If x is the interval (pi/2,pi) and y is in the interval (pi,3pi/2) and the sin x= 3/4 and cot y=5/6, evaluate each of the following.
a) sin (x+y) b) cos(x-y) c) tan(x-y)
Answers
The given trigonometric identities can be evaluated as (a) sin(x + y) = (-15 + 6√7)/4√61, (b) cos(x - y) =(5√7 - 18)/4√61 and (c) tan(x - y) = (-15 - 6√7)/(5√7 - 18).
What are trigonometric ratios?The trigonometric ratios are defined for a right angled triangle.
The example of these ratios are sin, cos, tan, cosec, sec and cot.
The trigonometric ratios are useful in determining the heights and distances of the large objects.
Given that,
The value sin(x) = 3/ 4 for π/2 < x < π.
And, cot(y) = 5/6 for π < y < 3π/2.
Since x is given in the second quadrant cos(x) is negative such that,
cos(x) = -√ (1 - sin²(x) )
= - √(1 - (3/4)²
= -√7/4
Since, y is in third quadrant sin(y) and cos(y) is negative.
sin(y) = -1/√(1 + cot²(y))
= -1/√(1 + (5/6)²)
= -6/√61
Cos(y) = -√ (1 - sin²(y))
= - √(1 - (-6/√61)²
= -5/√61
tan(x) = sin(x)/cos(x)
= -3/√7
tan(y) = sin(y)/cos(y)
= 6/5
Now, the following trigonometric identities can be evaluated as follows,
(a)
sin(x + y) = sin(x)cos(y) + cos(x)sin(y)
Substitute the respective values to get,
sin(x + y) = 3/4 × -5/√61 + -√7/4 × -6/√61
= (-15 + 6√7)/4√61
(b) cos(x - y) = cos(x)cos(y) + sin(x)sin(y)
= -√7/4 × -5/√61 + 3/4 × -6/√61
= (5√7 - 18)/4√61
(c) tan(x - y) = (tan(x) - tan(y))/(1 +tan(x)tan(y))
= (-3/√7- 6/5)/(1 +-3/√7 × 6/5)
= (-15 - 6√7)/(5√7 - 18)
Hence, the required values are sin(x + y) = (-15 + 6√7)/4√61, cos(x - y) =(5√7 - 18)/4√61 and tan(x - y) = (-15 - 6√7)/(5√7 - 18).
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Related Questions
Oceanside bike rental shop charges 11 dollars plus 6 dollars an hour for renting a bike. Joan paid 35 dollars to rent a bike . How many hours did she pay to have the biked checked out?
Answers
Answer:
4 hours
Step-by-step explanation:
Write and solve a proportion to answer the question. what number a is 0.4% of 40
Answers
Answer:
.16
Step-by-step explanation:
So, we're looking for 0.4% of 40. First, let's convert 0.4% to a decimal. Since a percent is really just PARTS of one hundred, this decimal really means 0.4/100. 0.4 divided by 100 is 0.004. Next, we need to figure out how to solve this problem! To find a percent of a number, just multiply the percent (in decimal form) by the number! So, we need to answer 0.004*40, which equals 0.16.
Answer: 0.16
Faizah is paid $11 per hour for her work at a factory. She works 9 hours a day and 24 days a month. She saves $594 a month. Express the amount she saves as a percentage of her income.
Answers
Answer:
The amount she saves is 25% of her income
Step-by-step explanation:
She is paid $11 per hour
She works 9 hours per day
and for 24 days per month
So, she works 9(24) hours per month
= 216 hours per month
Now, she is paid $11 hourly, so for 216 hours,
she will have 11(216) = $2376
Total income = $2376 per month
Saving = $594 per month
As a percentage, we divide the savings by the total income,
savings/(total income) = 594/2376 = 1/4 = 0.25
Hence we get 25%
Keirra’s mother gave her $7.50 to buy 8 spiral notebooks. With tax, the cost of each notebook is $1.05. Does Keirra have enough money? Use compatible numbers and estimation to help you decide.
