find the indefinite integral. (use c for the constant of integration.) tan3 x / sec6 x dx
Answers
The indefinite integral of tan^3 x / sec^6 x dx is -(1/5) sec^5 x + C, where C is the constant of integration.
We can start by simplifying the integrand using trigonometric identities:
tan3 x / sec6 x = (sin3 x / cos3 x) / (1 / cos6 x) = sin3 x cos6 x / cos3 x
Now, we can use the substitution u = cos x, du = -sin x dx:
∫ sin3 x cos6 x / cos3 x dx = ∫ sin3 x (cos x)6 / (cos x)3 dx
= ∫ (u2 - 1)3 u4 du
= ∫ (u12 - 3u10 + 3u8 - u6) du
= u13 / 13 - 3u11 / 11 + 3u9 / 9 - u7 / 7 + C
Substituting back for u, we get:
∫ tan3 x / sec6 x dx = cos13 x / 13 - 3cos11 x / 11 + 3cos9 x / 9 - cos7 x / 7 + C
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Related Questions
Given A(1, 7), B(8, 4) , and C(3, 10) ), which coordinate pair will make AB parallel to CD?
Answers
Answer:
I'm 50% sure it is B)8,4
We want to find the coordinates of a point D such that AB is parallel to CD.
The coordinates of D are: D (10, 7).
We have that:
A(1, 7)B(8, 4)C(3, 10)D(x, y).If we want CD to be parallel to AB, then the change in the components between D and C must be the same as the change in the components between B and A.
The change in the x-component between B and A is:
8 - 1 = 7
The change in the y-component between B and A is:
4 - 7 = -3
Then the coordinates of D are given by:
x = 3 + 7 = 10
y = 10 + (-3) = 7
The coordinates of D such that CD is parallel to AB are:
D(10, 7).
Notice that this is just an option, there are a lot of other possible coordinates that will also make CD parallel to AB, this is just the easier one to find.
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Which two points on the number line represent numbers that can be combined to make zero?
B and D
A and B
C and D
A and C
Answers
he BLS employer cost survey uses a sample to establish the average wage of receptionists. Based on a large number of observations, the distribution of receptionist wages is normally distributed with a mean $10.38/hour and a standard deviation of $2.05. What is the probability that the wages for a sample of 20 receptionists exceeds $11/hour
Answers
If the BLS employer cost survey uses a sample to establish the average wage of receptionists and the distribution of receptionist wages is normally distributed with a mean of $10.38/hour and a standard deviation of $2.05, then the probability that the wages for a sample of 20 receptionists exceed $11/hour is 38.16%
To find the probability, follow these steps:
z = (x - μ) / σ
where:
- x is the value we want to find the probability for (in this case, $11/hour)
- μ is the mean of the distribution ($10.38/hour)
- σ is the standard deviation of the distribution ($2.05)Let's calculate the z-score:
z = (11 - 10.38) / 2.05
= 0.3024Now, we need to find the probability of getting a z-score greater than 0.3024. We can use a standard normal distribution table or a calculator to find this probability. Assuming a two-tailed test, the probability can be calculated as:
P(Z > 0.3024) = 1 - P(Z < 0.3024)
Using a standard normal distribution table or a calculator, we can find that P(Z < 0.3024) is approximately 0.6184. Therefore, the probability that the wages for a sample of 20 receptionists exceed $11/hour is:
P(Z > 0.3024) = 1 - 0.6184
= 0.3816
So, the probability is approximately 0.3816 or 38.16%.
