1- Find a reduction formula and indicate the base integrals for the following integrals: Integral[ sec^n x] dx
Answers
To find a reduction formula for the given integral ∫ sec^n(x)dx, we can start by using integration by parts.
Here are the steps:
Step 1: Let u = sec^(n-2)(x) and dv = sec^2(x)dx.
Then, du/dx = (n-2)sec^(n-3)(x)tan(x) and v = tan(x).
Step 2: Using the formula for integration by parts, we have:
\(∫ sec^n(x)dx = sec^(n-2)(x)tan(x) - ∫ (n-2)sec^(n-3)(x)tan^2(x)dx\)
Step 3: Next, we substitute 1 + tan^2(x) for sec^2(x)
and simplify the expression to get:
\(∫ sec^n(x)dx = sec^(n-2)(x)tan(x) - (n-2)∫ sec^(n-2)(x)dx + (n-2)∫ sec^n(x)dx\)
Step 4: Rearranging the equation to solve for ∫ sec^n(x)dx, we get:
\(∫ sec^n(x)dx = (1/n-1)sec^(n-2)(x)tan(x) + (n-2)/(n-1)∫ sec^(n-2)(x)dx\)
The base case for this reduction formula is
∫ sec(x)dx = ln|sec(x) + tan(x)|.
Therefore, we can use this formula to find integrals of higher powers of sec(x) by repeatedly applying the reduction formula until we reach the base case.
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Related Questions
PLS HELP ME I WILL GIVE BRAIN THINGY
Answers
Write an equation that shows the number
of teaspoons of chili powder (y) per
teaspoons of cumin (x).
Answers
Answer:
y=4x
Step-by-step explanation:
Select the number line model that matches the expression
|8 - 1|
Answers
Answer:
B
Step-by-step explanation:
Trust
is the symbol used for the universal set
Answers
Answer:
I believe "U" is the symbol for your answer hope this helps!
Step-by-step explanation:
In a 4-bit system, what are the carry and overflow flags of following operations:
a. 0100 0010
b. 0100 0110
c. 1100 1110
d. 1100 1010
Answers
a. The carry and overflow flags for the operation 0100 0010 in a 4-bit system would depend on the specific operation being performed. Without knowing the operation, it is not possible to determine the carry and overflow flags.
b. Similarly, for the operation 0100 0110 in a 4-bit system, the carry and overflow flags cannot be determined without knowing the specific operation being performed.
c. In the case of the operation 1100 1110 in a 4-bit system, the carry flag would be set if there is a carry from the most significant bit (MSB) during addition or subtraction. The overflow flag would be set if there is a signed overflow, indicating that the result is too large or too small to be represented in the given number of bits. However, without knowing the specific operation being performed, it is not possible to determine the values of the carry and overflow flags.
d. Similarly, for the operation 1100 1010 in a 4-bit system, the carry and overflow flags cannot be determined without knowing the specific operation being performed.
To determine the carry and overflow flags, it is essential to know the specific arithmetic operation being performed, such as addition, subtraction, or other bitwise operations. The carry flag indicates whether a carry occurred during the operation, typically from the MSB to the next higher bit. The overflow flag indicates whether the result exceeds the range that can be represented in the given number of bits, considering signed or unsigned interpretation. Without this information, it is not possible to provide a definite answer for the carry and overflow flags in the given scenarios.
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help me solve this Algebra problem please
Answers
Answer:
39858075
Step-by-step explanation:
Hello,
One basic way to see it is to compute the values.
75 = 25 * 3
225 = 75 * 3
675 = 225 * 3
etc ...
