Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.Write the composed trigonometric function sin (arctan x) in terms of x. Explain your steps and/orshow your work. Remember to rationalize the denominator if necessary.
Answers
Given:
\(\sin(\tan^{-1}x)\)To write:
The trigonometric function in terms of x.
Explanation:
Let us take,
\(y=\sin(\tan^{-1}x).............(1)\)Let us assume that,
\(tan^{-1}x=p..............(2)\)So, the function becomes
\(y=\sin p............(3)\)From the equation (2),
\(\begin{gathered} x=\tan p \\ i.e)\tan p=\frac{x}{1}=\frac{Oppsite}{Adjacent} \end{gathered}\)Using Pythagoras theorem,
\(\begin{gathered} Hyp^2=Opp^2+Adj^2 \\ Hyp^2=x^2+1^2 \\ Hyp=\sqrt{x^2+1} \end{gathered}\)So, equation 3 becomes,
\(\begin{gathered} y=\sin p \\ =\frac{Opp}{Hyp} \\ y=\frac{x}{\sqrt{x^2+1}} \end{gathered}\)Therefore, the composed trigonometric function in terms of x is,
\(\sin(\tan^{-1}x)=\frac{x}{\sqrt{x^2+1}}\)Final answer:
The composed trigonometric function in terms of x is,
\(\sin(\tan^{-1}x)=\frac{x}{\sqrt{x^2+1}}\)Related Questions
7. What conjecture would you state for
the relationship between the length of
the hypotenuse and the length of the
legs of an isosceles right triangle?
The ratio will _____
Answers
Answer: C ;)
Step-by-step explanation:
There are 16 girls and 14 boys in Mr. Chay's class. This ratio holds true for the entire school. If there are 1500 students, how many girls attend the school?
Answers
Answer:
Step-by-step explanation:
16/(16 + 14) = XX/1500
1500(16) = 30XX
XX = 800 girls
answer:TThe ratio of boys to girls is 12 to 16, 12:16 or 12/16 (all different ways this can be written). The fraction form 12/16 can be reduced by dividing
A puppy and a kitten are 180 feet apart when they see each other. The puppy can run at a speed of 25 feet per second, while the kitten can run at a speed of 20 feet per second.
How long will it take the kitten to catch up to the puppy if the puppy runs away from the kitten, and the kitten simultaneously starts chasing the puppy?
Answers
Answer:
an infinitely long time
Step-by-step explanation:
You want to know the time it takes for a kitten running 20 ft/s to catch a puppy running 25 ft/s when they start 180 ft apart and the puppy runs away from the kitten.
NeverThe kitten runs slower than the puppy, so can never catch up to it.
<95141404393>
what is the value of 5/z when z =2?
Answers
Answer:
\(z = 2. \\ 5 \div z \\ 5 \div 2 \\ 2.5\)
2.5 is the correct answer .Thank you ☺️☺️
help pleasee
look in the photo
Answers
Answer: c
Step-by-step explanation:
Because group B has Pharrell lines
will mark brainleist pls help
Answers
Answer:
x = 31°
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180° , that is
x + 54° + 95° = 180°
x + 149° = 180° ( subtract 149° from both sides )
x = 31°
Use the table to work out the values of
a
,
b
,
c
, and
d
.
x
y
=
3
x
+
2
−
3
a
−
2
−
4
−
1
b
0
2
1
c
2
d
a
=
b
=
c
=
d
=
Answers
Line AC and line DB intersect at point P. Solve for angle BPQ.
To earn full credit for presenting and defending your mathematical solution, you must share the equation, show the steps to solving for the variable x, show the steps to solving for angle BPQ.
Answers
Answer:
Angle BPQ = 64°
Step-by-step explanation:
4x + 12 +2x = 90
6x + 12 = 90
- 12 -12
6x = 78
x = 13°
BPQ = ((4(13) + 12)°
(52 + 12)°
64°
The area of Louisiana is approximately 4 x
104 square miles. The area of the United
States is approximately 225 times greater
than the area of Louisiana. What is the
approximate area of the United States?
Answers
Answer:
93,600
Step-by-step explanation:
4x104= 416
416x225 = 93,600
Suppose that the credit remaining on a phone card (in dollars) is a linear function of the total calling time (in minutes). When graphed, the function gives a line with a slope of -0.16There is $29.00 in credit remaining on the card after 25 minutes of calls. How much credit was there after 18 minutes of calls?