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If you think you know the answers to this please let me know because I’ve been stuck on this for so long
Answers
The equations that express the relationship between the side lengths of the triangles are
10² = 6² + 8²\((\sqrt{8} )^{2} = (\sqrt{5} )^{2} + (\sqrt{3} )^{2}\)\((\sqrt{30} )^{2} = 5^{2} + (\sqrt{5} )^{2}\)\((\sqrt{37} )^{2} = 1^{2} + 6^{2}\)\(3^{2} = (\sqrt{2} )^{2} + (\sqrt{7} )^{2}\)Pythagorean tripleFrom the question, we are to write an equation that expresses the relationship between the side lengths of each triangle
From the Pythagorean theorem,
In a right triangle, the square of the longest side (hypotenuse) equals sum of squares of the other two sides
That is,
c² = a² + b²
Where c is the longest side (hypotenuse)
a and b are the other two sides
For 10, 6, 8
The equation is
10² = 6² + 8²
For \(\sqrt{5}, \sqrt{3}, \sqrt{8}\)The equation is
\((\sqrt{8} )^{2} = (\sqrt{5} )^{2} + (\sqrt{3} )^{2}\)
For \(5, \sqrt{5}, \sqrt{30}\)The equation is
\((\sqrt{30} )^{2} = 5^{2} + (\sqrt{5} )^{2}\)
For \(1, \sqrt{37}, 6\)The equation is
\((\sqrt{37} )^{2} = 1^{2} + 6^{2}\)
For \(3, \sqrt{2}, \sqrt{7}\)The equation is
\(3^{2} = (\sqrt{2} )^{2} + (\sqrt{7} )^{2}\)
Hence, the equations that express the relationship between the side lengths of the triangles are
10² = 6² + 8²\((\sqrt{8} )^{2} = (\sqrt{5} )^{2} + (\sqrt{3} )^{2}\)\((\sqrt{30} )^{2} = 5^{2} + (\sqrt{5} )^{2}\)\((\sqrt{37} )^{2} = 1^{2} + 6^{2}\)\(3^{2} = (\sqrt{2} )^{2} + (\sqrt{7} )^{2}\)Learn more on Pythagorean triple here: https://brainly.com/question/3223211
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define composite functions
I've gotchu iN My SigHts
Answers
Suppose a number cube is rolled twice. What is yhe probability that an odd number will show both times?
Answers
Answer: 1/6
Step-by-step explanation: Have a blessed day
Kevin paid $9.20 per hour. He worked 8 hours. He gave his mother 1/4 of his earnings. How much did Kevin have left?
Answers
Answer:
$55.2
Step-by-step explanation:
Find the domain and range of the following rational function. Use any notation. f(x)=(3)/(x-1) f(x)=(2x)/(x-4) f(x)=(x+3)/(5x-5) f(x)=(2+x)/(2x) f(x)=((x^(2)+4x+3))/(x^(2)-9)
Answers
Domain and Range of the given rational functions are:Given rational function f(x) = 3/(x-1)The denominator of f(x) cannot be zero.x ≠ 1 Therefore the domain of f(x) is {x | x ≠ 1}
The range of f(x) is all real numbers except zero.Given rational function f(x) = (2x)/(x-4)The denominator of f(x) cannot be zero.x ≠ 4 Therefore the domain of f(x) is {x | x ≠ 4}The range of f(x) is all real numbers except zero.Given rational function f(x) = (x+3)/(5x-5)The denominator of f(x) cannot be zero.5x - 5 ≠ 0x ≠ 1 Therefore the domain of f(x) is {x | x ≠ 1}The range of f(x) is all real numbers except 1/5.Given rational function f(x) = (2+x)/(2x)The denominator of f(x) cannot be zero.x ≠ 0 Therefore the domain of f(x) is {x | x ≠ 0}The range of f(x) is all real numbers except zero.Given rational function f(x) = (x^2+4x+3)/(x^2-9)For the denominator of f(x) to exist,x ≠ 3, -3
Therefore the domain of f(x) is {x | x ≠ 3, x ≠ -3}The range of f(x) is all real numbers except 1, -1. Function Domain Rangef(x) = 3/(x-1) {x | x ≠ 1} All real numbers except zerof(x) = (2x)/(x-4) {x | x ≠ 4} All real numbers except zerof(x) = (x+3)/(5x-5) {x | x ≠ 1} All real numbers except 1/5f(x) = (2+x)/(2x) {x | x ≠ 0} All real numbers except zerof(x) = (x^2+4x+3)/(x^2-9) {x | x ≠ 3, x ≠ -3} All real numbers except 1, -1
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Michelle pays $185.76 for a table and chair. If the actual price is $172, what is the sales tax rate?