We can notice that this is multiplied by 3 every 10 years so we can compute as below.
year population
1970 25
1980 75
1990 225
2000 675
2010 2025
2020 6075
2030 18225
2040 54675
2050 164025
2060 492075
2070 1476225
2080 4428675
2090 13286025
2100 39858075
So the correct answer is 39858075
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
A recent study reported that 60% of the children in a particular community were overwoight or obese. Suppose a random sample of 200 public school children is taken from this community. Assume the sample was taken in such a way that the conditions for using the Central Limit Theorem are met. We are interested in finding the probability that the proportion of overveightfobese children in the sample will be greater than 0.57. Complete parts (a) and (b) below. a. Before doing any calculations, determine whether this probability is greater than 50% or less than 50%. Why? A. The answer should be less than 50%. because 0.57 is less than the population proportion of 0.60 and because the sampling distribution is approximately Normal. B. The answer should be greater than 50%, because the resulting z-score will be positive and the sampling distribution is approximately Normal. C. The answer should be greater than 50%, because 0.57 is less than the population proportion of 0.60 and because the sampling distribution is approximately Normal. 0. The answer should be less than 50%, because the resulting z-score will be negative and the sampling distribution is approximately Normal.
Answers
The probability that the proportion of overweight or obese children in the sample will be greater than 0.57 is less than 50%.
The first paragraph summarizes the answer, stating that the probability is less than 50% because 0.57 is less than the population proportion of 0.60, and the sampling distribution is approximately normal.
In the second paragraph, we can explain the reasoning behind this conclusion. The Central Limit Theorem states that for a large sample size, the sampling distribution of the sample proportion will be approximately normal, regardless of the shape of the population distribution. In this case, the sample was taken in a way that meets the conditions for using the Central Limit Theorem.
Since the population proportion of overweight or obese children is 0.60, any sample proportion below this value is more likely to occur. Therefore, the probability of obtaining a sample proportion greater than 0.57 would be less than 50%. This is because the resulting z-score, which measures how many standard deviations the sample proportion is away from the population proportion, would be negative.
To summarize, the probability of the proportion of overweight or obese children in the sample being greater than 0.57 is less than 50% because 0.57 is less than the population proportion of 0.60, and the sampling distribution is approximately normal.
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Please help
Algebra 1
Look at the photo below...
Answers
horizontal line: x=9
vertical line: y=3
You can plug it into the application demos to see it visually just put y=3 on one line and x=9 on the other
A bee hive has an initial population of 10 bees. After one month, the population of bees will be three times the initial population. Then, the next month, the population of bees will be three times the population of bees the previous month. If this pattern continues, which of the following graphs represents the population of bees over time?
Graph Y
Graph X
Graph Z
Graph W
Answers
Answer:
Graph X
since it works ...............................................
(a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R, and (b) find the area of triangle PQR.P(1, 0, 1), Q(-2, 1, 3), R(4, 2, 5)
Answers
The vector orthogonal to the plane through the points P, Q, and R is (8, -8, 12), and the area of triangle PQR is \($\sqrt{301}$\).
For part (a), we can find a nonzero vector orthogonal to the plane through the points P, Q, and R by constructing a normal vector to the plane using the cross product of two vectors in the plane. The two vectors in the plane are \($\vec{PQ} = (1- (-2), 0-1, 1-3) = (3, -1, -2)$\) and \($\vec{PR} = (1-4, 0-2, 1-5) = (-3, -2, -4)$\). Taking the cross product of the two vectors gives us the normal vector to the plane, \($\vec{n} = \vec{PQ} \times \vec{PR} = (8, -8, 12)$\). Therefore, the vector orthogonal to the plane is \($\vec{n} = (8, -8, 12)$.\)
For part (b), the area of triangle PQR can be found using the formula for Heron's Formula, which states that the area of a triangle with sides a, b,and c is given by
\($A = \sqrt{s(s-a)(s-b)(s-c)}$\)
where \($s = \frac{a+b+c}{2}$\) . In this case, the sides are \($a = \|\vec{PQ}\| = \sqrt{3^2 + (-1)^2 + (-2)^2} = \sqrt{14}$, $b = \|\vec{QR}\| = \sqrt{(-2-4)^2 + (1-2)^2 + (3-5)^2} = \sqrt{14}$\), and\($c = \|\vec{PR}\| = \sqrt{(-3)^2 + (-2)^2 + (-4)^2} = \sqrt{29}$\). Plugging these values into the formula, we get
\(= \sqrt{s(s-a)(s-b)(s-c)} = \sqrt{\frac{7(7-\sqrt{14})(7-\sqrt{14})(7-\sqrt{29})}{4}} = \sqrt{7(7-\sqrt{14})^2(7-\sqrt{29})} = \sqrt{7(7-\sqrt{14})^2(\sqrt{14}+\sqrt{29})} = \sqrt{7(7-\sqrt{14})^2\sqrt{43}} = \sqrt{301}$\)Therefore, the area of triangle PQR is \($\sqrt{301}$\)
The vector orthogonal to the plane through the points P, Q, and R is (8, -8, 12), and the area of triangle PQR is \($\sqrt{301}$\).
