Find the indefinite integral by using the substitution x = 4 sec(θ). (Use C for the constant of integration.) x2 − 16 x d
Answers
Answer:
[tex]\frac{x^2-16}{2} + 16ln\frac{4}{x} +16C[/tex]
Step-by-step explanation:
Given the indefinite integral [tex]\int\limits{\frac{x^2-16}{x} } \, dx[/tex], using the substitute
x = 4 sec(θ)...1
The integral can be calculated as thus;
First let us diffrentiate the substitute function with respect to θ
dx/dθ = 4secθtanθ
dx = 4secθtanθdθ... 2
Substituting equation 1 and 2 into the integral function we will have;
[tex]\int\limits{\frac{(4sec \theta)^2-16}{4sec \theta} } \, 4sec \theta tan \theta d \theta\\\int\limits{\frac{16sec^2 \theta-16}{4sec \theta} } \, 4sec \theta tan \theta d \theta\\\int\limits{\frac{(16(sec^2 \theta-1)}{4sec \theta} } \, 4sec \theta tan \theta d \theta\\\\from \ trig \ identity,\ sec^2 \theta - 1 = tan^\theta\\\\\int\limits{\frac{16 tan^2 \theta}{4sec \theta} } \, 4sec \theta tan \theta d \theta\\\\\int\limits 16 tan^3 \theta d \theta\\\\[/tex]
Find the remaining solution in the attachment.
Related Questions
The following data represent the miles per gallon for a particular make and model car for six randomly selected vehicles. Compute the mean, median, and mode miles per gallon 24.2. 22.2. 37.8, 22.7. 35 4. 31.61. Compute the mean miles per gallon. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The mean mileage per gallon is _______B. The mean does not exist 2. Compute the median miles per gallon. Select the correct choice below and, if necessary, fill in the answer box to complete your choice A. The median mileage per gallon is __________B. The median does not exist. 3. Compute the mode miles per gallon. Select the correct choice below and, if necessary,fill in the answer box to complete your choice. A. The mode is _________B. The mode does not exist.
Answers
Answer:
A. The mean mileage per gallon is _____ 28.99__
A. The median mileage per gallon is _____27.905_____
B. The mode does not exist.
Step-by-step explanation:
Mean= Sum of values/ No of Values
Mean = 24.2 + 22.2+ 37.8+ 22.7 + 35.4 +31.61/ 6
Mean = 173.91/6= 28.985 ≅ 28.99
The median is the middle value of an ordered data which divides the data into two equal halves. For an even data the median is the average of n/2 and n+1/2 value where n is the number of values.
Rearranging the above data
22.2 , 22.7 , 24.2 , 31.61 , 35.4, 37.8
Third and fourth values are =24.2 + 31.61 = 55.81
Average of third and fourth values is = 55.81/2= 27.905
Mode is the values which is occurs repeatedly.
In this data there is no mode.
What percent of the area underneath
this normal curve is shaded?
the answer is not 36%
Answers
Answer:
95%
Step-by-step explanation:
Answer:
99.7
Step-by-step explanation:
hope this helps !
I the horizontal change between two points on a line.
Answers
Answer:
m = rise /run = (y2-y1)/(x2-x1)
Step-by-step explanation:
In math, slope is the ratio of the vertical and horizontal changes between two points on a surface or a line. The vertical change between two points is called the rise, and the horizontal change is called the run. The slope equals the rise divided by the run.
Answer: Run is the horizontal change between two points on a line.
Step-by-step explanation:
Please help me in this
Answers
Answer:
the first question:a half is 1/2 = 0.5
10 perecent ⇒ (0.5*10)/100= 0.05
the second question :the percentage of 19⇒ (19*100)/20 = 95 percent
What is 10% of a half?
= 0.05
10% of 0.5 is 0.05.
Divide 0.5 by 10 and move the decimal point one place to the left.
---------------------------
What percentage of 20 is 19?
= 95%
Convert the fraction
Steps:
19/20 =
19 divided by 20 =
0.95
0.95 x 100/100 =
0.95 x 100% =
(0.95 x 100)% =
95%
Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter: 116 meters
Answers
Answer:
Length = 29 m
Width = 29 m
Step-by-step explanation:
Let x and y be the length and width of the rectangle, respectively.
