2 sin²(x) + 3 sin(x) + 1 = 0
(2 sin(x) + 1) (sin(x) + 1) = 0
2 sin(x) + 1 = 0 OR sin(x) + 1 = 0
sin(x) = -1/2 OR sin(x) = -1
The first equation gives two solution sets,
x = sin⁻¹(-1/2) + 2nπ = -π/6 + 2nπ
x = π - sin⁻¹(-1/2) + 2nπ = 5π/6 + 2nπ
(where n is any integer), while the second equation gives
x = sin⁻¹(-1) + 2nπ = -π/2 + 2nπ
2 cot(x) sec(x) + 2 sec(x) + cot(x) + 1 = 0
2 sec(x) (cot(x) + 1) + cot(x) + 1 = 0
(2 sec(x) + 1) (cot(x) + 1) = 0
2 sec(x) + 1 = 0 OR cot(x) + 1 = 0
sec(x) = -1/2 OR cot(x) = -1
cos(x) = -2 OR tan(x) = -1
The first equation has no (real) solutions, since -1 ≤ cos(x) ≤ 1 for all (real) x. The second equation gives
x = tan⁻¹(-1) + nπ = -π/4 + nπ
sin(x) cos²(x) = sin(x)
sin(x) cos²(x) - sin(x) = 0
sin(x) (cos²(x) - 1) = 0
sin(x) (-sin²(x)) = 0
sin³(x) = 0
sin(x) = 0
x = sin⁻¹(0) + 2nπ = 2nπ
2 cos²(x) + 2 sin(x) - 12 = 0
2 (1 - sin²(x)) + 2 sin(x) - 12 = 0
-2 sin²(x) + 2 sin(x) - 10 = 0
sin²(x) - sin(x) + 5 = 0
Using the quadratic formula, we get
sin(x) = (1 ± √(1 - 20)) / 2 = (1 ± √(-19)) / 2
but the square root contains a negative number, which means there is no real solution.
2 csc²(x) + cot²(x) - 3 = 0
2 (cot²(x) + 1) + cot²(x) - 3 = 0
3 cot²(x) - 1 = 0
cot²(x) = 1/3
tan²(x) = 3
tan(x) = ± √3
x = tan⁻¹(√3) + nπ OR x = tan⁻¹(-√3) + nπ
x = π/3 + nπ OR x = -π/3 + nπ
translation: 4 units left and 4 units up
J(−1, −2), A(−1, 0), N(3, −3)
Answer:
(-5,2), (-5,4), and (-1,1)
Step-by-step explanation:
Chapter 4
Solve.
1. Two trains leave a station at the same time, heading in opposite directions.
One train is traveling at 80 km/h, the other at 90 km/h. How long will it
take for the trains to be 425 km apart?
Answer:
8850
Step-by-step explanation:
coz the train goes too slowly and lazy
PLEASE MARK ME AS BRAINLIEST
In a certain state's lottery, 45 balls numbered 1 through 45 are placed in a machine and eight of them are drawn at random. If the eight numbers drawn match the numbers that a player had chosen, the player wins $1,000,000. In this lottery, the order in which the numbers are drawn does not matter.
Compute the probability that you win the million-dollar prize if you purchase a single lottery ticket. Write your answer as a reduced fraction.
P
(win) =
A single lottery ticket costs $2. Compute the Expected Value, to the state, if 10,000 lottery tickets are sold. Round your answer to the nearest dollar.
Answer: $
A single lottery ticket costs $2. Compute the Expected Value, to you, if you purchase 10,000 lottery tickets. Round your answer to the nearest dollar.
Answer: $
Step-by-step explanation:
The order of the numbers doesn't matter, so we'll use combinations instead of permutations. The number of combinations is:
₄₅C₈ = 215,553,195
So the probability of a ticket having the winning combination is 1 / 215,553,195.
The expected value to the state is:
E(X) = 10,000 (1) ($2) + 10,000 (1 / 215,553,195) (-$1,000,000)
E(X) = $19954
The expected value to you is:
E(X) = 10,000 (1) (-$2) + 10,000 (1 / 215,553,195) ($1,000,000)
E(X) = -$19954
What is AOM under what type of equation?