Answers
The linear function there after 18 minutes of calls, then the credit was = $29
The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
Given that,
Slope = -0.16
There linear function is $29.00 in credit remaining on the card after 25 minutes of calls
There after 18 minutes of calls?
Slope m = -0.16
Let us assume,
x = 25 minutes
y = $29.00 in credit
Substitute this values,
So,
We can write,
y = mx + b
$29.00 = (-0.16) (25) + b
$29.00 = -24.84 + b
b = $29.00 + 24.84
b = $53.84
We can substitute b value,
y = mx + b
y = (-0.16) x + $53.84
y = \(-0.16x\) + $53.84
y = (-0.16)(25) + $53.84
y = -24.84 + $53.84
y = $29
Therefore,
The linear function there after 18 minutes of calls, then the credit was = $29
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What ordered pairs are the solutions of the system of equations shown in the graph below?
Answers
Answer:
(4,0) & (9,5)
Step-by-step explanation:
Where the equations cross are the solutions!
Hope this Helps! :)
Happy Studies
$100,000 is shared among three friends, Anna, Louise and Lacey in the ratio.7: 10:13 respectively. Calculate the amount each receives.
Answers
Answer:
Step-by-step explanation:
Set up an equation:
7x + 10x + 13x = 100000 and solve for x:
30x = 100000 so
x = 3333.33
Anna gets 7(3333.33) = 23333.31
Louise gets 10(3333.33) = 33333.33
Lacey gets 13(3333.33) = 43333.29
For the EOQ model, which of the following relationships is incorrect?
a. As the order quantity increases, the number of orders placed annually decreases.
b. As the order quantity increases, annual holding cost increases.
c. As the order quantity increases, annual ordering cost increases.
d. As the order quantity increases, average inventory increases.
Answers
Answer: As the order quantity increases, annual ordering cost increases
Step-by-step explanation:
The Economic Order Quantity (EOQ) is simply referred to as the amount of units that should be added by a company to its inventory with each order in order to minimize total inventory costs such as order costs, holding costs, and shortage costs.
The incorrect option is that "as the order quantity increases, annual ordering cost increases". It should be noted that ordering costs are simply the expenses that are incurred in order for an order to be created and processed to a supplier. It should be noted that as the ordering quantity increases, it doesn't mean that the annual ordering costs also increase.
Please help me
Will give brainly if you actually answer the question
Answers
Answer:
B
Step-by-step explanation:
3x-10>2
get x alone
3x>12
x>4
5x-15<-5
5x<10
x<2
Question 7 (1 point) The two tables below show the amount of tip, y, included on a bill charging x dollars. A 2-column table with 3 rows titled Restaurant A. Column 1 is labeled x with entries 10, 20, 30. Column 2 is labeled y with entries 1, 2, 3. A 2-column table with 3 rows titled Restaurant B. Column 1 is labeled x with entries 25, 50, 75. Column 2 is labeled y with entries 5, 10, 15. Which compares the slopes of the lines created by the tables?
Answers
The slope of restaurant B is twice that of restaurant A
How to compare the slopes?The tables of values are given as
X(Bill) Y(Tip) X(Bill) Y(Tip)
Rest A 10 1 Rest B 25 5
Rest A 20 2 Rest B 50 10
Rest A 30 3 Rest B 75 15
The slopes are calculated using
Slope = (y2 - y1)/(x2 - x1)
Using the table of values, we have:
Rest A = (2 - 1)/(20 - 10)
Rest A = 0.1
Rest B = (10 - 5)/(50 - 25)
Rest B = 0.2
By comparing the slopes, we have:
Rest B = 2 * Rest A
This implies that the slope of restaurant B is twice that of restaurant A
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30
A restaurant used 231 eggs last week. Of these, 46 were brown in color. The remaining
eggs were white in color. Which equation can be used to solve for w, the number
of white eggs used last week?
A 231 +46w=0
B 46+ w = 231
C w = 231 +46
D 231 = 46w
Answers
D 231 = 46w can be used to solve for w, the number of white eggs used last week.
The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is four
times the measure of the first angle. The third angle is 12 more than the second. Let x, y, and z represent the measures of
the first, second, and third angles, respectively. Find the measures of the three angles.
Answers
Answer:
x = 36°
y = 66°
z = 78°
Step-by-step explanation:
General outline:Setup equations for each sentenceSolve the resulting systemSetup equations:
Allowing the first angle to be x, the second to be y, and the third to be z, the three sentences describing the relationships between angle measures are given below:
Eq1: x + y + z = 180°Eq2: y + z = 4xEq3: z = y + 12°Solve the systemSubstituting equation 3, into equations 1 and 2
Eq1: x + y + z = 180°
x + y + (y+12°) = 180°
x + 2y + 12° = 180°
x + 2y = 168°
x = 168° - 2y
Eq2: y + z = 4x
substituting the result from equation 1, and Equation 3...
y + (y+12°) = 4*(168° - 2y)
2y + 12° = 672° - 8y
10y = 660°
y = 66°
Substituting back into Equation 3...