Answers
Answer:
The sales tax is 13.72
Step-by-step explanation:
What are the steps to solve this
Answers
The explanation of the steps that Marlena used to solve the given equation is as follows;
step1: 3x+5=-10 ( When X crosses the equal to sign it becomes a positive X.)
step 2: 3x= -15(When 5 crosses the equal to sign it becomes a negative 5)
step 3 : X = -5(when -15 is divided by 3)
How to calculate the missing value of the given equation using the steps?The equation that was given = 2x+5 = -10-x
Bring the like terms together;
2x+X = -10-5
Note that when X crosses the equal to sign it becomes a positive X.
3x = -15
Divide through using 3 as a common factor;
X = -15/3 = -5
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Abby counts 12 large boxes and 18 small boxes of pencils in the supply cabinet. Each large box contains 144 pencils . Each small box contains 24 boxes. Estimate the total number of of pencils. Explain why it might be better to have an underestimate rather than an overestimate.
Answers
Answer:
2,160 pencils
Step-by-step explanation:
Large boxes = 12
Small boxes = 18
Each large box contains 144 pencils . Each small box contains 24 pencils
Total pencil in large boxes = Total large boxes × number of pencils per box
= 12 × 144
= 1,728 pencils
Total pencil in small boxes = Total small boxes × number of pencils per box
= 18 × 24
= 432 pencils
Estimate the total number of of pencils
Total number of pencils = total pencils in large boxes + total pencil in small boxes
= 1,728 pencils + 432 pencils
= 2,160 pencils
It is better to have an underestimate than an overestimate so that you won't disappoint your buyers when they request for a quantity of supply. If it is underestimated; you can meet demand, if it is overestimated; you can't meet demand
If 3% of a number equals 2, find 18% of that number.
Answers
Answer:
3% of 66.7 is 2.001 or 2.00
18% of 66.7 is 12.006 or 12.01
In State College, PA the average outside temperature during the month of January was 35 degrees F. Calculate the HDD for the month of January.
Answers
The HDD for the month of January in State College, PA is 930.
To calculate the HDD (Heating Degree Days) for the month of January in State College, PA, we need to subtract the average daily temperature from 65 degrees Fahrenheit, which is considered the standard temperature for indoor heating.
HDD = 65°F - 35°F
HDD = 30°F
Therefore, the HDD for the month of January in State College, PA is 30 degrees Fahrenheit.
Hi! To calculate the Heating Degree Days (HDD) for the month of January in State College, PA with an average outside temperature of 35 degrees F, follow these steps:
1. Determine the base temperature: In the US, the base temperature is commonly 65 degrees F.
2. Subtract the average temperature from the base temperature: 65 - 35 = 30 degrees.
3. Multiply the difference by the number of days in the month: January has 31 days, so 30 * 31 = 930.
So, the HDD for the month of January in State College, PA is 930.
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To calculate the HDD for the month of January in State College, PA, we need to first determine the base temperature. The base temperature is the temperature below which a building needs to be heated in order to maintain a comfortable indoor temperature. In this case, we will use a base temperature of 65 degrees F.
To calculate the HDD, we need to subtract the average daily temperature from the base temperature and sum up the values for each day of the month. If we assume that January has 31 days, we can calculate the HDD as follows:
HDD = (65 - 35) x 31
HDD = 930
So the HDD for the month of January in State College, PA is 930. This means that during the month of January, there were 930 heating degree days, which indicates the amount of heating required to maintain a comfortable indoor temperature. It is important to note that the HDD can vary depending on the base temperature used, so it is important to choose a base temperature that is appropriate for the climate and the building being heated.
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Samantha wants to buy a bicycle for $129.99. If the sales tax is 6%, what is the total amount she will pay for the bicycle?
Answers
Answer:
About $137.79
Step-by-step explanation:
Hope this helps!