The area and perimeter are given by:
[tex]A=xy\\p=116=2x+2y\\y=58-x[/tex]
Rewriting the area as a function of x:
[tex]A(x) = x(58-x)\\A(x) = 58x-x^2[/tex]
The value of x for which the derivate of the area function is zero, is the length that maximizes the area:
[tex]A(x) = 58x-x^2\\\frac{dA}{dx}=0=58-2x\\ x=29\ m[/tex]
The value of y is:
[tex]y = 58-29\\y=29\ m[/tex]
Length = 29 m
Width = 29 m
Use the equation Y = 3/27x - 54 +5.
Which is an equivalent equation of the form
y=aVx-h+k
y=-273x +2 +5
y=-3x + 2 + 5
y=33x-2+5
y=27*X-2 +5
Answers
Answer:
In the picture below for both parts
Step-by-step explanation:
Edge 2021
The solution is Option C.
The value of the equation is y = 3∛ ( x - 2 ) + 5
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
y = ∛ ( 27x - 54 ) + 5 be equation (1)
On simplifying the equation , we get
y = ∛27 ( x - 2 ) + 5
The cube root of 27 is ∛27 = 3
So , the equation will be
y = 3∛ ( x - 2 ) + 5
Therefore , the value of y is 3∛ ( x - 2 ) + 5
Hence , the equation is y = 3∛ ( x - 2 ) + 5
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A pen in the shape of an isosceles right triangle with legs of length x ft and hypotenuse of length h ft is to be built. If fencing costs $ 2 divided by ft for the legs and $ 4 divided by ft for the hypotenuse, write the total cost C of construction as a function of h.
Answers
Answer
(4h/√2)+4h
Explanation:
the side length as a function of h will be needed, so we will compute it first,
Let x be the side length of the right isosceles triangle, then using Pythagorean theorem.
CHECK THE ATTACHMENT FOR DETAILED EXPLANATION
A 6-pound bag of wheat costs $47.04. What is the price per ounce?
Answers
Answer:
$0.49
Step-by-step explanation:
Using the conversion
1 pound = 16 ounces , then
6 pounds = 6 × 16 = 96 ounces, thus
cost of 1 ounce = [tex]\frac{47.04}{96}[/tex] = $0.49
7. The mean age at first marriage for respondents in a survey is 23.33,
with a standard deviation of 6.13. For an age at first marriage of 33.44,
the proportion of area beyond the Z score associated with this age is
.05. What is the percentile rank for this score?
Answers
Answer:
[tex] \mu = 23.33, \sigma =6.13[/tex]
And for this case we are analyzing the value os 33.44 and we can use the z score formula given by:
[tex] z=\frac{X -\mu}{\sigma}[/tex]
And replacing we got:
[tex] z=\frac{33.44 -23.33}{6.13}= 1.649[/tex]
We know that the proportion of area beyond the Z score associated with this age is .05 so then the percentile would be: 95
Step-by-step explanation:
For this case we have the following parameters:
[tex] \mu = 23.33, \sigma =6.13[/tex]
And for this case we are analyzing the value os 33.44 and we can use the z score formula given by:
[tex] z=\frac{X -\mu}{\sigma}[/tex]
And replacing we got:
[tex] z=\frac{33.44 -23.33}{6.13}= 1.649[/tex]
We know that the proportion of area beyond the Z score associated with this age is .05 so then the percentile would be: 95
ABC bank requires a 20% down payment on all its home loans. if the house is priced at $105,000, what is the amount of the down payment required by the bank?
A) $21,000
B) $210,000
C) $14,500
D) $18,000
correct answer is A) $21,000
Answers
Answer:
A) $21,000
Step-by-step explanation:
Percentage of down payment that ABC bank requires to be paid = 20%
Price of the house = $10500
Then
Amount of down payment
that needs to be made = (20/100) * 105000
= 21000 dollars
The answer is A) $21,000
20% is 1/5
1/5 of 105,000 is 21,000
If -5(x+8) =-25, then x=-3
Answers
Answer:
Correct!
Step-by-step explanation:
-5(x+8)=-25
x+8=5
x=-3
Answer:
here, -5(x+8)=-25
or, -5x +(-40)= -25
or, -5x=-25+40
or, x= 15/-5
therefore the value of x is -3....ans..
hope u understood..
The number of calories you eat and the amount of weight you gain indicates what type of correlation?
Answers
Answer: A positive correlation
Step-by-step explanation:
Correlation tells the relation between two variables.
A positive correlation exists when two variables are proportional to each other.A negative correlation exists when two variables are inversely proportional to each other.As we know that the amount of weight you gain depends upon the number of calories you eat.