AOM is under zero, as stated in the sequential equation
B^2 + 11b + 18 ( Factor the question)
Help please!
Answer:
=b^2+(9+2)b+18
=b^2+9b+2b+18
=b(b+9)+2(b+9)
=(b+9)(b+2)
Find the simple interest earned after 12 years on $1,350 at an interest rate of 8%.
Answer:
1296$
Step-by-step explanation:
0.08*1350 = 108
108* 12= 1296
Thats the simplest way I can tell you
<3
RedMarco reads that a honeybee can fly up to 2.548 meters per second. He rounded the number to 2.55. To which place value did Marco round the speed of a honeybee?
Answer: Nearest hundredth
Step-by-step explanation:
Given: cos(3x – 180°) = Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction, where 0 ≤ x < 180°
Which values represent the solutions to the equation?
{10°, 110°, 130°}
{20°, 100°, 140°}
{30°, 330°, 390°}
{60°, 300°, 420°}
Answer:
A: {10°, 110°, 130°}
Step-by-step explanation:
Did on edge
The solution to the equation is:
10° , 110° , 130°
Given,
cos(3x - 180) = -√3/2
Now,
To solve the trigonometric function,
cos(3x - 180) = -√3/2
Taking inverse of cos,
3x - 180° = [tex]cos^{-1} (-\sqrt{3}/2 )[/tex]
[tex]cos^{-1} (-\sqrt{3}/2 )[/tex] = 150°
3x - 180° = 150°
x = 10°
Hence the solutions of equation is the value of x that satisfies the relation .
x = {10° , 110° , 130° }
Know more about trigonometry,
https://brainly.com/question/13971311
#SPJ6
Kumar is opening a lemonade stand. He spent $4.50 to build the stand and $2.50 for lemons and sugar. He has enough ingredients to make 20 glasses of lemonade. How much should he charge for one glass of lemonade to cover his expenses and make $10 in profit?
Round to the nearest cent.
Timed test
Answer:
profit = revenue - cost
10 = 20x - (4.5 + 2.5)
10 = 20x - 7
10 + 7 = 20x
17 = 20x
17/20 = x
0.85 = x
check...
profit = revenue - cost
10 = 20(0.85) - 7
10 = 17 - 7
10 = 10 (correct)
so he would have to sell each cup at 0.85 ccents to make a profit of $ 10
Step-by-step explanation:
Answer:
I cant find the next one hehrh
4,378 divided by 15help
Answer:
291
Step-by-step explanation:
Answer:291.87
Step-by-step explanation:
URGENT!!!!!!!! PLS HELP DUE IN 5 MINUTESSS
The graphs show the costs of four canoe outfitters on the Brazos River The outfitters charges a minimum fee to rent une
In addition to a rental charge for each hour.
Which graph shows a minimum fee of $10
A) A
B) B
C) C
D) D
Answer:
it should be A
Step-by-step explanation:
The x-axis is going up by 2 meaning that it should be half of 10 on the y'axis (so sorry if this is wrong)
what is the largest six digit number you can make that ends in an even number using 134569.
Answer:
965314
Step-by-step explanation:
Please mark me brainlest and hope that help (=
Big chickens: The weights of broilers (commercially raised chickens) are approximately normally distributed with mean 1387 grams and standard deviation 192 grams. Use the TI-84 Plus calculator to answer the following. (a) What proportion of broilers weigh between 1150 and 1308 grams? (b) What is the probability that a randomly selected broiler weighs more than 1510 grams? (c) Is it unusual for a broiler to weigh more than 1610 grams? Round the answers to at least four decimal places.
Answer:
a) 0.2318
b) 0.2609
c) No it is not unusual for a broiler to weigh more than 1610 grams
Step-by-step explanation:
We solve using z score formula
z-score is is z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.
Mean 1387 grams and standard deviation 192 grams. Use the TI-84 Plus calculator to answer the following.
(a) What proportion of broilers weigh between 1150 and 1308 grams?