It is appropriate to use the uniform distribution to describe a continuous random variable x whena. the shape of the histogram of all possible values of x is nonsymmetrical.b. the area under the probability curve = 1.c. relative frequencies of all possible values of x are about the same.d. the probability curve f(x) > 0.
Answers
For an appropriate use the uniform distribution is to describe a continuous random variable x when relative frequencies of all possible values of x are about the same. So, option(d) is right one.
The uniform distribution is a distribution in which all values are equal. The interval [a,b] of a continuous variable X is said to be divided into one or four parts, meaning that all values in the distribution are equal or equal. If the probability density function equals f(x) = 1/(b−a), x∈[a,b] and is 0 elsewhere, we write X∼U(a,b). A curve is "uniform" when all events have the same probability. That is all occurrences of events have the same frequency. Accordingly, the correct answer is option (c).
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6,926,300,000 in scientific notation.
Answers
Answer:
6.9263 × 109
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
2k=ak+7
Solve for k
Show your work
Answers
Answer:
k=a+7
Step-by-step explanation:
Take 1 k away from both sides. I hope you found this useful!
Answer:
k = \(\frac{7}{2-a}\)
Step-by-step explanation:
2k = ak + 7 ( subtract ak from both sides )
2k - ak = 7 ← factor out k from each term on the left side
k(2 - a) = 7 ( isolate k by dividing both sides by (2 - a) )
k = \(\frac{7}{2-a}\)
PLS HELP ASAP - algebra 2
India is studying microbiology and is doing an experiment with bacteria. She notices that one of her colonies is dying at a rate of 5% per day. if the original number of colonies was 2757, answer the following:
a. write the equation to model the data that India is witnessing
b. sketch a graph of your equation from part a.
Answers
An equation to model the data that India is witnessing is f(x) = 2757(0.95)^x.
A graph of this exponential equation is shown in the image attached below.
What is an exponential function?In Mathematics, an exponential function can be modeled by using this mathematical expression:
f(x) = ab^x
Where:
a represents the initial value or y-intercept.x represents time.b represents the rate of change.Since her colonies is dying at a rate of 5% per day, this ultimately implies that the relationship is geometric and the rate of change (decay rate) is given by:
Rate of change (decay rate) = 100 - 5 = 95% = 0.95.
Substituting the parameters into the exponential equation, we have the following;
f(x) = 2757(0.95)^x
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solve by elimination - 4x- 8y=83x- 5y=16
Answers
Given the system of equations:
\(\begin{gathered} -4x-8y=8 \\ 3x-5y=16 \end{gathered}\)The solution of the system will be as follows:
\(\begin{gathered} -4x-8y=8\rightarrow\times3 \\ 3x-5y=16\rightarrow\times4 \\ ------------ \\ -12x-24y=24 \\ 12x-20y=64 \\ ------------ \\ (12x-12x)+(-24y-20y)=24+64 \\ \\ -44y=88 \\ \\ y=\frac{88}{-44}=-2 \end{gathered}\)Substitute with y into the first equation to find x:
\(\begin{gathered} -4x-2\cdot-8=8 \\ -4x+16=8 \\ -4x=8-16 \\ -4x=-8 \\ \\ x=\frac{-8}{-4}=2 \end{gathered}\)So, the solution of the system is:
\(\begin{gathered} x=2 \\ y=-2 \\ (x,y)=(2,-2) \end{gathered}\)Answer:
See below
Step-by-step explanation:
-4x -8y = 8
3x-5y = 16 <===== multiply this equation by 4/3 to get
4x - 20/3 y = 64/3 <=====add to first equation...this will eliminate 'x'
-8y - 20/3 y = 8 + 64/3 solve for y = -2
use this value of y in any of the equations to compute x
-4x - 8(-2) = 8
-4x = 8-16 shows x = 2
help this is worth a lot of points
Answers
Answer:
ok
Step-by-step explanation:
There is no options, just a box to type in your answer. PLEASE HELP!!!! 50 POINTS AND BRAINLIEST TO CORRECT ANSWER!!!!!!!!!
