Answers
The solution to the integral ∫ [csc x · (cot x + csc x)] dx is - (csc x + cot x) + C. (Correct choice: A)
How to solve an integral by integral tables
In this problem we find the case of an integral involving trigonometric functions, this can be solved quickly by means of algebra properties and integral tables. Integral tables are an useful resource to find the result of integrals that require a lot of time to be solved.
First, write the function within the integration operator and simplify by algebra properties:
csc x · (cot x + csc x)
csc x · cot x + csc² x
Second, rewrite the integral by integral properties:
∫ [csc x · (cot x + csc x)] dx = ∫ csc x · cot x dx + ∫ csc² x dx
Third, use integral tables to find the solution to the integral:
∫ [csc x · (cot x + csc x)] dx = - csc x - cot x + C
∫ [csc x · (cot x + csc x)] dx = - (csc x + cot x) + C
Where is C is the integration constant.
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Related Questions
I need to know the system of equations for both graphs 3 and 4
Answers
The equations are 4x - y - 2 = 0 and x + 3y + 6 = 0. The solution has been obtained using two-point form.
What is two-point form?
One of the crucial forms for algebraically representing a straight line is the two-point form. Each and every point on a line fulfils the equation for that line, making it the representation of the entire line.
We are given two lines on the graph
Both the lines meet on the y-axis at (0,-2)
This means (0,-2) is the common solution.
Another point of the steeper line is (1,2)
Another point of the flatter line is (3,-3)
Now, as we know the two points of the line, using the two-point form, we get
[tex]\frac{y - y_{1}}{x-x_{1} } = \frac{y_{2} - y_{1}}{x_{2} -x_{1} }[/tex]
⇒ (y+2)/(x-0) = (2+2)/(1-0)
⇒ y+2 = 4x
⇒ y = 4x-2
⇒ 4x - y - 2 = 0
Similarly,
⇒ (y+3)/(x-3) = (-2+3)/(0-3)
⇒ (y+3)/(x-3) = -1/3
⇒ (y+3) = -(x-3)/3
⇒ y+3 = -x/3 + 1
⇒ y = -x/3 - 2
⇒x + 3y + 6 = 0
Hence, the equations are 4x - y - 2 = 0 and x + 3y + 6 = 0.
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Since there are multiple questions so, the question answered above is attached below
The base of a triangular pyramid is an equilateral triangle. Each side of the base measures 6 in. The area of the base is 15.6 in². The slant height of the pyramid is 8 in.
What is the surface area of the pyramid?
Answers
Answer: The area of the base of the triangular pyramid is given as 15.6 in² and each side of the base is 6 in, so we can use the formula for the area of an equilateral triangle to find the height of the base:
A = (s^2 * sqrt(3)) / 4
where s is the side length of the triangle. Plugging in the values, we get:
15.6 = (6^2 * sqrt(3)) / 4
Solving for the height of the base, h:
h = (4 * 15.6) / (6^2 * sqrt(3)) = 4 / sqrt(3)
Next, we can use the Pythagorean theorem to find the height of the pyramid, since the slant height is given:
h^2 + (base/2)^2 = slant height^2
where base is the length of one side of the base of the pyramid. Plugging in the values, we get:
h^2 + (6/2)^2 = 8^2
Solving for h:
h = sqrt(64 - 9) = sqrt(55)
Finally, the surface area of the pyramid can be found using the formula:
SA = base area + (perimeter * slant height) / 2
where perimeter is the total length of the sides of the base. Plugging in the values, we get:
SA = 15.6 + (3 * 6 * 8) / 2 = 15.6 + 36 = 51.6 in²
So, the surface area of the triangular pyramid is 51.6 in².
Step-by-step explanation:
Answer to the question posted below
Answers
The change will be approximately $100 million by solving through simple algebra.
The purpose of percentage calculationsThe use of percentages is widespread and diverse. For instance, percentages are used to convey discounts in stores, bank interest rates, inflation rates, and various statistics in the media. For comprehending the financial aspects of daily life, percentages are crucial.
The simple percentage method is what?Divide the whole number by 100, then multiply the result by the requested percentage to find a percentage of the given number: For instance, 12% of 250 equals (250 100) x 12 = 30.