For 1150 grams
z = 1150 - 1387/192
= -1.23438
Probability value from Z-Table:
P(x = 1150) = 0.10853
For 1308 grams
z = 1308 - 1387/192
= -0.41146
Probability value from Z-Table:
P(x = 1308) = 0.34037
Proportion of broilers weigh between 1150 and 1308 grams is:
P(x = 1308) - P(x = 1150)
0.34037 - 0.10853
= 0.23184
≈ 0.2318
(b) What is the probability that a randomly selected broiler weighs more than 1510 grams?
1510 - 1387/192
= 0.64063
Probabilty value from Z-Table:
P(x<1510) = 0.73912
P(x>1510) = 1 - P(x<1510) = 0.26088
≈ 0.2609
(c) Is it unusual for a broiler to weigh more than 1610 grams?
1610- 1387/192
= 1.16146
Probability value from Z-Table:
P(x<1610) = 0.87727
P(x>1610) = 1 - P(x<1610) = 0.12273
≈ 0.1227
No it is not unusual for a broiler to weigh more than 1610 grams
The relationship between the total amount spent on food and drinks by the customers that a waiter serves at a restaurant during a particular week and the waiter's total income for that week can be modeled by the equation y = 0.2x + 300, where x is the amount spent by the customers in dollars and y is the waiter's total income in dollars. By how much does the waiter's weekly income increase for every $500 spent by his customers during that week?
A
$100
B
$300
C
$400
D
$500
Answer:
A
320
B
360
C
380
D
400
Step-by-step explanation:
You would insert your given numbers to x and solve.
Example (A)
y=100(0.2) + 300
y=20 + 300
y=320
If you would like me to explain the rest just ask!
Hope this helps! :))
Please help I don’t know what to do and I have a whole test on it
Answer:
a
Step-by-step explanation:
<dfh=<ehgfh=hg<dhf=<hgfA biker cycles 9 miles in 2/3 of an hour.
The distance here varies directly with time. What is the constant of variation? (It is the hikers’ rate .)
Answer:
this is for you RSM people.
1 hour=13.5
2 hours=27
3 hours=40.5
3.5 hours=47.25
Step-by-step explanation:
The constant variation of the biker is the speed of the biker, Hence, the constant variation is 13.5 mph
Giveb the Parameters :
Distance biked = 9 miles Time taken = 2/3 hoursRecall :
Speed = distance / timeSpeed = 9 ÷ 2/3
Speed = 9 × 3/2
Speed = 27/2 = 13.5 miles per hour.
Therefore, the constant variation is 13.5 mph.
Learn more : https://brainly.com/question/18796573
Which statement describes how to geometrically divide a complex number, z, by a second complex number, w?
O Scale z by the modulus of w, then rotate clockwise by the argument of w.
O Scale z by the modulus of w, then rotate counterclockwise by the argument of w.
O Scale z by the reciprocal of the modulus of w, then rotate clockwise by the argument of w.
O Scale z by the reciprocal of the modulus of w, then rotate counterclockwise by the argument of w.
Answer: C
Step-by-step explanation:
I just took the quiz and I got it right
Statement describes how to geometrically divide a complex number z by a second complex number w is Option (C) Scale z by the reciprocal of the modulus of w, then rotate clockwise by the argument of w.
What is Complex number?In mathematics, a complex number is an element of a number system that contains the real numbers and a specific element denoted i, called the imaginary unit
What is Modulus of a complex number?Modulus of the complex number is the distance of the point on the argand plane representing the complex number z from the origin
Given,
Complex number z divides by a second complex number w
To divide a complex number a complex number then multiply the conjugate with the numerator and the denominator of the complex fraction
From the given statements Scale of z by the reciprocal of the modulus of w, then rotate clockwise by the argument of w
Hence, Statement describes how to geometrically divide a complex number z by a second complex number w is Option (C) Scale z by the reciprocal of the modulus of w, then rotate clockwise by the argument of w.
Learn more about Complex number and Modulus of a complex number here
https://brainly.com/question/19554199
#SPJ2
Michael exercises more than 35 minutes per day.
Use t to represent Michael's amount of exercise (in minutes per day).
Answer:
t>35
Step-by-step explanation:
Since Michael exercises more than 35 days, t is greater than 35. To express that in an inequality, the answer is t>35. Hope this helped!