Answers
Answer:
No
Step-by-step explanation:
each notebook is $1.05 and the is $7.50
there is only enough for seven notebooks not eight.
Two friends, Francisco and Zoe, had just bought their first cars. Zoe uses 14 gallons of gas to drive 390.6 miles in her car. The graph below represents the number of miles, y, that Francisco can drive his car for every x gallon of gas.
Answers
Using linear function to solve this problem, for every 1 gallon of gas, Francisco travelled 27.9 miles
Linear FunctionA linear function is a function that represents a straight line on the coordinate plane. For example, y = 3x - 2 represents a straight line on a coordinate plane and hence it represents a linear function. Since y can be replaced with f(x), this function can be written as f(x) = 3x - 2. A linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line. where m is slope of the line and b is the y - intercept
We can use the data given in writing out our equation
y = Number miles coveredx = number of gallon390.6 = 14x
If 14 gallons = 390.6 miles
1 gallon = x miles
x = 390.6 / 14
x = 27.9 miles
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Lillian bought snacks for her team's practice. She bought a bag of apples for $2.36 and a 4-pack of juice bottles. The total cost before tax was $6.48. How much was each bottle of juice?
Answers
The price of each bottle of juice is $1.03
What is an equation?
A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.
Let 'x' be the price of each bottle of juice. Then,
According to the question,
2.36 + 4x = 6.48
or, 4x = 6.48 - 2.36
or, 4x = 4.12
or, x = 4.12/4
or, x = 1.03
Hence, the price of each bottle of juice is $1.03
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calculate problems one and two.
Answers
Answer:
Question 1) 2/3
Question 2) -3
Step-by-step explanation:
Question 1)
The formula of a slope is (increase in y)/(increase in x), so in the graph, all we need to do is find two precise points and look at the distance difference.
1. The two points that I've found were (0,3) and (3,5). The change in y is 3 --> 5, which is 2. The change in x is 0 --> 3, which is 3.
2. The slope will be 2/3.
Question 2)
In this question, we can consider n as x and f(n) as y.
1. The two points I chose were (4, -31) and (7,-40). The change in y is -31 --> -40, which is -9. The change in x is 4 --> 7, which is 3.
2. The slope will be -9/3.
3. -9/3 can be simplified to -3 since we can divide both the numerator and the denominator by 3.
4. The final slope will be -3.
Which of the following statements is correct? A. Steven Strange is single and is claimed as a dependent by his parents. Steven has salary income of $15,000 and files his own tax return. The basic standard deduction for Steven is $15,350. B. Wanda (gross income: $5,000) is married and files a separate tax return (MFS). Since Wanda's gross income ($5,000) is smaller than the basic standard deduction for MFS ($12,550), she does not have to file her tax return. C. In general, a $1 deduction for AGI is better than a $1 non-refundable tax credit. D. A greater deduction from AGI leads to a greater deduction for AGI. E. All of above are incorrect. 2. Which of the following statements is incorrect regrading a self-employed taxpayer? A. Qualified job-related expenses (e.g., auto, travel, gift expenses) are classified as deduction for AGI. B. If 30% of the travel time is business purpose, transportation expense (e.g., airfare) is not deductible. C. In addition to the $0.575 per mile auto expenses, the self-employed taxpayer who chooses the standard mileage method (rather than the actual cost method) can claim deduction on depreciation, gas and oil, repair, insurance, license expenses. D. The auto expenses related to commuting between home and his/her job are not qualified for deduction. E. Job-related education expenses where the education maintains or improves current job skills are deductible.
Answers
The correct statement is: E. All of the above are incorrect.
Statement A is incorrect because the basic standard deduction for 2021 is $12,550 for single filers, not $15,350.
Statement B is incorrect because the gross income threshold for filing a separate tax return (MFS) in 2021 is $5, as opposed to the basic standard deduction for MFS.
Statement C is incorrect because a non-refundable tax credit directly reduces the amount of tax owed, whereas a deduction for AGI reduces taxable income before calculating the tax liability. Therefore, a non-refundable tax credit is generally more valuable than a deduction for AGI.