Answers
Answer:
16.4 TRUST ME
Step-by-step explanation:
Mark as brainliest
How to find a prime number?
Answers
Prime numbers are numbers with no factors other than 1 and themselves.
Use the prime factorization method to find the prime number. Factors should be 1 and the number itself.
What is a prime number?
Natural numbers known as prime numbers can only be divided by one (1) and by the number itself. In other terms, prime numbers are positive integers greater than one that only have the number itself and the number's first digit as factors. 2, 3, 5, 7, 11, 13, and other prime numbers are only a few examples.
A number is prime if it only has the factors 1 and itself. Therefore, we may quickly discover a prime number by prime factorising the provided number.
For example take - 11
The prime factorisation of 11 is 1 × 11 since 11 has only two factors 1 and itself, hence it is a prime number.
Some prime numbers in between 1 to 50 are -
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
Therefore, a prime number has a factor which is 1 and the number itself.
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5. Today, everything at a store is on sale. The store offers a 25% discount.
A. The regular price of a T-shirt is $20. What is the discount price?
B. If the regular price of an item is x dollars, what is the discount price in dollars?
C. The discount price of a hat is $10. What is the regular price?
Answers
Answer:
A. $15
B. x - .25x
C. $12.50
Step-by-step explanation:
A. .25 x $20 = $5
$20-$5 = $15 discounted price of T-shirt
B. x - .25x
C. x + .25x = $10
1.25x = $10
x = $12.50
Seshni wants to cover six cushions, each measuring 36 cm x 36 cm, with fabric. She adds 1.5 cm extra for each seam. The fabric she wants to buy is 90 cm wide and costs R59,99/m excluding VAT. How much fabric must be bought to cover all six cushions? How much will the fabric cost, including VAT?
Answers
If Seshni wants to cover six cushions, each measuring 36 cm x 36 cm, with fabric.
a. Seshni needs to buy 0.84375 square meters of fabric.
b. It will cost R64.66 including VAT.
How to find the fabric cost ?a. The dimensions of each cushion are 36 cm x 36 cm, and with the added 1.5 cm seam allowance, each cushion will require fabric with dimensions of (36 + 1.5) cm x (36 + 1.5) cm = 37.5 cm x 37.5 cm.
The total area of fabric required to cover all six cushions is:
6 cushions x (37.5 cm x 37.5 cm) = 8437.5 square centimeters
To convert to square meters, we need to divide by 10000:
8437.5 square centimeters / 10000 = 0.84375 square meters
So, Seshni needs to buy 0.84375 square meters of fabric.
b. Next, we can calculate the cost of the fabric.
0.84375 square meters / 0.9 meters = 0.9375 meters
The cost per meter is R59.99 excluding VAT, so the cost of the fabric is:
0.9375 meters x R59.99/meter = R56.23
To calculate the cost including VAT, we need to add the VAT amount. Assuming the VAT rate is 15%, the VAT amount is:
0.15 x R56.23 = R8.43
So the total cost including VAT is:
R56.23 + R8.43 = R64.66
Therefore, Seshni needs to buy 0.84375 square meters of fabric, and it will cost R64.66 including VAT.
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a factor of 30 is chosen at random, what is the probability that the number has 2 digits?
Answers
Answer:
3/8
Step-by-step explanation:
Let's first start by figuring out all the factors of 30.
They are as follows: 1, 2, 3, 5, 6, 10, 15, 30
30 has 8 factors in total.
3 of the factors have 2 digits.
Probability is number of desired outcomes/number of total outcomes.
We have 3 desired outcomes and 8 total outcomes.
Therefore, the probability that the factor chosen at random will have 2 digits is 3/8.
For each of the following, say whether the state satisfies the quantified predicate (and if not, briefly why). Give a witness value (for satisfied existentials) or a counterexample (for unsatisfied universals).
Does {x = 4, y = 7, b = (5, 4, 8)} ⊨ (∃ x. ∃ m. b[m] < x < y) ? If not, why?