That means the amount of weight is directly proportional to the number of calories you eat ( if not burn by exercise).
That means there is a positive correlation.
So, the correct answer is " a positive correlation."
If a hypothesis is not rejected at the 0.10 level of significance, it: a. may be rejected at the 0.05 level. b. must be rejected at the 0.025 level. c. must be rejected at the 0.05 level. d. will not be rejected at the 0.05 level.
Answers
Answer:
Option D - Will not be rejected at the 0.05 level.
Step-by-step explanation:
The significance level, which is denoted as "α", is a measure of the strength of the evidence that must be present in a sample before we can reject the null hypothesis and conclude that the effect is statistically significant. Now, this significance level must be determined before conducting an experiment.
Now, in the context of this question, the significance level is the probability of rejecting the null hypothesis when it is true. For example, a significance level of 0.05 means a 5% risk of concluding that a difference exists when there is no actual difference. Now, lower significance levels will indicate that we require stronger evidence before we can reject the null hypothesis.
Thus, if we don't reject at α = 0.1,we obviously will not reject at higher values.
Thus, looking at the options, we will not reject at 0.05 significance level.
Evaluate the expression (image provided). A.) 1.5 B.) 6 C.) 6^15 D.) 1.5^6
Answers
Answer:
1.5
Step-by-step explanation:
6 to the log base of 6 will be one (they essentially cancel each other out, log is the opposite of exponents) and we are left with 1.5.
11/n = 8/5 solve for n
Answers
Answer:
n = 55/8
Step-by-step explanation:
You can solve it by cross multiplying. Where you multiply the denominator of the fraction on the left side with the numerator on the right side, and vice versa.
11/n = 8/5
n x 8 = 11 x 5
8n = 55
n = 55/8
(or 6.875)
Answer:
[tex]\boxed{\pink{n = 7 \frac{3}{8} }}[/tex]
Step-by-step explanation:
[tex] \frac{11}{n} = \frac{8}{5} \\ [/tex]
Use cross multiplication
[tex]11 \times 5 = 8 \times n \\ 55 = 8n \\ \frac{55}{8} = \frac{8n}{8} \\ n = 7 \frac{3}{8} [/tex]
1) What is the square root of 81
Answers
When deriving the quadratic formula by completing the square, what expression can be added to both sides of the
equation to create a perfect square trinomial?
Answers
Answer:
The element you add is [tex]b^2 / 4a[/tex]
Step-by-step explanation:
The element you add is [tex]b^2 / 4a[/tex]
Remember that
[tex]a x^2 + bx +c \\= a ( x^2 +(b/a)x ) + c[/tex]
So, in order to complete the square you add [tex](b/2a)^2[/tex]
But when you multiply times [tex]a[/tex] you get
[tex]b^2 / 4a[/tex]
it can also be explained as D on edg if you still needed the answer :)
Fill in the table using this function rule.
Answers
Answer:
1, 2.2, 5.5, 10.2.
Step-by-step explanation: these are simplified to the nearest tenth
Stats A simple random sample of FICO scores is listed below. The mean FICO score is reported to be 678. Assuming that the standard deviation of all FICO scores is known to be 58.3, use a 0.01 significance level to test the claim that these sample FICO scores come from a population with a mean equal to 678. DATA: 714, 751, 664, 789, 818 , 779, 698, 836, 753, 834, 693, 802.
Answers
Step-by-step explanation:
The sample mean is:
(714+751+664+789+818+779+698+836+753+834+693+802) / 12
≈ 760.9
At 0.01 significance level and 11 degrees of freedom, the critical value is t = 3.106.
The standard error is 58.3 / √12 = 16.8.
The confidence interval is:
760.9 ± 3.106 × 16.8
(708.6, 813.2)
678 is outside of the confidence interval, so we can conclude with 99% confidence that the sample does not come from a population with a mean of 678.
To test the claim that the sample FICO scores come from a population with a mean equal to 678, we can use a one-sample t-test.
What is t-test?A t-test is a statistical test used to determine if there is a significant difference between the means of two groups.
It is often used when the sample size is small or when the population standard deviation is unknown.
To test the claim that the sample FICO scores come from a population with a mean equal to 678, we can use a one-sample t-test.