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12x+25x+36x=0
what is the answer help needed
Answers
Combine like terms:
73x = 0
Divide both sides by 73:
x = 0
Hope this helped
What's the greatest number 26 or 5.2
Answers
Answer:
26
Step-by-step explanation:
26 is the greatest number because 5.2 is a single digit and has lower value than 26.
26 > 5.2
Hope this helps!
We begin our study of regression with what is called simple linear regression (slr). the most basic statistical model says that for an observation xi (called the independent variable), the response variable yi is where which of the following data sets do you think will follow this model?
Answers
To determine which data set will follow the simple linear regression (SLR) model, we need to look for a relationship between the independent variable (xi) and the response variable (yi).
The SLR model assumes that there is a linear relationship between the two variables, meaning that as the value of xi increases or decreases, the value of yi also increases or decreases in a straight line.
Therefore, the data set that shows a clear linear relationship between xi and yi is most likely to follow the SLR model. We can use a scatter plot to visualize the relationship between the two variables and determine if it is linear.
If the scatter plot shows a roughly straight line relationship between xi and yi, then the data set is likely to follow the SLR model. On the other hand, if the scatter plot shows a curved or non-linear relationship between xi and yi, then the data set is not likely to follow the SLR model.
So, in summary, the data set that shows a clear linear relationship between xi and yi is the one that is most likely to follow the simple linear regression (SLR) model.
Simple linear regression (SLR), it is important to note that SLR is a method used to model the relationship between a response variable (yi) and an independent variable (observation xi). In this model, the response variable yi is a linear function of the independent variable xi.
Since you have not provided specific data sets to choose from, I am unable to directly indicate which data set will follow this model. However, to identify a data set that would likely follow the simple linear regression model, look for one that exhibits a linear relationship between the independent variable (xi) and the response variable (yi). In such a data set, you would observe a pattern where, as xi increases or decreases, yi would also consistently increase or decrease in a relatively straight line.
To summarize, to determine if a data set follows the simple linear regression model, check if it exhibits a linear relationship between the independent variable (observation xi) and the response variable (yi).
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If m ABC = 122°, and m
then m
Answers
Answer:
m < DBC = 51
Step-by-step explanation:
Looking at the picture, we know <ABD and <DBC make up <ABC. Knowing this, we can set up an equation like so, plug in the known values, and solve to find m<DBC:
\(m<ABC = m<ABD + m<DBC\\122 = 71 + m<DBC\\m<DBC = 122 - 71\\m<DBC = 51\)
reposting again
i will give brainliest to best answer
Answers
Answer:
the answer is c plz trust
Step-by-step explanation:
The 5-foot pole casts a shadow of 3 feet. The building casts a shadow of 12 feet. What is the height of the building?
Answers
Answer:
20 ft
Step-by-step explanation:
Because your are scaling the shadow by 4, you have to scale the height by 4
Answer: 20 foot tall.
Step-by-step explanation: the shadow of the pole is 3 feet. and the shadow from the building is 12 feet.