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9 create factor trees of the following 8 20 27 36 72
Answers
Factor Trees are diagrams that show the prime factorization of a number by breaking it down into smaller factors until only prime numbers are left.
Here are the factor trees for the numbers you provided:
The Factor Trees8:
8
/
2 4
/
2 2
20:
20
/
2 10
/
2 5
27:
27
/
3 9
/
3 3
36:
36
/
2 18
/
2 9
/
3 3
72:
72
/
2 36
/
2 18
/
2 9
/
3 3.
To solve this, I used the process of prime factorization. Prime factorization is the process of finding the prime numbers that multiply together to form a given number.
The steps I followed to solve this problem are:
Starting with the first number, I divided it by 2 until I couldn't divide it anymore.If the result of the division is not a prime number, I divided it again by the smallest possible prime number.I repeated this process until all the factors of the number were prime numbers.I repeated this process for all the numbers provided.I then organized the prime factors in a tree-like structure, with the original number at the top and the prime factors branching off into their own factors, until all the factors were prime numbers.Read more about factor trees here:
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One of the world's heaviest hailstones weighed 2.2 pounds. Which is more appropriate to express its mass, 1 kilogram or 1 gram?
Answers
Answer:
Well, it depends, but I'd reckon kilograms.
Step-by-step explanation:
2.2 pounds is approximately 0.998 kg, which can be rounded off to 1 kg. However, you really do have to be precise, you may measure it in grams (that's, 998 grams).
So, the most appropriate way is to use 1 kilogram, as a hailstone can be considered quite heavy and we may not be keen on looking for a really precise measurements, as they're measured in hundreds of grams!
Hope this helps :)
Find Sn for the arithmetic series where a1= 3 , an= 36, n= 12
Find sn for the arithmetic series where a1= 3, d= 2, n= 100
Answers
The value of the sum of the series is are 234 and 10200
How to determine the sum of the seriesIn an arithmetic series, the sum of the first "n" terms (Sn) is given by the formula:
Sn = n/2 * (a1 + an)
Where "a1" is the first term and "an" is the nth term.
For the first series, we have
In this series, a1=3 , an=36 , n=12
Plugging these values into the formula, we get:
Sn = 12/2 * (3 + 36)
Sn = 234
For the second series, we have
In this series, a1=3 , d = 2 , n=100
So, we have
an = a + (n - 1)d = 3 + 99 * 2 = 201
Plugging these values into the formula, we get:
Sn = 100/2 * (3 + 201)
Sn = 10200
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One inequality in a system is y ≥ 2x + 3. Write another
possible inequality in the system so that (-2, 6) is a solution of the
system.
ystem of
Answers
Answer:
Step-by-step explanation
y≥ 2x + 3 is -6,2
can someone please help me answer 1, 2, and 5! Thank you so muchhhh here’s 30 points for it!!! Please do it right, thank you.
Answers
Answer: i don't know give me more info
Step-by-step explanation:
43) A tree 13 feet high grows at the rate of3feet each year. How many years will it take for the tree to grow to a height of 28 feet?
Answers
After x years, the height of the tree will be 13 + 3x.
Since the height of the tree is 28 feet, we set the two heights equal and solve for x:
28 = 13 + 3x
Subtract 13 from both sides:
15 = 3x
Divide both sides by 3:
5 = x
So, it will take 5 years for the tree to grow to a height of 28 feet.
Which of the following tables represents a linear relationship that is also proportional?
x −2 0 2
y −4 −3 −2
x −1 0 1
y 0 2 4
x −1 0 1
y −4 −1 2
x −3 0 3
y −1 0 1
Answers
The only table that represents both a linear and proportional relationship is table 4
How to identify a proportional relationship?A proportional relationship is a mathematical relationship between two variables in which their ratio is always equal.
In the first table, we see that the proportion of y to x are;
-4/-2 = 2
-3/0 = undefined
-2/2 = -1
Second table shows that;
0/-1 = 0
2/0 = undefined
4/1 = 4
Third table shows that;
-4/-1 = 4
-1/0 = undefined
2/1 = 2
Fourth table shows that;
-1/-3 = 1/3
0/0 = 0
1/3 = 1/3
Looking at the tables. the only one that is a proportional relationship is table 4
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Answer:
The only table that represents both a linear and proportional relationship is table 4
How to identify a proportional relationship?
A proportional relationship is a mathematical relationship between two variables in which their ratio is always equal.