First, we need to calculate the t-value using the following formula:
t = (x - μ) / (s / sqrt(n))
We are given that x = 678, μ = 678, s = 58.3, and n = 12. Substituting these values into the formula, we get:
t = (678 - 678) / (58.3 / sqrt(12))
t = 0
Next, we need to find the critical t-value using a t-distribution table or calculator with 11 degrees of freedom (df = n - 1) and a 0.01 significance level. The critical t-value is 3.106.
Since the calculated t-value of 0 is less than the critical t-value of 3.106, we fail to reject the null hypothesis that the sample FICO scores come from a population with a mean equal to 678.
Thus, in other words, there is not enough evidence to support the claim that the sample FICO scores have a different mean than the population mean of 678.
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Jeremy makes $57,852 per year at his accounting firm. How much is Jeremy’s monthly salary? (There are 12 months in a year.) How much is Jeremy’s weekly salary? (There are 52 weeks in a year.)
Answers
Answer:
Monthly: $4,821
Weekly: $1112.54
Step-by-step explanation:
Monthly
A monthly salary can be found by dividing the yearly salary by the number of months.
salary / months
His salary is $57,852 and there are 12 months in a year.
$57,852/ 12 months
Divide
$4,821 / month
Jeremy makes $4,821 per month.
Weekly
To find the weekly salary, divide the yearly salary by the number of weeks.
salary / weeks
He makes $57,852 each year and there are 52 weeks in one year.
$57,852 / 52 weeks
Divide
$1112.53846 / week
Round to the nearest cent. The 8 in the thousandth place tells use to round the 3 up to a 4 in the hundredth place.
$1112.54 / week
Jeremy makes $1112.54 per week
An auto race consists of 15 laps. Jon Kimm completes the first 3 laps at an average speed of 195 mph, and the remaining laps at an average speed of 205 miles per hour. Let d represent the length of one lap. Choose the time in terms of d that it takes the driver to complete the race.
Answers
Answer:
equation is inconclusive
Step-by-step explanation:
you average the two speeds getting 200 mph. then you need to know the time is took to fully complete the race to get the unit rate which you would multiply to find yiur time.
What is a15 of the sequence −7,2,11,…
?
Answers
Step-by-step explanation:
a=-7
d=9
n=15
we have to find a15
a(n)= a+(n-1)d
a(15)= -7+(15-1)9
a(15)= -7+126
a(15)=119
so 15 term of the sequence is 119
The 15th term in the given sequence is 119.
The given sequence is −7,2,11,…
Here, a=-7, d=9
What is the formula to find the nth term of the sequence?The formula to find the nth term of the sequence is [tex]a_{n} =a+(n-1)d[/tex].
Now, [tex]a_{15} =-7+(15-1) \times9=119[/tex].
Therefore, the 15th term in the sequence is 119.
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In a survey, 205 people indicated they prefer cats, 160 indicated they prefer dots, and 40 indicated they don’t enjoy either pet. Find the probability that if a person is chosen at random, they prefer cats
Answers
Answer: probability = 0.506
Step-by-step explanation:
The data we have is:
Total people: 205 + 160 + 40 = 405
prefer cats: 205
prefer dogs: 160
neither: 40
The probability that a person chosen at random prefers cats is equal to the number of people that prefer cats divided the total number of people:
p = 205/405 = 0.506
in percent form, this is 50.6%
Key west,Florida to Seattle, Washington is 3,518 miles. If it takes 7hours and 15 minutes to fly there, what is the average speed ?
Answers
Answer:
485.24 miles per hour
Step-by-step explanation:
The required average speed of the flight is 485.25 miles per hour.
Given that,
Key west, Florida to Seattle, Washington is 3,518 miles. If it takes 7 hours and 15 minutes to fly there, what is the average speed is to be determined?
The average of the values is the ratio of the total sum of values to the number of values.
What is speed?Speed is defined as when an object is subjected to move, the distance covered by the object in a certain time interval is the speed of that object.
Total distance to fly = 3,518 miles
Total time = 7 hours 15 minutes = 7 + 15/60
= 7.25 hour
Speed = distance / time
= 3, 518 / 7.25
= 485.25 miles / hours,
Thus, the required average speed of the flight is 485.25 miles per hour.
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Please help. !!!!! Only if you are good at college algebra
Answers
A musician plans to perform 5 selections for a concert. If he can choose from 9 different selections,
how many ways can he arrange his program?
Answers
Answer:
since order of songs matter in a concert as well, every scenario of the 5 songs being played in different order will be a different scenario.
so, we will permute 5 from 9.
