)
=-4/4
=-1
Step-by-step explanation:
1 light second into Kilometers
Answer by using two significant figures
Answers
Answer:
3.0 x 10^5 km
Step-by-step explanation:
c = 299,792,458 metres per second
c = 299,792 km per second
1 light second = 299,792 km
To two significant figures
300,000 km
3.0 x 10^5 km
In 1 light second there are \(3\times 10^5\) kilometers.
\(1 \text{light seconds}=3.0\times 10^5 km\)
Step-by-step explanation:
The definition of speed is the distance covered per unit time.The speed of the light in a vacuum is \(3.0\times 10^8 m/s\)..The 1 light second is defined as the distance traveled by light in 1 second in free space.To find:
Value of 1 light second into Kilometers
Solution:
Speed of light in space = \(3.0\times 10^8 m/s\)
This means that in 1 second light travels \(3.0\times 10^8 m/s\).
1 m = 0.001 km
The distance traveled by the light in Km in a second will be:
\(3\times 10^8 m= 3\times 10^8\times 0.001 km =3.0\times 10^5 km\)
So, from this, we can conclude that in 1 light second there are \(3\times 10^5\) kilometers.
\(1 \text{light seconds}=3.0\times 10^5 km\)
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Question 1 of 10
Which expressions are equivalent to the one below? Check all that apply.
log 2-log 4
A. log(¹)
B. log 1
C. log(2) + log(¹)
D. log 2
Answers
"The correct option is C." The only expression that is equivalent to log 2 - log 4 is option C: log(2) + log(¹).
The expression "log 2 - log 4" can be simplified using logarithmic properties. Specifically, the property states that "log(a) - log(b) = log(a/b)." Applying this property to the given expression, we have "log 2 - log 4 = log(2/4) = log(1/2) = -log(2)."
The expression log 2 - log 4 can be simplified using logarithmic properties. Let's analyze each option:
A. log(¹): This expression is not equivalent to log 2 - log 4. The logarithm of 1 is 0, but it does not cancel out the terms log 2 and log 4.
B. log 1: This expression is equivalent to 0, but it does not cancel out the terms log 2 and log 4.
C. log(2) + log(¹): This expression is equivalent to log 2 + 0, which simplifies to just log 2. It is not equivalent to log 2 - log 4.
D. log 2: This expression is not equivalent to log 2 - log 4. It represents the logarithm of 2, but it does not account for the subtraction of log 4.
Option C, "log(2) + log(¹)," again uses an exponentiation notation without an exponent and is not a valid mathematical expression.
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I need this plz I don’t understand this
Answers
Use the graph to find the following.
Answers
Answer:
where?
Step-by-step explanation:
Solve for y. 2(y-2) -6y=-28
Answers
Answer:
y = -8
Step-by-step explanation:
2(y-2)- 6y-28 = 0
2y - 4 -6y - 28 = 0
-4y = 32
y = -8
r. Yi buys vegetables at a market. He purchases 6 pounds of potatoes, p, and 3 pounds of onions, n, for $18. Onions cost twice as much as potatoes. To determine the unit price for each item, his daughter sets up and solves the system of equations shown. 6p + 3n = 18 and 2n = p 6(2n) + 3n = 18 12n + 3n = 18 15n = 18; n = $1.20 Onions cost $1.20 per pound. Analyze the daughter’s solution. Which statements are true? Check all that apply. The equation 2n = p should be 2p = n. The equation 6p + 3n = 18 should be 6n + 3p = 18. The actual cost of the onions is $3.00 per pound. Potatoes cost $0.60 per pound. Potatoes cost $1.50 per pound. Potatoes cost $2.40 per pound.
Answers
Answer:
The equation 2n = p should be 2p = n. The actual cost of the onions is $3.00 per pound. Potatoes cost $1.50 per pound.Step-by-step explanation:
The wording "onions cost twice as much as potatoes" is understood to mean the cost per pound of onions (n) is equal to two times the cost per pound of potatoes (2p). Then the appropriate equation would be ...
2p = n
Then the solution is ...
6p +3(2p) = 18
12p = 18
p = 18/12 = 1.50
n = 2p = 2(1.50) = 3.00
__
The equation should be 2p = n; onions cost $3.00 per pound; potatoes cost $1.50 per pound.
