Answers
The solution for integrals are -1/3 (2 + cos² (x))[tex]^\frac{3}{2}[/tex] +C
How do we solve for the integral?If we are finding the following integral below
∫ (√2 + (cos x)² / secx × cscx) dx instead of ∫ (√(2 + cos²x)) / (secx × csc) dx
then
secx = 1/cosx and cscx = 1/sinx
∫ (√(2 + cos²x)) × sinx × cosx dx
givn that sin²x + cos²x = 1
sin²x = 1 - cos²x
u = cosx,
du = -sinx dx.
-∫ (√u) / (2sinxcosx) du.
-√u + C.
When you substitute the original equation into the result
1/3 (2 + cos²x)^(3/2) + C.
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Related Questions
In 1990, a total of $641 billion was spent on food and drinks in a particular country. In 2003, the total spent was $1016 billion.
(a) Find the equation of the exponential function that can be used to model the total 7 spent (in billions of dollars) on food and drinks in this country as a
function of the number of years t since 1990. (Round your decimal value to four decimal places.)
x
T=
(b) Use your model to predict the amount spent (in billions of dollars) in 2000. (Round your answer to the nearest integer.)
billion dollars
(c) What is your prediction for the total sales of food and drink (in billions of dollars) in 2018? (Round your answer to the nearest Integer.)
billion dollars
(d) Estimate when the total sales will reach $2 trillion if this exponential trend continues. (Round your answer to two decimal places.)
t=
Answers
Part(a),
The exponential function that models the total spent on food and drinks as a function of the number of years since 1990 is:
[tex]T(x) = 641 \times ((\dfrac{1016}{641})^{(\frac{1}{13}))^x[/tex]
Part(b),
The predicted amount spent in 2000 is 964 billion dollars (rounded to the nearest integer).
Part(c),
The predicted total sales of food and drink in 2018 is 1756 billion dollars
Part(d),
If the exponential trend continues, the total sales will reach 2 trillion dollars approximately 32.72 years after 1990, which is around the year 2022.
(a) To model the total spent on food and drinks as an exponential function of the number of years since 1990, we can use the general form of an exponential function:
[tex]T = a \times b^t[/tex]
where T is the total spent in billions of dollars, t is the number of years since 1990, a is the initial amount spent in 1990, and b is the growth factor or base of the exponential function.
Using the given information, we can set up two equations:
T(0) = 641 (total spent in 1990)
T(13) = 1016 (total spent in 2003, which is 13 years after 1990)
Substituting these values into the exponential function, we get:
[tex]641 = a \timrd b^0[/tex] => a = 641
[tex]1016 = a b^{13[/tex] => [tex]b = (\dfrac{1016}{641})^{\frac{1}{13}[/tex]
Therefore, the exponential function that models the total spent on food and drinks as a function of the number of years since 1990 is:
[tex]T(x) = 641 \times ((\dfrac{1016}{641})^{(\frac{1}{13})^x[/tex]
(b) To predict the amount spent in 2000, we need to substitute t = 10 (since 2000 is 10 years after 1990) into the exponential function:
[tex]T(10) = 641 \times ((\dfrac{1016}{641})^{(\frac{1}{13}))^{10[/tex] ≈ 964
Therefore, the predicted amount spent in 2000 is 964 billion dollars (rounded to the nearest integer).
(c) To predict the total sales of food and drink in 2018, we need to substitute t = 28 (since 2018 is 28 years after 1990) into the exponential function:
[tex]T(28) = 641 \times ((\dfrac{1016}{641})^{(\frac{1}{13}))^{28[/tex] ≈ 1756
Therefore, the predicted total sales of food and drink in 2018 is 1756 billion dollars (rounded to the nearest integer).