Eq3: z = y + 12°
z = (66°) + 12°
z = 78°
Substituting both y, and z into Equation 1...
x + y + z = 180°
x + (66°) + (78°) = 180°
x + 144° = 180°
x = 36°
So, the three angle measures are:
x = 36°
y = 66°
z = 78°
Verification"The sum of the measures of the angles of a triangle is 180."
x + y + z = 180°
36° + 66° + 78° = 180°
True
"The sum of the measures of the second and third angles is four times the measure of the first angle"
y + z = 4x
66° + 78° = 4*(36°)
144° = 144°
True
"The third angle is 12 more than the second"
z = y + 12°
78° = 66° + 12°
True
Data from Ivy Tech's advising center shows the wait times as a normal distribution with the average as 20 min and a standard deviation as 5 min.
Using the empirical rule, what percent of students wait between 15 and 25 minutes?
Answers
9514 1404 393
Answer:
68%
Step-by-step explanation:
According to the empirical rule, 68% of the distribution lies within 1 standard deviation of the mean.
Here, the mean is 20 and the standard deviation is 5. The bounds on 1 standard deviation from the mean are 20±5 = [15, 25]. This is precisely the interval of interest.
68% of students wait between 15 and 25 minutes
please help khan academy
Answers
The inequality represented by the graph is given as follows:
y > 3x - 4.
How to define a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.The graph crosses the y-axis at y = -4, hence the intercept b is given as follows:
b = -4.
When x increases by 1, y increases by 3, hence the slope m is given as follows:
m = 3.
Hence the equation of the line is:
y = 3x - 4.
The inequality is composed by the values to the right (greater) of the line, and has an open interval due to the dashed line, hence:
y > 3x - 4.
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A frame around a family portrait has a perimeter of 90 inches. The
length is fifteen inches less than twice the width. Find the dimensions
(the length and the width) of the frame.
Answers
Answer:
Let x be the width of the rectangular family portrait , then its length will be 2x-15.
I hope this is helpful!
True or false question someone plz helppp!!! I’ll cash you Fr !
Answers
Answer:
yes it will......I'm not to sure
Plsss help!, bRAInLIST!!
Answers
7kg of dough x 6 hours = 42 kg
Olga Semargl's medical care bills for a recent illness were $4,620. Her major medical policy did not
cover $312 of the bill. Olga's policy had a coinsurance feature that paid 80% of all covered expenses
over a $500 deductible. What was the amount paid by the major medical policy?
Answers
The amount paid by the major medical policy is $3,046.40.
First, we need to calculate the covered expenses before the coinsurance feature comes into play. Since Olga's major medical policy did not cover $312 of the bill, the covered expenses will be:
Covered expenses = Total bill - Amount not covered
Covered expenses = $4,620 - $312
Covered expenses = $4,308
Next, we need to calculate the amount of the covered expenses that is subject to the coinsurance feature. Since Olga's policy has a $500 deductible, the covered expenses subject to coinsurance will be:
Covered expenses subject to coinsurance = Covered expenses - Deductible
Covered expenses subject to coinsurance = $4,308 - $500
Covered expenses subject to coinsurance = $3,808
The coinsurance feature pays 80% of the covered expenses subject to coinsurance, so the amount paid by the major medical policy will be:
Amount paid = Coinsurance rate x Covered expenses subject to coinsurance
Amount paid = 0.8 x $3,808
Amount paid = $3,046.40
Therefore, the amount paid by the major medical policy is $3,046.40.
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What is the effective annual rate of an account that pays interest at the nominal rate of
7% per year, compounded daily? Compounded hourly?
Answers
Answer:
To find the effective annual rate (EAR) of an account that pays interest at the nominal rate of 7% per year, compounded daily, we can use the following formula:
EAR = (1 + r/n)^n - 1
where r is the nominal annual interest rate (expressed as a decimal), and n is the number of times the interest is compounded in a year.