Simplify these expressions
2a + 5a
12x-3x
3p+2p-p
Answers
Step-by-step explanation:
1.solution
=2a+5a
=7a
2.solution
=12x-3x
=9x
3.solution
=3p+2p-p
=5p-p
=4p
Hope it helps you.
Hey there!
1. “2a + 5a”
COMBINE your LIKE TERMS
2 + 5 = 7
So this means that: 2a + 5a has to equal 7a
Answer: 7a ☑️
2. “12x – 3x”
COMBINE your LIKE TERMS
12 – 3 = 9
So that means 12x – 3x has to equal 9x
Answer: 9x ☑️
3. “3p + 2p – p”
Side note: “P” by itself is understood as 1
Equation: 3p + 2p – 1p
COMBINE your LIKE TERMS
3p + 2p – 1p
3 + 2 = 5
Which makes 3p + 2p have to equal to 5p
5 – 1 = 4
So this means that 5p – 1p has to equal to 4p
Answer: 4p ☑️
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
This is one part to the question.Select the correct choice below and fill in the blank if necessary.
Answers
Answer:
\(\text{ There is one vertical asymptote. Its equation is x=2.}\)Step-by-step explanation:
Oblique asymptotes occur when the degree of the denominator of a rational function is one less than the degree of the numerator.
If the degree of the denominator is equal to the degree of the numerator, there will be a horizontal asymptote at the ratio between the coefficients of the highest degree of the function. A horizontal asymptote at y = 0 means that the degree of the denominator is greater than the degree of the numerator
A vertical asymptote with a rational function occurs when there is division by zero.
Therefore, for the given function:
\(f(x)=\frac{7}{x-2}\)Since for x=2 the denominator could be 0, there is a vertical asymptote at x=2.
Horizontal asymptote at y=0 means that the degree of the denominator is greater than the degree of the numerator.
Drag each tile to the correct box. Not all tiles will be used.
Consider the following function.
f(x)=2x+5
Place the steps for finding f -1(x) in the correct order.
I NEED THIS 50 POINTS!!!
Answers
Answer:
y = 2x +5
X=2y + 5
X-5 =2y
X-5 / 2 = y
f-1 (x) = x-5/2
Step-by-step explanation:
Answer
This is correct for sure
Step-by-step explanation:
Please Give Me The Answer
Answers
The area covered by the signal is 181.37 m²
What is the area covered by the signal?Here we can see that the area covered by the signal is the fourth of a circle of radius R = 15.2m
The area of a circle of radius R is given by:
A = 3.14*R²
Then the area of a fourth of a circle is:
A = (3.14/4)*R²
Replacing the value of the radius in the formula we will get:
A = (3.14/4)*(15.2m)² = 181.37 m²
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A house owner pays a property tax of $10 for every $1,000 of assessed property value. What is the tax for a home assessed at $150,000.
Answers
Tax the assesed home would increase the total amount paid
The tax of a home assesed at $150,000 is $1500
How to determine the tax amount?The given parameter can be represented using the following ratio:
Ratio = Tax : Amount
So, we have:
$10 : $1000 = Tax : $150000
Express as fraction
10/1000 = Tax/$150000
Multiply both sides by $150000
Tax = $1500
Hence, the tax of a home assesed at $150,000 is $1500
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Bank of America offers a 5-year 8% continuously compounded investment option.
Find the amount accrued if $1450 is invested.
Answers
Answer:
A = $2130.49
Step-by-step explanation:
Given the following data;
Time, t = 5 years
Interest rate, r = 8%
Principal = $1450
To find the future value, we would use the compound interest formula;
\( A = P(1 + \frac{r}{100})^{t}\)
Where;
A is the future value.
P is the principal or starting amount.
r is annual interest rate.
t is the number of years for the compound interest.
Substituting into the equation, we have;
\( A = 1450(1 + \frac{8}{100})^{5}\)
\( A = 1450(1 + 0.08)^{5}\)
\( A = 1450(1.08)^{5}\)
\( A = 1450 * 1.4693 \)
A = $2130.49
For which pair of triangles could the Angle-Side-Angle Postulate (ASA) be used to prove that △ABC≅△XYZ ? I only have an hour pls help.