12 can be divided by 3, 4 times. we know for every 3 foot shadow, the actual object is 5 feet tall.
we just multiply 5 by 4 to get 20.
we can also check our work by dividing 3 by 5. this is 0.6.
then we divide 12 by 20. that is also 0.6.
hence that is the answer.
4x2+16x+8=0 by completing the square
Answers
Answer:
Add
8
to both sides of the equation.
2
x
2
+
16
x
=
8
Divide each term by
2
and simplify.
Tap for more steps...
x
2
+
8
x
=
4
To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of
b
.
(
b
2
)
2
=
(
4
)
2
Add the term to each side of the equation.
x
2
+
8
x
+
(
4
)
2
=
4
+
(
4
)
2
Simplify the equation.
Tap for more steps...
x
2
+
8
x
+
16
=
20
Factor the perfect trinomial square into
(
x
+
4
)
2
.
(
x
+
4
)
2
=
20
Solve the equation for
x
.
Tap for more steps...
x
=
±
2
√
5
−
4
The result can be shown in multiple forms.
Exact Form:
x
=
±
2
√
5
−
4
Decimal Form:
x
=
0.47213595
…
,
−
8.47213595
…
Step-by-step explanation:
7. You are taking a survey. You ask five students which movie they prefer-Black Panther, Captain Marvel, or Avengers: Endgame. What is the probability that all five students picked the Avengers: Endgame movie?
Answers
Answer:
Coming from a student, pretty dang high. Captain Marvel was boring and Black Panther wasn't all that great compared to endgame. Sure, it was good but Endgame was the ending of a legacy. All the films over the years led up to endgame.
Step-by-step explanation:
Which of these is an example of typing at a rate of 42 words per minute?
A
typing 21 words in 2 minutes
B
typing 84 words in 3 minutes
С
typing 210 words in 5 minutes
D
typing 400 words in 10 minutes
Answers
Answer:
C. typing 210 words in 5 minutes
Step-by-step explanation:
Because 210 divided by 5 equals 42 over 1. :)
Answer:
C. Typing 210 words in 5 minutes
Step-by-step explanation:
42 words per minute, so think about this. 42 plus 42 is 84, so it is not A cause a to less than 84. And it is not Ba either cause 84 words is 2 minutes. 42×5=210
. A man bought a car for $60 320. After using it for 2 years he decides to trade in the car. The company estimated a depreciation of 10% for the first year of its use and a further 15% on its reduced value for the second year.(a) Calculate the value of the car after two years.(b) Express the value of the car after two years as a percentage of the original value. *
Answers
Answer:
(a) 39,208
(b) 65%
Step-by-step explanation:
(a) The car loses 10% the first year and 15% the second year so that’s 35% lost in total after two years.
35% of 60,320 is 21,112
60,320 - 21,112 = 39,208
39,208 ÷ 60,320 = 0.65 (65%)
The unit selling price p (in dollars) and the quantity demanded x (in pairs) of a certain brand of women's gloves is given by the demand equation p= 106e0.0002x, (0 ≤x≤ 20,000) (a) Find the revenue function R. (Hint: R(x) = px.) (b) Find the marginal revenue function R. (c) What is the marginal revenue when x= 100? $ /pair
Answers
(a) Revenue function R(x) = (106e^(0.0002x))x. (b) Marginal revenue function R'(x) = 106e^(0.0002x) + 0.0212xe^(0.0002x). (c) Marginal revenue when x = 100 is determined by substituting x = 100 into R'(x) and evaluating the expression.
(a) The revenue function R(x) represents the total revenue generated from selling x pairs of gloves. To calculate it, we multiply the unit selling price p with the quantity demanded x, giving R(x) = px.
(b) The marginal revenue function R'(x) shows how the revenue changes as the quantity demanded changes. It is obtained by taking the derivative of the revenue function R(x) with respect to x. We use the product rule and the chain rule to differentiate the terms.