For daily compounding, n = 365 (since there are 365 days in a year), so we have:
EAR = (1 + 0.07/365)^365 - 1 = 0.0725 or 7.25%
To find the effective annual rate for hourly compounding, we need to adjust the value of n to account for the fact that interest is compounded more frequently. There are 365 days * 24 hours = 8,760 hours in a year, so we can use n = 8,760:
EAR = (1 + 0.07/8760)^8760 - 1 ≈ 0.0727 or 7.27%
Therefore, the effective annual rate for hourly compounding is approximately 7.27%.
“Snoqualmie” is a name shared by a waterfall and a tribe of Native Americans. In a study of the cultural importance of the waterfall, two groups of the Snoqualmie tribe were randomly surveyed. One group consisted of Snoqualmie members living less than 25 miles from the waterfall. Another group consisted of Snoqualmie members living more than 25 miles from the waterfall. The researchers asked each member to rate the cultural importance of the waterfall as low, medium, or high. Data from the study are presented in the following table.
Answers
Answer: E ( (17)(50)/88 )
Step-by-step explanation:
(Row total * column total) / table total
g silicone implant augmentation rhinoplasty is used to correct congenital nose deformities. the success of the procedure depends on various biomechanical properties of the human nasal periosteum and fascia. an article reported that for a sample of 20 (newly deceased) adults, the mean failure strain (%) was 26.0, and the standard deviation was 3.4.
(p. 277 #35)
a. Assuming a normal distribution for failure strain, estimate true average strain in
a way that converys information about precision and reliability.
b. Predict the strain for a single adult in a way that conveys information about
precision and reliability. How does the prediction compare to the estimate
calculated in part (a)?
Answers
The confidence level for the true average strain is (24.69,27.31) and the prediction level is (20.01,31.99) and also it is estimated that prediction level is much wider than the confidence level
Given that sample size is 20, mean is 26%, standard deviation is 3.4, confidence level is 95%.
a)
We must calculate the true average strain in a way that conveys precision and reliability.
We have to use t-test in our problem because sample size is less than 30.
We Know that,
True average value is determined by formula,
\(\mu\pm t*\frac{S}{\sqrt{n}}\)
where μ is sample mean,
s is sample standard deviation.
Degree of freedom=n-1
=20-1
=19
t-value at 95% confidence interval=1.7281
\(26\pm 1.728*\frac{3.4}{\sqrt{20}}\\\\=26\pm1.728*0.7606\\\\=26\pm1.31\\\\=24.69,\ 27.31\)
b)
predicted value can be calculated by formula,
\(\mu \pm t*S\sqrt{1+\frac{1}{n}}\\\\=26\pm 1.728*3.4\sqrt{1+\frac{1}{20}}\\\\=26\pm 1.728*3.4*1.02\\\\=26\pm5.99\\\\=20.01,\ 31.99\)
As a result, we conclude that the prediction interval is greater than the confidence interval.
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8 pencils for$2.24 i need help with my math can some one help me with it
Answers
Answer:
8 x 2.24 = 17.92
Pls mark me brainliest
Are you trying to find the price of 1 pencils?
If Yes The Answer is below.
Answer:
0.28
Step-by-step explanation:
To find the price of 1 pencils.
Divide 2.24 by 8 which gives you 0.28
Therefore the price of 1 pencils is 0.28
help so i cna get out of class
Answers
Based on the given conditions, the lock solution is 205.
How to solve a lock?To solve the lock, to calculate the total score based on the given conditions:
Crocus: + 20
Daffodil: + 25
Snowflake: - 50
Tulip: + 30
Bird-Red: + 25, else + 10
Calculating the scores for each input:
TULIP: +30
CROCUS: +20
DAFFODIL: +25
TULIP: +30
DAFFODIL: +25
TULIP: +30
DAFFODIL: +25
CROCUS: +20
Total score = 30 + 20 + 25 + 30 + 25 + 30 + 25 + 20 = 205
Therefore, the solution for the lock is 205.
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Image transcribed:
SPRING NOW LOADING.
<IF CROCUS, THEN +20>
<IF DAFFODIL, THEN +25>
<IF SNOWFLAKE, THEN -50>
<IF TULIP, THEN +30>
<IF BIRD-RED, THEN +25, ELSE + 10>
TULIP
CROCUS
DAFFODIL
TULIP
DAFFODIL
TULIP
DAFFODIL
CROCUS
Solve Lock
By what fraction equal to 1 should 2/3 be multiplied to form 8/11 ?
Answers
help me in math pls :(
Answers
Answer:
V = 36
Step-by-step explanation:
Given
V = a(b - 5)² ← substitute a = 4, b = 8
V = 4(8 - 5)² = 4(3)² = 4 × 9 = 36