Statement D is incorrect because a greater deduction from AGI does not necessarily lead to a greater deduction for AGI. Deductions from AGI reduce taxable income, while deductions for AGI are claimed before calculating AGI.
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Mary ran 2 miles in 23 minutes how long will it take her to run 15 miles
Answers
Select all ordered pairs that satisfy the function
(-3, -1)
(-2, -1)
0 (
33)
Answers
please help me 20 points
Answers
Add up the number of students within the random sample data:
32+26+28+22 = 108
We can then use proportional fractions / cross-multiply to answer the question.
In a sample size of 108 students, 32 of them preferred Movie A.
There are 900 students in total.
\(\frac{32}{108} =\frac{x}{900}\)
32*900 = 28800
108*x = 108x
108x = 28800
x = \(266\frac{2}{3}\) or \(\frac{800}{3}\)
In decimal form that is approximately 266.667 and round that to the nearest whole number, you get 267 students who would prefer Movie A.
How many number of terms does -7n^3 + 10n - 13 have
Answers
Answer:
3 terms
Step-by-step explanation:
- 7n^3 is a term
10n is a term
-13 is a term
The speeds of the fastballs thrown by major league baseball pitchers were measured by radar gun. The mean speed was 87 miles per hour. The standard deviation of the speeds was 3 mph. Which of the following speeds would be classified as an outlier?
a. 84 mph b. 92 mph c. 97 mph d. 81 mph
Answers
Thus, the answer is option (c) 97 mph.
An outlier is a value that lies significantly away from the rest of the values in the dataset. For a given dataset, we can determine outliers using z-scores.According to the problem statement, the mean speed of the fastballs thrown by major league baseball pitchers is 87 mph, and the standard deviation is 3 mph. To determine which speed is an outlier, we need to find its corresponding z-score.z = (x - μ) / σHere, x is the speed we want to test, μ is the mean speed, and σ is the standard deviation of speeds.Using the formula above, we can calculate the z-scores for each speed given in the options:a. z = (84 - 87) / 3 = -1b. z = (92 - 87) / 3 = 1.67c. z = (97 - 87) / 3 = 3.33d. z = (81 - 87) / 3 = -2Since a z-score of ±2 or higher is generally considered an outlier, the speeds of 97 mph and 81 mph are classified as outliers. Thus, the answer is option (c) 97 mph.
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y=(x+4)^3 what transformation will the following equation have from its parents ?
Answers
Answer:
shift left 4 units
Step-by-step explanation:
When shifting left or right, the x has to be added or subtracted by the term for it to be shifting that term either left or right.
However, when shifting up or down, that number has to be added after the exponent.
Both graphs attached
Guys Help please asapppp
Answers
2. Square both sides of the equation
( usually the first sentence is different but I think that’s the answer, hope that helped :) )
The swim team is going to finals. If the meet is in 85 days, determine how many seconds there are until the meet.
seconds
Answers
Answer:
There are 7,344,000 seconds until the swim team meet.
Step-by-step explanation:
First we have to figure out how many seconds in a day.
There are 86,400 seconds in a day.
Then we multiply the seconds in one day by the number of days:
86,400 x 85 = 7,344,000
I hope this was helpful! If it was, please consider rating, pressing thanks, and giving my answer 'Brainliest.' Have a wonderful day! :)
50 points for this
The 35 members of a drill team are trying to raise at least $1,200 to cover travel costs to a training camp. They have already raised $500. How much should each member still raise, on average, to meet the goal?
w
Please write it as a inequality
Answers
Answer:
$20
Step-by-step explanation:
1200-500=700
700/35=20
The climate in which Jonah lives is mild all year long except during the hotter summer months. For 3 months out of the year, Jonah needs to use 4 portable fans to cool his home. If the electricity to use one fan costs 1 cent per hour and each fan is on for about 96 hours per month, what is his total electricity cost for the fans during one year? a. $6. 72 b. $3. 84 c. $11. 52 d. $2. 88 Please select the best answer from the choices provided A B C D.
Answers
Using proportions, it is found that his total electricity cost for the fans during one year is given by:
b. $3.84
What is a proportion?A proportion is a fraction of a total amount.