(c) To find the marginal revenue at a specific quantity, we substitute the given value of x into the marginal revenue function R'(x). In this case, x = 100, so we evaluate R'(100) to determine the marginal revenue when x = 100.
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a hospital director is told that 54% of the treated patients are insured. the director wants to test the claim that the percentage of insured patients is below the expected percentage. a sample of 200 patients found that 100 were insured. find the value of the test statistic. round your answer to two decimal places.
Answers
The value of test statistic is -1.14
Define Standard error.
The standard error (SE)of a statistic (usually an estimate of a parameter) is the standard deviation of its sampling distribution or an estimate of that standard deviation. If the statistic is the sample mean, it is called the standard error of the mean (SEM).
Null Hypothesis
P = 0.54
Alternate Hypothesis
P < 0.54
For 0.05 level , the value of Z = 1.645
Decision rule ,
reject null Hypothesis if test statistic Z < -1.645
sample size (n) = 200
sample success (x) = 100
Standard error SE = √(p * (1 - p) / n
= √0.54 * (1 - 0.54) / 200
Standard error SE= 0.0352
Sample proportion (р) = x/n
= 100 / 200 ⇒ 0.5
test statistic Z = (р - P) / SE
= (0.5 - 0.54) / 0.0352
test statistic Z = -1.136 or -1.14
Therefore, the value of test statistic is -1.14
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Andy wants to be able to do a 180 degree turn on his skateboard. He can now do a 120 degree turn. How many more degrees does he need to meet his goal?
Answers
Answer: \(60^{\circ}\)
Step-by-step explanation:
Given
Andy wants to turn \(180^{\circ}\) on his skateboard
Currently, he can make a turn of \(120^{\circ}\)
The difference between the required and current turn degree meets his goal i.e.
\(\Rightarrow 180^{\circ}-120^{\circ}\\\Rightarrow 60^{\circ}\)
Thus, he needs to turn by \(60^{\circ}\) to meet his goal
Anyone know how to solve this !!
Answers
Answer:
It's 60
Step-by-step explanation:
All triangles angles have to add up to 180 degrees. 60 plus 60 plus 60 is `80.
Answer:
C. 120°
Step-by-step explanation:
Just by looking at it, you can see that it is over 90° which automatically makes it not 60° and your only option left is 120°
x+ 2 / X + 3 =5 plz give me and
Answers
Answer:
The answer is x = -13/4
Step-by-step explanation:
-13/4 + 2 / -13/4 +3 = 5
Michael bought 4 pairs of socks.
He paid $7.16 after using a $2-off
coupon. Write an equation that can
be used to find the regular price, p,
of a pair of socks.
Answers
Answer:
4p - 2=7.16 is a formula that can be used to determine the standard price of a pair of socks.
Step-by-step explanation:
The information that we know is...
- Michael purchased four pairs of socks.
- After utilizing a $2 off coupon, he spent $7.16.
We're expected to figure out what formula we should apply to get the standard price of a pair of socks so...
We start by writing 4p.
4 represents a pair of socks, and p represents the normal price of socks.
4p - 2
Then subtract 2 since he utilized a $2 off coupon.
4p - 2 = 7.16
Lastly, add = 7.16 because he paid in total $7.16.
So, 4p - 2=7.16 is a formula that can be used to determine the standard price of a pair of socks.
Hope this helps! :D
PLSSS HLEPP ME OUTT ITS URGENTTTT
Answers
Answer:
\(P(B) = \frac{4}{18} = \frac{2}{9} = 0.2\)
Step-by-step explanation:
Sample space 2+5+7+4=18
Answer:
4/18 or 2/9
Step-by-step explanation:
The total number of balls = 2 + 5 + 7 + 4 = 18
4 out of the 18 balls are blue ∴ the probability is 4/18 or 2/9
Hope this helps!
Chad buys pineapples, watermelons, and a bag of grapes for a fruit salad. He spends a total of $29.68 on the fruit salad. Pineapples
cost $2.15 each, and watermelons cost $3.75 each. The bag of grapes costs $4.48.