Because of high production-changeover time and costs, a director of manufacturing must convince management that a proposed manufacturing method reduces costs before the new method can be implemented. The current production method operates with a mean cost of per hour. A research study will measure the cost of the new method over a sample production period. a. Develop the null and alternative hypotheses most appropriate for this study. : - Select your answer - : - Select your answer - b. Comment on the conclusion when cannot be rejected. We - Select your answer - conclude that the new method reduces costs. c. Comment on the conclusion when can be rejected. Consider implementing the new method based on the conclusion that it - Select your answer - the mean cost per hour.
Hi, you've asked an incomplete question. The full question reads;
Because of high production-changeover time and costs, a director of manufacturing must convince management that a proposed manufacturing method reduces costs before the new method can be implemented. The current production method operates with a mean cost of $220 per hour. A research study will measure the cost of the new method over a sample production period.
a. Develop the null and alternative hypotheses most appropriate for this study.
b. Comment on the conclusion when H0 cannot be rejected.
c. Comment on the conclusion when H0 can be rejected
Explanation:
Remember, the null hypothesis usually represents the view the researcher has and that he wants to test or verify, while the alternative hypothesis refers to the opposite expected outcome.
a) Therefore, the null hypothesis is that the newly proposed manufacturing method will reduce the mean cost to lesser than $220.
While the alternative hypothesis is that the newly proposed manufacturing method will not reduce the cost to lesser than $220.
b) When H0 (null hypothesis) cannot be rejected, it means that indeed the research data proved to show that the newly proposed manufacturing method will reduce the mean cost to lesser than $220.
c) When H0 (null hypothesis) can be rejected it means that research data proved to show that the newly proposed manufacturing method would not reduce the mean cost to lesser than the current mean cost of $220. Hence, the manager's proposal would not be accepted.
What is oppesite of running 150 feet east
Answer:
150 feet west?
Step-by-step explanation:
lol ion know
Which of the following equations has exactly one solution?
O A. 4x - 4 + 2x = 6x - 4
O B. 2(4x + 5) = 8x + 10
C. 4x - 8 = 4(x - 4)
O D. 3x + 5 = 2x - 6
The absolute value on number line
Which of the expressions below will have a 8 in the thousandths place of the quotient? Select all that apply.
A) 765.812 ÷ 100
B) 98.14 ÷ 1,000
C) 18.723 ÷ 100
D) 22.38 ÷ 10
Answer:
A
Step-by-step explanation:
It too Mrs. phillips 1.6 hours to run the 13.2 miles. What was his average speed
Answer:
13.2 miles/ 1.6 hours= 8.25 miles/hour.Mr. Phillips's speed was 8.25
Use the figure above to answer the questions.
A Name the quadrilateral.
B. Name the sides.
C. Name the angles.
D. Identify the congruent angles and the congruent sides.
Answer:
the answer is d
Step-by-step explanation:
the shape of it as well
Aaron gets paid $152.80 for 8 hours of work. How much does he get paid for
every hour?
Answer:
19.10
Step-by-step explanation:
Answer:
19
Step-by-step explanation:
Mr. Kiernan decides to purchase a new West Virginia flag for his room that is double
in size of the one he currently has. He purchased the flag for $48.00. In Virginia
Beach, there is a 4.5% sales tax. What is the total cost of the flag, including tax?
Answer:
$50.16
Step-by-step explanation:
There is a sale tax on the item to be purchased, and the tax is 4.5% of the amount of the flag i.e 4.5% × $48.00 = $2.16
After the rate of the sale tax has been changed to dollars, we then add the amount of the sales to the amount of the flag to give the total amount to be paid i.e $2.16 + $48.00 = $50.16
Thank You
3.22 divided by 2.[tex]3.22 divided by 2[/tex]
What is the slope of the line shown
Answer:
-1/2
Step-by-step explanation:
using rise over run, we can see that we go down one and to the left 2. one divided by two is 1/2 meaning 1/2 is the correct answer.
How do you write 554.1 in words
Answer:
Five hundred fifty-four and 10/100.
Step-by-step explanation:
I think? I hope this helps :/