(d) To estimate when the total sales will reach 2 trillion dollars, we need to solve for t in the exponential function when T(t) = 2000 (since 2 trillion dollars is equivalent to 2000 billion dollars):
[tex]2000 = 641 \times ((\dfrac{1016}{641})^{(\frac{1}{13}))^t[/tex]
[tex]ln(\dfrac{2000}{641}) = t \times ln((\dfrac{1016}{641})^{(\frac{1}{13})[/tex]
[tex]t = \dfrac{ln(\dfrac{2000}{641})} { ln((\dfrac{1016}{641})^{(\frac{1}{13})) }}[/tex]
t = 32.72
Therefore, if the exponential trend continues, the total sales will reach 2 trillion dollars approximately 32.72 years after 1990, which is around the year 2022.
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State the formula.
cos(x − y) =
Answers
Answer:
Step-by-step explanation:
сosx*cosy+sinx*siny
Miguel has a stick that is 2/3 yd long. He cuts it in to pieces, as shown in the model
HELP I CANT SOLVE THIS ONE:
The model shows that there are __ pieces that are each __ yd long
Answers
Answer:
Solution: It is given that Miguel needs to cut a board that is Two-thirds of a yard long into 3 equal pieces. It means is divided in 3 equal parts.
Step-by-step explanation:
The table below lists the capacity, in quarts, of four different fish tanks at a pet store.
FISH TANK CAPACITY
Fish Tank
A Pacific
B Fresh
C. Tropic
D Bahama
Pacific
Fresh
Tropic
Bahama
Which fish tank has capacity of 60 gallons?
Capacity (quarts)
240
15
120
60
Answers
The fish tank that has a capacity of 60 gallons is given as follows:
A. Pacific.
How to obtain the fish tank?The fish tank that has a capacity of 60 gallons obtained applying the proportions in the context of the problem.
The rate between quarts and gallons is given as follows:
1 gallon = 4 quarts.
Hence the capacity in quarts equivalent to 60 gallons is given as follows:
60 x 4 = 240 quarts.
Meaning that the Pacific fish tank has a capacity of 60 gallons.
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A pet store has 11 puppies, including 5 poodles, 3 terriers, and 3 retrievers. If Rebecka selects one puppy at random, the pet store replaces the puppy with
a puppy of the same breed, then Aaron chooses a puppy at random. Find the probability that they both select a poodle.
The probability is
Answers
The probability that they both select a poodle is bigger. The probability is 0.074
How is this so?In the store, there are 11 puppies, and 3 of them are poodles.
If Rebeca and Aaron chose at random, then the probabilities are; for Rebbeca, there is a 3/11 probability to get a poodle ( because there are 3 poodles of eleven dogs) and the probability for Aaron is 2/10 because now there are one less poodle (and in consequence one less puppy)
now, the joint probability of these two events happening is the product of each probability, this is:
p = (3/11)*(2/10) = 6/110, that we can simplify at 3/55 if we divide both denominator and numerator by 2.
If the dog is replaced after Rebeca picked hers, then Aaron also has a 3/11 probability of picking a poodle, and in that case, the joint probability is:
q = (3/11)*/3/11) = 9/121
now, p = 3/55 = 0.055 and q = 9/121 = 0.074
Thus, this means that the probability of both of them selecting a poodle is bigger when the dog is replaced (which makes a lot of sense)
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Yasin has a bag containing five red balls and two white balls. Yasin is going to pick a ball at random. How many more white balls should Yasin put in the bag so that it is just as likely that he will pick a red ball as a white ball?
Answers
Let x be the number of white balls Yasin needs to add to the bag. Then, the total number of balls in the bag will be 5 + x red balls and 2 + x white balls.
The probability of picking a red ball will be (5)/(7 + x) and the probability of picking a white ball will be (2 + x)/(7 + x).
We can set up an equation:
5 / (7 + x) = (2 + x) / (7 + x)
Solving for x, we get:
5(7 + x) = (2 + x)(7 + x)
35 + 5x = 14 + 9x + x^2
x^2 + 4x - 21 = 0
(x + 7)(x - 3) = 0
The solution x = 3 makes sense since if Yasin adds 3 more white balls, then the bag will have 5 red balls and 5 white balls, making it equally likely to pick a red ball or a white ball.
In order to afford a down payment how much would Jocelyn need to save each year for the next three years to save $4000?