Create an equation to model this situation, where p represents the number of pineapples Chad can purchase and w represents the
number of watermelons he can purchase.
Answers
An equation that models the situation, where p represents the number of pineapples Chad can purchase and w represents the number of watermelons he can purchase will be; 2.15p + 3.75w = 25.20.
Let's use the given information to create an equation to model this situation. We know that Chad spends a total of $29.68 on the fruit salad, so we can start with;
2.15p + 3.75w + 4.48 = 29.68
This equation represents the total cost of the fruit salad, which includes the cost of the pineapples (2.15p), the cost of the watermelons (3.75w), and the cost of the bag of grapes (4.48).
To make this equation more specific to the problem of finding the number of pineapples and watermelons Chad can purchase, we need to use the variables p and w to represent those quantities. We can set up a second equation based on the information given about the total number of fruits;
p + w + 1 = T
Here, T represents the total number of fruits in the salad, and we add 1 to account for the bag of grapes.
Now we can use substitution to eliminate the variable T. Solving for T in terms of p and w;
T = p + w + 1
Substitute this expression for T into first equation;
2.15p + 3.75w + 4.48 = 29.68
Simplify;
2.15p + 3.75w = 25.20
Therefore, the model of this situation is; 2.15p + 3.75w = 25.20
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Moon Software Inc. is planning to issue two types of 25-year, noncallable bonds to raise a total of $6 million, $3 million from each type of bond. First, 3,000 bonds with a 10% semiannual coupon will be sold at their $1,000 par value to raise $3,000,000. These are called "par" bonds. Second, Original Issue Discount (OID) bonds, also with a 25 -year maturity and a $1,000 par value, will be sold, but these bonds will have a semiannual coupon of only 7.75%. The OID bonds must be offered at below par in order to provide investors with the same effective yield as the par bonds. How many OID bonds must the firm issue to raise $3,000,000 ? Disregard flotation costs, and round your final answer up to a whole number of bonds.
3,776
3,096
3,927
2,870
4,456
Answers
Moon Software Inc. must issue approximately 3,927 OID bonds to raise $3,000,000.
The par bonds have a coupon rate of 10% and a par value of $1,000. To raise $3,000,000, Moon Software Inc. needs to issue 3,000 par bonds since $3,000,000 divided by $1,000 equals 3,000.
The OID bonds have a semiannual coupon rate of 7.75% and a par value of $1,000. Since these bonds need to provide investors with the same effective yield as the par bonds, they must be offered at a discount. To calculate the number of OID bonds required, we need to determine the discount needed to match the effective yield of the par bonds.
The effective yield of the par bonds is 10%. The OID bonds have a coupon rate of 7.75%, so the discount needed to match the effective yield is 10% - 7.75% = 2.25%.
To raise $3,000,000 with OID bonds, we divide the amount by the discount rate: $3,000,000 / 2.25% = $133,333,333.33.
Since each OID bond has a par value of $1,000, we divide the total amount by $1,000: $133,333,333.33 / $1,000 = approximately 133,333.33 bonds.
Since we need a whole number of bonds, we round up to the nearest whole number, which gives us 133,334 bonds.
Therefore, Moon Software Inc. must issue approximately 133,334 OID bonds to raise $3,000,000.
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A recipe that serves 6 calls for 3/4 cup of sour cream. How much sour cream is needed to serve 8?
Answers
Answer:
1 cup
Step-by-step explanation:
8/6 times 3/4 = 1 cup -crispin
To serve 8 calls, 1 cup of sour cream is required.
What is a Ratio?A ratio indicates the number of times one number contains another.
Given that,
6 serve = 3/4 cup of sour cream
1 serve = (3/4×6) cup of sour cream
8 serve = (3/4×6)×8 cup of sour cream
8 serve = 1 cup of sour cream
Hence, to serve 8 calls, 1 cup of sour cream is required.
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