Answers
The pair that support Angle-Side-Angle Postulate (ASA) be used to prove that △ABC≅△XYZ is option B
What are congruent triangles?Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules
examples of these rules are
Angle - Side - Angle = ASASide - Side - Side = SSSSide - Angle - Side = SASAngle - Angle - Side = AASHypotenuse and one leg = HLThe problem requires the prove by Angle - Side- Angle = ASA to ensure that the the triangles are congruent
The Angle - Side - Angle = ASA have it that the two triangles being compared should have their two angles and the included side being equal
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Estimate 32.79 dived by 8.1
Answers
(BRAINLIEST to best answer) - Write a linear equation that goes through (1, 3) and (2, 6).
Answers
Answer:
y = 3xStep-by-step explanation:
Using the given points find the slope and the y- intercept.
y = mx + bThe slope is:
m = (6 - 3)/(2 - 1) = 3/1 = 3The y- intercept is:
3 = 3*1 + b3 = 3 + bb = 0The line is:
y = 3xSlope
m=6-3/2-1m=3Equation in point slope form
y-3=3(x-1)y-3=3x-3y=3x2) [8 points] Benjamin wishes to strengthen a mixture that is 10% alcohol to
one that is 30% alcohol. How much pure alcohol should they add to 12L of
the 10% mixture?
Answers
you need to add 3.43 liters of pure alcohol to reach a concentration of 30%.
How much pure alcohol should they add to 12L of the 10% mixture?Let's define the variable x as the number of liters of the 30% that you need to use.
The concentration of the mixture then will be:
1*x + 0.1*12
Where the concentration for the x liters is 100%, because this is pure alcohol, and for the 12 liters we use a concentration of 10%.
Now, that must be equal to a mixture with a concentration of the 30%, then we can write:
x + 0.1*12 = (x + 12)*0.3
Now we just need to solve this linear equation for x.
x + 1.2 = x*0.3 + 12*0.3
x - x*0.3 = 12*0.3 - 1.2
x*0.7 = 12*0.3 - 1.2
x = (12*0.3 - 1.2)/0.7 = 3.43
This means that you need to add 3.43 liters of pure alcohol to reach a concentration of 30%.
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hurry and anwser please im dying
Answers
Answer:
the answers to your question would be 65 aka D
You can afford a $1050 per month mortgage payment. You've found a 30 year loan at 7% interest.
a) How big of a loan can you afford? Round your answer to the nearest dollar.
S
b) How much total money will you pay the loan company? Round your answer to the
nearest dollar.
C) How much of that money is interest? Round your answer to the nearest dollar.
S
Question Help: D Postito forum
Submit Question
Answers
9514 1404 393
Answer:
loan: $157,823repaid: $378,000interest: $220,177Step-by-step explanation:
For a loan value of 1, the monthly payment on a 30 year loan at 7% is ...
A = (0.07/12)/(1 -(1 +0.07/12)^(-12·30)) ≈ 0.00665302495
Then the amount repaid after 360 payments is ...
360A = 2.39508898 . . . times the principal amount
__
a) For a monthly payment of $1050, the principal can be ...
$1050/0.00665302495 ≈ $157,823
__
b) The amount repaid to the loan company is ...
$157,823×2.39508898 ≈ $378,000
__
c) The amount that is interest is ...
$378,000 -157,823 = $220,177
A null hypothesis is rejected if the value of a test statistic lies in the:A. Rejection regionB. Acceptance regionC. Both (a) and (b)D. Neither (a) nor (b)
Answers
Step 1:
critical region
if the value of the test statistic falls inside the critical region, then the null hypothesis is rejected at the chosen significance level. if the value of the test statistic falls outside the critical region, then there is not enough evidence to reject the null hypothesis at the chosen significance level.
Step 2
Explanation: If a Null Hypothesis is accepted then the value of Test statistic lies in the Acceptance region. For a rejected Null Hypothesis the value lies in the Rejection region.
Step 3
The null hypothesis is rejected if the value of a test statistic lies in the:
Rejection region
Final answer
A. Rejection region
A null hypothesis is rejected if the value of a test statistic lies in the rejection region. Option B is correct.