Answers
Jocelyn would need to save $1333.33 each year with 7% interest.
To calculate how much Jocelyn needs to save for the down payment over the next three years, we first need to determine the total down payment required. If the down payment is stated as $4000, then that is the total amount needed.
Assuming that Jocelyn wants to make the down payment in three years, we can calculate how much she needs to save each year by dividing the total down payment by three:
$4000 / 3 years = $1333.33 per year
So Jocelyn would need to save approximately $1333.33 each year for the next three years in order to have enough for the $4000 down payment.
Correct Question :
JUST $4000 DOWN PAYMENT!
LOW 7% INTEREST RATE!
5 YEARS TO REPAY YOUR LOAN!
In order to afford the down payment, how much will Jocelyn need to save for each of the next three years
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(b) What is the probability that a random sample of n=45 oil changes results in a sample mean time less than 10 minutes? The probability is approximately enter your response here.
Answers
Probability that a random sample of 45 oil changes result in a sample mean time less than 10 minutes is 0.0001
Given information:
The mean time is, = 16.2 min.
The standard deviation = 3.4 min.
Let X' is sample mean time :
Now the sample mean time is given by the equation
Z = (X' - μ) / (σ/√n)
Where, μ population mean time
(σ) is Standard deviation
(A) Probability of random sample of 45 oil changes:
p (X' < 10) = 1 - p (Z ≤ 12.33)
Z = (10 - 16.2) / (3.4 √45)
p (X' < 10) = 1 - 0.9999
p (X' < 10) = 0.0001
Hence,
As, the highest critical value of Z is given as 4.40 which has an area of 0.9999.
Thus, Probability that a random sample of 45 oil changes result in a sample mean time less than 10 minutes is 0.0001.
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Complete question is,
The shape of the distribution of the time required to get an oil change at a 15-minute oil-change facility is unknown. However, records indicate that the mean time is 16.2 minutes, and the standard deviation is 3.4 minutes.
(a) What is the probability that a random sample of n = 45 oil changes results in a sample mean time less than 10 minutes?
your goal is to create a college fund for your child. suppose you find a fund that the fees an apr of 4% . how much should you deposit monthly to accumulate $88,000 in 17 years?
Answers
To accumulate $88,000 (future value) in 17 years in a fund that attracts an APR of 4%, the monthly deposit should be $301.89
How the monthly deposit is computed:The monthly deposit can be determined from the future value using an online finance calculator.
N (# of periods) = 204 months (17 years x 12)
I/Y (Interest per year) = 4%
PV (Present Value) = $0
FV (Future Value) = $88,000
Results:
PMT (Monthly Deposits) = $301.89
Sum of all periodic payments = $61,585.56
Total Interest = $26,414.44
Thus, when $301.89 is deposited monthly in a fund earning 4% APR, the future value can become $88,000.
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Danielle was completing her science project and mixed saline solutions A and B. Brand A was a six gallon 18% saline solution and she ended up with an 18 gallon 8% saline solution mixture. Find the percent of saline solution in brand B.
A. 2.1%
B. 21%
C. 3%
Answers
Brand B contains 3% saline solution by volume. Then, C is the right answer.
Percentage of saline solution in brand B, let x be.
We know that the overall volume of saline solution in the combination is 18% of 6 gallons plus x% of (18 - 6) gallons since Danielle blended brands A and B to make a total of 18 gallons of 8% saline solution.
Then the equation is given as,
0.18(6) + 0.01x(18 - 6) = 0.08(18)
Simplifying and solving for x, we get:
1.08 + 0.12x = 1.44
0.12x = 0.36
x = 3
Therefore, the percentage of saline solution in brand B is 3%.
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Lcm of 2/3^2 - 1/3
Any help would be useful
Answers
Answer:
9
Step-by-step explanation:
You want the least common denominator for the fraction in the sum ...
(2/3)² -1/3
SimplifyWhen the sum is simplified, it is ...
4/9 -1/3
The denominator 9 is a multiple of the denominator 3, so the least common denominator of these two fractions is 9.