In this problem, for 3 months, he uses 4 portable fans, and each fan is on for about 96 hours per month, hence the total number of hours he uses it is:
4 x 96 = 384 hours.
The cost is one one cent per hour, hence:
$0.01 x 384 = $3.84.
Which means that the total cost is of $3.84, and option b is correct.
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Drag a statement or reason to each box to complete the proof.
If 3(x−4)=x+4, then x=8.
Answers
Distributive property
Addition property
3x=x+16
Subtraction property
2x=16
And then if you move further than what is shown in the photo it should be x=8 by the division property.
The store owner buys clothes at wholesale and adds 80% to the wholesale
price to set the retail price. The retail price of a pair of pants is $36.00.
What is the wholesale price?
Answers
Answer:
$28.80
Step-by-step explanation:
36 * 80%
Evaluate the volume generated by revolving the area bounded by the given curves using the washer method: y² = 8x, y = 2x; about y = 4
Answers
The volume generated by revolving the area bounded by the curves y² = 8x and y = 2x about the line y = 4 can be evaluated using the washer method.
To evaluate the volume using the washer method, we need to integrate the cross-sectional areas of the washers formed by revolving the area bounded by the curves. The given curves are y² = 8x and y = 2x. We can rewrite the equation y = 2x as y² = 4x. The curves intersect at (0,0) and (8,16).
The distance between the line of revolution y = 4 and the upper curve y² = 8x is given by (4 - √(8x)). Similarly, the distance between the line of revolution and the lower curve y² = 4x is given by (4 - √(4x)). The radius of each washer is the difference between these distances, (4 - √(8x)) - (4 - √(4x)), which simplifies to √(8x) - √(4x).
Integrating the volume of each washer over the interval [0,8] and summing them up, we can determine the total volume generated by revolving the area.
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a circular pool is surrounded by a brick walkway 3 m wide. find the ra- dius of the pool if the area of the walk- way is 198 m*.
Answers
The radius of the pool is 9.01 m.
Given,
In the question:
A circular pool is surrounded by a brick walkway 3 m wide.
The area of the walk- way is 198 m^2.
To find the Radius of the pool.
Now, According to the question:
"Area of the circle bounded by the outside edge of the walkway" minus "area of the pool" = "area of the walkway".
Let R = Radius of the pool
Area of the circle bounded by the outside edge of the walkway is:
\(\pi\)(R +3)^2
Area of the pool is:
\(\pi R^2\)
Now, Our equation is:;
\(\pi\)(R +3)^2 - \(\pi R^2\) = 198
\(\pi\)((R+3)^2 - \(R^2\)) = 198
Open the inner bracket :
\(\pi\)(\(R^2+6R+9-R^2\)) = 198
\(\pi\)(6R +9) = 198
6R+9 = 198/\(\pi\)
6R = 198/\(\pi\) - 9
R = (198/\(\pi\) - 9)/6
R = (198/(3.14) - 9)/6
R = (63.057 - 9)/6
R = 54.057/6
R = 9.01 meters
Hence, The radius of the pool is 9.01 m.
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Amber got a raise. her hourly wage increased from $8 to $10 an hour. How much did amber's hourly wage increase. Show your work.
Answers
Answer:
2
Step-by-step explanation:
Pls give brainlist
Answer:
it increased by 25 percent
Step-by-step explanation:
8/2=4
100/4=25
hope this helps (:
we draw a random sample of size 36 from the normal population with variance 2.1. if the sample mean is 20.5, what is a 95% confidence interval for the population mean?
Answers
The 95% confidence interval for the population mean is approximately [20.03, 20.97].
What is confidence interval?The percentage (frequency) of acceptable confidence intervals that include the actual value of the unknown parameter is represented by the confidence level.
To calculate the 95% confidence interval for the population mean based on a sample of size 36 with a known variance of 2.1 and a sample mean of 20.5, we can use the formula for a confidence interval for a population mean:
CI = \(\bar X\) ± z * (σ / √n),
where:
CI is the confidence interval,
\(\bar X\) is the sample mean,
z is the z-score corresponding to the desired level of confidence (in this case, 95% confidence),
σ is the population standard deviation,
n is the sample size.