What are the null hypothesis and alternative hypothesis?The null and alternative hypotheses are two generalizations about a population that are strictly contradictory. The null hypothesis can be denoted by H₀ and the alternative hypothesis can be denoted by H₁.
The "probability value" is the p-value. It is what indicates whether or not your hypothesis statement is likely to be accurate. You can reject the null hypothesis if the value is in the rejection region, which indicates statistically significant results.
Thus, the null hypothesis is rejected if the value of a test statistic lies in the rejection region. Option B is correct.
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The vector ⇀
= ⟨2, 3⟩ is multiplied by the scalar –4. Which statements about the components, magnitude, and direction of the scalar product –4⇀
are true? Select all that apply.
A. The component form of −4⇀
is ⟨–8, –12⟩.
B. The magnitude of −4⇀
is 4 times the magnitude of ⇀
.
C. The direction of −4⇀
is the same as the direction of ⇀
.
D. The vector −4⇀
is in the fourth quadrant.
E. The direction of −4⇀
is 180° greater than the inverse tangent of its components.
Answers
Answer:
Therefore, the correct statements are A, B, and E.
Explanation:
Based on my knowledge, a vector is a quantity that has both magnitude and direction. A scalar is a quantity that has only magnitude. When a vector is multiplied by a scalar, the magnitude of the vector is multiplied by the absolute value of the scalar, and the direction of the vector is either preserved or reversed depending on the sign of the scalar.
To answer your question, we need to find the component form, magnitude, and direction of the scalar product –4⇀
.
- The component form of −4⇀
is obtained by multiplying each component of ⇀
by –4. Therefore, −4⇀
= ⟨–8, –12⟩. This means that statement A is true.
- The magnitude of −4⇀
is obtained by multiplying the magnitude of ⇀
by 4. The magnitude of ⇀
is √(2^2 + 3^2) = √13. Therefore, the magnitude of −4⇀
is 4√13. This means that statement B is true.
- The direction of −4⇀
is opposite to the direction of ⇀
because the scalar –4 is negative. This means that statement C is false.
- The vector −4⇀
is in the third quadrant because its components are both negative. This means that statement D is false.
- The direction of −4⇀
is 180° greater than the inverse tangent of its components because it is opposite to ⇀
. The inverse tangent of its components is tan^(-1)(–12/–8) = tan^(-1)(3/2). Therefore, the direction of −4⇀
is 180° + tan^(-1)(3/2). This means that statement E is true.
Therefore, the correct statements are A, B, and E.
Motorbikes have two wheels and cars have four wheels. There are a number of
motorbikes and cars in a parking lot. There are 14 motorbikes. Altogether, there are
324 wheels. How many cars are in the parking lot?
A.74 cars
B.148 cars
C.296 cars
D.310 cars
Answers
Answer:
74 Cars
Step-by-step explanation:
If each motorbike has 2 wheels then we need to find how many wheels the motorbikes already take up.
We do this by doing 14*2 and we get 28 wheels.
Afterwards, we subtract this from the total of 324 to see how many wheels are left over. 324-28=296
Now we know the remaining amount of wheels and with this we can get our final answer!
Since there are 296 remaining wheels and each car takes up 4 we can divide 296 by 4 to see how many cars would be able to get their full set of tires.
296/4 = 74 and that;s how you get 74 cars!
*I think LOL*
Find the unit rate (constant of proportionality) of the distance traveled.
Number of hours
0.25 1.5 2.5 3
Distance traveled (km) 3 18 30 36
Answers
Answer:
12.
Step-by-step explanation:
if to re-write the given condition, then
\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)
it is clear, the required constant is 12 (12 per hour).
what equation in slope-intercept form represents the line that passes through the points (0,–7) and (–8,3)
Answers
Answer:
y=-.5x-7
Step-by-step explanation:
What is 60 increased
by 20%
Answers
Answer:
72.00
Step-by-step explanation:
hope this helps! :D
Solve for x.
A. 6/3
B. 5
C. 12
D. 12.5
Answers
Answer:
x=12
Step-by-step explanation:
Using Proportion:
\(\tt \cfrac{x}{16} =\cfrac{9}{x}\)
\(\tt x^2=9(16)\)
\(\tt x=12\)