__
Additional comment
Using that denominator, the sum is ...
4/9 -3/9 = 1/9
<95141404393>
0.35+0.63*100÷0.4-0.34
Answers
Please answer the question
Answers
Answer: $105
Step-by-step explanation:
I would take 5+2=7 then take 7×15=105
Answer is $105 to ship.
In the expression 5 * y/7 what value of y would make a product greater than 5
Answers
5 * y/7 > 5
First, we can simplify the inequality:
y/7 > 1
Then, we can multiply both sides by 7:
y > 7
Therefore, any value of y greater than 7 would make the product greater than 5 in the expression 5 * y/7. Hope this helps!
In math questions answers each questions are solved with explanation. The questions are based from different topics. Care has been taken to solve the questions in such a way that students can understand each and every step.
1. Which is greater than 4?
(a) 5,
(b) -5,
(c) -1/2,
(d) -25.
Answers
Answer:
A is correctStep-by-step explanation:
The option that is greater than 4 is option (a) 5. This is because 5 is a positive value that is larger than 4. Option (b) -5 is a negative value that is less than 4. Option (c) -1/2 is also negative and less than 4. Option (d) -25 is the most negative option and therefore less than 4. So, the only option that is greater than 4 in this case is 5.
Answer:
a
Step-by-step explanation:
got it right on edge
If male and female students of section B in DPS and DAV are in ratio 3 : 2 and 4:3 respectively then male students of section B are how much percent more than female students of section B considering both the schools (approx). (A) 50% (C) 36% (B) 25% (D) 40
Answers
If male and female students of section B in DPS and DAV are in ratio 3 : 2 and 4:3 respectively then male students of section B are 40% more than female students of section B considering both the schools (approx).
(A) 50% (C) 36% (B) 25% (D) 40%.
Hence, the correct option is D.
Let us assume that there are 3x male students and 2x female students in section B of DPS, and there are 4y male students and 3y female students in section B of DAV. We can set up the following equations to represent the given ratios
3x : 2x = male : female in DPS section B
4y : 3y = male : female in DAV section B
By simplifying these ratios, we get
3 : 2 = x/y for DPS section B
4 : 3 = x/y for DAV section B
Solving for x and y, we get
x = 6y for DPS section B
x = 4.5y for DAV section B
Now, let us add the male and female students in section B from both schools.
Male students = 3x + 4y = 3(6y) + 4(4.5y) = 30y
Female students = 2x + 3y = 2(6y) + 3(4.5y) = 21y
So, the ratio of male to female students in section B from both schools combined is
30y : 21y = 10 : 7
Therefore, male students are (10 - 7)/7 = 3/7 = 0.4286 (approx. 43%) more than female students in section B from both schools combined.
However, the question asks for the percentage more, so we need to multiply this answer by 100 to get a percentage.
0.4286 x 100 ≈ 42.86%
Therefore, male students in section B are approximately 42.86% more than female students in section B from both schools combined. Rounding to the nearest percent that is 40%.
Hence, the correct option is D.
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A circle is inscribed in a square as illustrated. A wheel, whose radius is 10 inches,
rolls along the circle. How many complete revolutions will the wheel make to
travel around the circle once? Use 3.14 as an approximation for .
Answers
The wheel will make one complete revolution around the circle after travelling a distance of 62.8 inches.
What is the circumference of the circle?The distance that the wheel travels around the circle once is equal to the circumference of the circle.
The formula for circumference of a circle is given as;
D = 2πr
where;
r is the radius of the circleThe radius of the circle = 10 inches
The circumference of the circle is calculated as follows;
D = 2 x 3.14 x 10
D = 62.8 inches
Thus, the circumference of the circle is determined as 62.8 inches.
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Find the 3rd term in the expansion of ( 5 � − 7 � ) 3 (5x−7y) 3 in simplest form.
Answers
The third term in the expansion of the expression (5x - 7y)³ is 735xy².
Given expression is,
(5x - 7y)³
We have to expand this.