Does {x = 1, b = (2, 8, 9)} ⊨ ( ∀x. ∀k. 0 < k < 3 → x < b[k] ) ? If not, why?
Does {x = 0, b = (5, 3, 6)} ⊨( ∀x. ∀k. 0 < k < 3 ∧ x < b[k] ) ? If not, why?
Answers
We are given that{x = 4, y = 7, b = (5, 4, 8)}We have to check whether it satisfies the following quantified predicate or not.(∃ x. ∃ m. b[m] < x < y)
We have to prove whether this statement is true or false.Let us try to prove it as true. Let us choose an arbitrary value for x and m.
Let us choose m=1
Then, b[m]=4And, x=6
Therefore, 4<6<7, satisfies the predicate. Hence, the given statement is true.2) We are given that{x = 1, b = (2, 8, 9)}
We have to check whether it satisfies the following quantified predicate or not.(∀x. ∀k. 0 < k < 3 → x < b[k] )
We have to prove whether this statement is true or false.Let us try to prove it as false. For that, we have to find a counterexample. We have to disprove this statement.
That is if the statement is false, then the negation of this statement should be true, and that would mean the existence of a counterexample that satisfies the negation of the statement.
Therefore, (∃x. ∃k. 0 < k < 3 ∧ x ≥ b[k] )For k=1 and k=2, we get 2 values 8 and 9. Both of them are greater than or equal to x.So, the above statement holds true, which contradicts the initial statement.
Therefore, the given statement is false.3) We are given that{x = 0, b = (5, 3, 6)}
We have to check whether it satisfies the following quantified predicate or not.(∀x. ∀k. 0 < k < 3 ∧ x < b[k] )We have to prove whether this statement is true or false.Let us try to prove it as true.
Let us choose an arbitrary value for x and k.We have, 0< k <3 and x< b[k].
Let us choose k=2.
Then, b[k]=3
Therefore, the statement x<3 holds true.So, the above statement holds true for the given state.
Therefore, the given statement is true.
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In the past, jackie has won the100-meter dash 92% of the time. if she runs the 100-meter dash 58 times this year, about how many times should she win the event? round to the nearest whole number.
Answers
Jackie should win the event about 53 times.
Given that Jackie has won the 100-meter dash 92% of the time in the past and she runs the 100-meter dash 58 times this year, we have to find about how many times she should win the event. We need to round the answer to the nearest whole number.We know that Jackie has won the 100-meter dash 92% of the time.
So the number of times Jackie won the event = 92/100 × 58= 53.36 ≈ 53 timesRounding 53.36 to the nearest whole number, we get 53 as the nearest whole number.Therefore, Jackie should win the event about 53 times.
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AB is a diameter of the
circle. Find the angle
BCO.
A 70°
B 20°
C 60°
D50°
Answers
Answer:
70°, ,have a nice day
Answer:
∠BCO = 70°
Step-by-step explanation:
AO = CO = BO because all radii of the same circle are equal.
∠ACO = 20° because it is an isosceles triangle.
∠BCA = 90° because a triangle with it's hypotenuse being the diameter of a circle is a right triangle.
∠BCA - ∠ACO = ∠BCO
90° - 20° = 70°
∠BCO = 70°
In an endurance race, Alyson rode her bicycle 7 miles less than Jeff. Together they rode 39 miles. How far did Alyson ride?
Answers
Answer:
Distance cover by Alyson = 16 miles
Step-by-step explanation:
Given:
Distance cover together = 39 miles
Assume;
Distance cover by Jeff = a
Distance cover by Alyson = a - 7
Find:
Distance cover by Alyson
Computation:
a + (a - 7) = 39
2a - 7 = 39
2a = 46
a = 23
Distance cover by Alyson = a - 7
Distance cover by Alyson = 23 - 7
Distance cover by Alyson = 16 miles
Find the median of the data set.
525 511 493 576 554 506 563 539
533
O 525
O
565
532
$
*
Answers
Answer:
353
Step-by-step explanation:
Add 506+563 =1059÷2=353