Since we have the population variance (2.1), we can calculate the population standard deviation as σ = √2.1 ≈ 1.45.
Now, let's calculate the confidence interval:
CI = 20.5 ± z * (1.45 / √36).
The z-score corresponding to a 95% confidence level is approximately 1.96 (you can look this up in a standard normal distribution table or use a statistical software).
Substituting the values:
CI = 20.5 ± 1.96 * (1.45 / √36).
Calculating the values within the confidence interval:
CI = 20.5 ± 1.96 * 0.2417.
CI = 20.5 ± 0.4741.
Finally, we can calculate the lower and upper bounds of the confidence interval:
Lower bound = 20.5 - 0.4741 ≈ 20.03.
Upper bound = 20.5 + 0.4741 ≈ 20.97.
Therefore, the 95% confidence interval for the population mean is approximately [20.03, 20.97].
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classify the quadrilateral by its most specific name. then find the missing angle measure(s)
Answers
The specific name of the quadrilateral is kite
The measures of the missing angles are 75 degrees each
How to determine the quadrilateralTo determine the measure of the angle, we need to know the different properties of a kite.
The properties of a kite includes;
Two pairs of adjacent sides are equal.Two diagonals intersect each other at right angles.The longer diagonal bisects the shorter diagonal.The angles opposite to the main diagonal are equal.Since the adjacent angles are equal, we have that;
105+ x = 180
collect the like terms, we have;
x = 180 - 105
x = 75 degrees
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The quadrilateral is a kite and the missing angles are 105° and 45°
What is a kite?A kite is a quadrilateral that has 2 pairs of equal-length sides and these sides are adjacent to each other.
A kite has a pair of equal angle and the diagonals of a kite meets at 90°.
In a kite , there are two pairs of congruent or equal sides.
This means that the missing angles are
The opposite angle to 105 is also 105°
The fourth angle is calculated as;
105+105+105+x = 360
= 315 +x = 360
x = 360- 315
x = 45°
Therefore the quadrilateral is a kite and the missing angles are 105° and 45°
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Samantha owes her father $7 she just got paid $5.50 for babysitting if she gives that money to her dad how much will she still owe him
Answers
Answer:
$1.5
Step-by-step explanation:
$7- 5.50= 1.5
Which of the following is not a real number?
Answers
Answer: A
Step-by-step explanation: common sense
Answer:
its a -2 because its a negative and when u count u dont start with a negative do u?
Step-by-step explanation:
(In the pic) why do we have to change signs?? I don’t get it pls help
Answers
Answer:
x = -2
x = 3
Step-by-step explanation:
Solve. −56=−14−710x Enter your answer as a fraction in simplest form in the box.
Answers
Answer:
x = 21/355
Step-by-step explanation:
. −56 = −14−710x
-56+14 = -14+14-710x
-42/-710 = -710x/-710
x = 21/355
Therefore x is 21/355
Triangle BCD was dilated using the rule D Subscript Q, one-half.
What are the values of the unknown measures?
m∠C'B'D' =
°
CQ =
B'D' =
Answers
The values of the missing angles and sides after dilation are:
m∠C'B'D' = 95°, CQ = 6 and B'D' = 11.
What are the values of the angles after transformation?m∠C'B'D = 180° - m∠B'C'D' - m∠B'D'C'
m∠B'C'D = m∠BCD, m∠B'D'C' = m∠BDC (dilation)
m∠C'B'D = 180° - 34° - 51° = 95°
Thus, by way of scale factor we can say that:
BC/B'C' = BD/B'D' = 36/18 = 2
B'D' = ¹/₂BD = ¹/₂ * 22 = 11
ΔC'P'Q ∼ ΔCPQ
Thus:
C'Q'/CQ = C'D'/CD = D'Q'/DQ
CQ = 2C'Q' = 2 * 3 = 6
Therefore, m∠C'B'D' = 95°, CQ = 6 and B'D' = 11.
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