We know that,
(a + b)³ = a³ - 3a²b + 3ab² - b³
Using this,
(5x - 7y)³ = (5x)³ - (3 × (5x)² × 7y) + (3 ×(5x) × (7y)²) - (7y)³
= 125x³ - (3 × 25x² × 7y) + (3 × 5x × 49y²) - 343y³
= 125x³ - 525x²y + 735xy² - 343y³
Here the third term is 735xy².
Hence the third term is 735xy².
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What is 00.00 in 12 hour clock time
Answers
Answer:
00:00 in 12-hour clock time is equivalent to 12:00 midnight. It is the start of a new day and is the first minute of the 12-hour time cycle.
12:00 am.
rango de y=5/(x^2-25)
Answers
Answer: x = -5, 5 y= 0
Step-by-step explanation:
vertical asymptotes = x= -5, 5
horizontal asymptotes = y= 0
1. A limit imposed by the government on the quantity of a good or product that can be brought into the
country is called a
000
a. tariff
b. quota
OOO
c. foreign bill of exchange
d. value added tax
2. Which of the following would not be an effective argument for the U.S, to enact trade restrictions?
a. they shield U.S. workers from competition by cheap foreign labor
b. they may benefit the security and defense of the nation
c. they help the U.S. maintain diverse industries
d. they make foreign products cheaper to U.S. shoppers
3. What does It mean If a country is on the gold standard?
a. It sets the value of its currency in relation to a specific amount of gold
b. It creates specific standards by which gold is made into jewelry
c.
it uses gold instead of paper currency
none of these
Od.
4. Economists tend to classify a country as less developed if the country's average level of income is less
than
a. $9,500 per person
b. the average per-person-income of neighboring countries
c. $3,040 per person
d. a U.S. welfare recipient's income
5. Which of the following would not be considered a barrier to economic development?
a high levels of political corruption
Ob. low population growth
c. low human capital
d. shortage of investment capital
Answers
We can answer the questions in the following way:
A limit imposed by the government on the quantity of a good or product that can be brought into the country is called b. a quota.That d. They make foreign products cheaper to U.S. shoppers would not be an effective argument for the U.S, to enact trade restrictions. If a country is on the gold standard, it means a. It sets the value of its currency in relation to a specific amount of gold.Economists tend to classify a country as less developed if the country's average level of income is less than c. $3,040 per person.b. low population growth would not be considered a barrier to economic development.What are barriers to economic development?Barriers to economic development are all those things that hinder the growth and development of an economy of a nation.
Many factors act as barriers to economic development, like lack of education, healthcare, inadequate infrastructure, lack of access to capital, etc.
These barriers can hinder people's ability to achieve their full potential, and lead to lower levels of economic growth and development.
Taking care of these issues by the government is important to promoting sustainable economic development.
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pls help ☹️!! this coordinate algebra
Answers
Answer:
(b) 0.083
Step-by-step explanation:
You want the probability that a part is New and Passed the test, given the distribution of parts as shown in the table.
Probability"This group" consists of all the parts described by the table. That is a total of ...
5 + 23 + 2 + 30 = 60
parts.
Of those 60 parts, the number that is found in the table cell (New, Passed) is 5. This means 5/60 = 1/12 ≈ 0.083 of the total number of parts shown were New and Passed the test.
The probability of choosing one of those parts at random is 0.083.
__
Additional comment
This is not "coordinate algebra". It is probability.
Use the image to determine the direction and angle of rotation.
Graph of polygon ABCD in quadrant 2 with point A at negative 6 comma 5. A second polygon A prime B prime C prime D prime in quadrant 4 with point A prime at 6 comma negative 5.
90° clockwise rotation
90° counterclockwise rotation
180° counterclockwise rotation
270° clockwise rotation
Answers
The direction and angle of rotation include the following: C. 180° counterclockwise rotation.
What is a rotation?In Mathematics and Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).
Furthermore, the mapping rule for the rotation of a geometric figure about the origin is given by this mathematical expression:
(x, y) → (-x, -y)
Coordinates of point A (-6, 5) → Coordinates of point A' = (6, -5)
In conclusion, this transformation rule (x, y) → (-x, -y) is used for the 180° rotation of a geometric figure about the origin in a clockwise or counterclockwise (anticlockwise) direction.