9!/4!
15120 different scenarios
Given a right triangle with a hypotenuse length of radical 26 and base length of 3. Find the length of the other leg (which is also the height).
Answers
Answer:
√17
Step-by-step explanation:
The Pythagorean theorem can be used for the purpose.
hypotenuse² = base² +height²
(√26)² = 3² +height²
26 -9 = height²
height = √17
The length of the other leg is √17.
A college student is taking two courses. The probability she passes the first course is 0.7. The probability she passes the second course is 0.67. The probability she passes at least one of the courses is 0.79. Give your answer to four decimal places. a. What is the probability she passes both courses
Answers
Answer:
0.58 = 58% probability she passes both courses
Step-by-step explanation:
We have two events, A and B.
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
In which:
[tex]P(A \cup B)[/tex] is the probability of at least one of these events happening.
P(A) is the probability of A happening.
P(B) is the probability of B happening.
[tex]P(A \cap B)[/tex] is the probability of both happening.
In this question:
Event A: Passes the first course.
Event B: Passes the second course.
The probability she passes the first course is 0.7.
This means that [tex]P(A) = 0.7[/tex]
The probability she passes the second course is 0.67.
This means that [tex]P(B) = 0.67[/tex]
The probability she passes at least one of the courses is 0.79.
This means that [tex]P(A \cup B) = 0.79[/tex]
What is the probability she passes both courses
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
[tex]0.79 = 0.70 + 0.67 - P(A \cap B)[/tex]
[tex]P(A \cap B) = 0.58[/tex]
0.58 = 58% probability she passes both courses
The length of a rectangle is six times its width. The area of the rectangle is 384 square centimeters. Find the dimensions of the rectangle.
Answers
Answer:
Width = 8 cm
Length = 48 cm
Step-by-step explanation:
Area of a Rectangle Formula: A = lw
Step 1: Write out expression:
l = 6w
w = w
Step 2: Plug in known variables
384 = 6w(w)
Step 3: Solve for w
385 = 6w²
w² = 64
w = 8
Step 4: Find l
l = 6(8)
l = 48
the length is 48
Suppose you pay a dollar to roll two dice. if you roll 5 or a 6 you Get your dollar back +2 more just like it the goal will be to find the amount of money you can expect to win or lose if you play this game 100 times. How many times would you win? how many times would you lose?
Answers
Answer:
(a)$67
(b)You are expected to win 56 Times
(c)You are expected to lose 44 Times
Step-by-step explanation:
The sample space for the event of rolling two dice is presented below
[tex](1,1), (2,1), (3,1), (4,1), (5,1), (6,1)\\(1,2), (2,2), (3,2), (4,2), (5,2), (6,2)\\(1,3), (2,3), (3,3), (4,3), (5,3), (6,3)\\(1,4), (2,4), (3,4), (4,4), (5,4), (6,4)\\(1,5), (2,5), (3,5), (4,5), (5,5), (6,5)\\(1,6), (2,6), (3,6), (4,6), (5,6), (6,6)[/tex]
Total number of outcomes =36
The event of rolling a 5 or a 6 are:
[tex](5,1), (6,1)\\ (5,2), (6,2)\\( (5,3), (6,3)\\ (5,4), (6,4)\\(1,5), (2,5), (3,5), (4,5), (5,5), (6,5)\\(1,6), (2,6), (3,6), (4,6), (5,6), (6,6)[/tex]
Number of outcomes =20
Therefore:
P(rolling a 5 or a 6) [tex]=\dfrac{20}{36}[/tex]
The probability distribution of this event is given as follows.
[tex]\left|\begin{array}{c|c|c}$Amount Won(x)&-\$1&\$2\\&\\P(x)&\dfrac{16}{36}&\dfrac{20}{36}\end{array}\right|[/tex]
First, we determine the expected Value of this event.
Expected Value
[tex]=(-\$1\times \frac{16}{36})+ (\$2\times \frac{20}{36})\\=\$0.67[/tex]
Therefore, if the game is played 100 times,
Expected Profit =$0.67 X 100 =$67
If you play the game 100 times, you can expect to win $67.
(b)
Probability of Winning [tex]=\dfrac{20}{36}[/tex]
If the game is played 100 times
Number of times expected to win
[tex]=\dfrac{20}{36} \times 100\\=56$ times[/tex]
Therefore, number of times expected to loose
= 100-56
=44 times