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The histogram shows the result of a survey about the number of hours students watch television on the weekend.
How many students participated in the survey?
Answers
The number of students who participated in the survey, based on the histogram showing the number of hours students watch television on the weekend, is 125.
What is a histogram?A histogram is a pictorial or graphical representation of categorical data, proportional to the frequency of a variable and whose width is equal to the class interval.
The number of students who watched between 0 - 4 hours = 20
The number of students who watched between 5 - 9 hours = 40
The number of students who watched between 10 - 14 hours = 30
The number of students who watched between 15 - 19 hours = 20
The number of students who watched between 20 - 24 hours = 15
The total number of students who participated = 125
Thus, using the histogram, the total number of students who participated in the survey was 125.
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Polygon D has been dilated to create polygon D′.
Polygon D with top and bottom sides labeled 8 and left and right sides labeled 9.5. Polygon D prime with top and bottom sides labeled 6.4 and left and right sides labeled 7.6.
Determine the scale factor used to create the image.
Scale factor of 0.6
Scale factor of 0.8
Scale factor of 1.2
Scale factor of 1.6
Answers
Answer: The scale factor used to create the image is 0.8
Step-by-step explanation: To determine the scale factor used to create the image, we can divide the corresponding side lengths of the dilated polygon D' by the corresponding side lengths of the original polygon D.
For example, the top and bottom sides of polygon D have a length of 8, while the corresponding sides of polygon D' have a length of 6.4.
So, the scale factor used to create the image is:
6.4 / 8 = 0.8
Therefore, the scale factor used to create the image is 0.8.
Set up an equation for x and solve to the nearest degree
Answers
Answer:
Almost equals 28°
Step-by-step explanation:
cos(x)= 12/18
x= cos^-1 (12/18)
So it equals 48.1896°
Suppose a trapezoid is defined as a quadrilateral with at least 1 pair of parallel sides. How would the quadrilateral venn Diagram change?
Answers
Suppose a trapezoid is defined as a quadrilateral with at least 1 pair of parallel sides. Thus, trapezoids will change the venn Diagram by being classified as under 1 pair of parallel sides.
In geometry, a quadrilateral with at least one set of parallel sides is referred to as a trapezium in American or Canadian English, or a trapezium in British as well as other forms of English. In Euclidean geometry, a trapezium is a convex quadrilateral by definition. The bases of a trapezium are the parallel sides. Thus, trapezoids will change the venn Diagram by being classified as under 1 pair of parallel sides.
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Work out percentage change 20 from 50
Answers
Answer:
Therefore, the percentage change from 20 to 50 is an increase of 150%.
Step-by-step explanation:
To work out the percentage change from 20 to 50, we can use the following formula:
((New Value - Old Value) / Old Value) x 100%
Plugging in the numbers, we get:
((50 - 20) / 20) x 100%
= (30 / 20) x 100%
= 1.5 x 100%
= 150%
HELP PLS
1st: Find the volume of the pyramid shown and round your answer to the nearest tenth.
2nd: Find the slant height x of the regular pyramid shown and round your answer to the nearest tenth.
3rd: Find the Surface Area of this Pyramid.
Answers
1. The volume of the pyramid = 12 mm³.
2. Slant height (x) x ≈ 4.3 mm
3. Surface area of square pyramid = 86.4 mm²
How to Find the Volume of a Square Pyramid?1. The volume of the pyramid (V) = 1/3*a²h, where:
a is the base edge = 3 mm
h is the height = 4 mm
Plug in the values:
The volume of the pyramid (V) = 1/3*3²*4 = 12 mm³.
2. Slant height (x) = √(1.5² + 4²)
x ≈ 4.3 mm
3. Surface area of square pyramid = 6bs + b² = 6(3)(4.3) + 3²
= 86.4 mm²
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What is the area of this polygon on a coordinate plane?
Answers
Answer:
The area of this polygon is 14 square units.