In the first table, we see that the proportion of y to x are;
-4/-2 = 2
-3/0 = undefined
-2/2 = -1
Second table shows that;
0/-1 = 0
2/0 = undefined
4/1 = 4
Third table shows that;
-4/-1 = 4
-1/0 = undefined
2/1 = 2
Fourth table shows that;
-1/-3 = 1/3
0/0 = 0
1/3 = 1/3
Looking at the tables. the only one that is a proportional relationship is table 4
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Step-by-step explanation:
A cylinder has a height of 10cm.
The diameter of the cylinder is
4/5
its height.
Calculate the volume of the cylinder in terms of π.
Answers
The radius is the center of circle to its edge or half of a diameter so half of 4/5 is 0.4 since 0.8 / 2 = 0.4.
To find the volume we need to do the equation π r² h.
So, π x 0.4^2 x 10 = 5.02654825.
Round 5.02654825 to the nearest hundredth and it is 5.03.
Volume is 5.03.
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The graph below shows an exponential function and a quadratic function.
m c012-1.j pg
How do the functions compare over the interval m c012-2.j pg?
The exponential grows at approximately half the rate of the quadratic.
The exponential grows at approximately the same rate as the quadratic.
The exponential grows at approximately twice the rate of the quadratic.
The exponential grows at approximately four times the rate of the quadratic.
Answers
The exponential grows at the same rate as the quadratic in the interval
0 ≤ x ≤ 1.
What is the Average Rate of Change function?The average Rate of Change function is defined as the average rate at which one quantity is changing with respect to something else changing. In simple terms, an average rate of change function is a process that calculates the amount of change in one item divided by the corresponding amount of change in another.
The average rate of change of a function A = [tex](f(a) - f(b))/(b-a)[/tex]
Given an exponential function, say f(x), such that f(0) = 1 and f(1) = 2.
A quadratic function, say g(x), such that g(0) = 0 and g(1) = 1.
The rate of change of a function f(x) over an interval a ≤ x ≤ b is given by
[tex](f(a) - f(b))/(b-a)[/tex].
Thus, the rate of change (growth rate) of the exponential function, f(x) over the interval 0 ≤ x ≤ 1 is given by
= (2-1)/1 = 1
Similarly, the rate of change (growth rate) of the quadratic function, g(x) over the interval 0 ≤ x ≤ 1 is given by
=(1 - 0)/1 = 1
Therefore, the exponential grows at the same rate as the quadratic in the interval 0 ≤ x ≤ 1.
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Work out the equation of the line which has a gradient of 2 and passes through the point (1, 4)
Answers
The equation of line having a slope of 2 and passing through the point (1,4) is y = 2x + 2.
What is the equation of the line?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given that the line has a gradient of 2 and passes through the point (1, 4).
x₁ = 1y₁ = 4Slope m = 2Plug the given values into the point-slope formula and solve for y.
y - y₁ = m( x - x₁ )
y - 4 = 2( x - 1 )
y - 4 = 2x - 2
Add 4 to both sides of the equation
y - 4 + 4 = 2x - 2 + 4
y = 2x - 2 + 4
y = 2x + 2
Therefore, the equation of the line is y = 2x + 2.
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In a class full of men and women
2
9
of the class are women. What is the ratio of men to women in its simplest form?
Answers
Explanation: if 2/9 of the class is female, that means that 7/9 of the class is male.
So now, our ratio is7/9:2/9
Notice that both numbers have the common denominator, so we can multiply both sides to eliminate the 9 from the denominator, like so:
7:2
However, we can divide 7 by 2, to get a decimal value:
3.5:1
I hope this helps!
$6,446 $ 6,446 is invested, part at 13% 13 % and the rest at 10% 10 % . If the interest earned from the amount invested at 13% 13 % exceeds the interest earned from the amount invested at 10% 10 % by $568.65 $ 568.65 , how much is invested at each rate? (
Answers
The amount invested at 10% by $568.65 and investment rate is -
amount invested at 13%. is $5275
amount invested at 10%. is $1171
What is the compound interest?Compound interest is when you earn interest on both the money you've saved and the interest you earn.
Formula:
A = P(1 + {r}/{n})^{n.t}
here, we have,
Let x represent the amount invested at 13%.
Let y represent the amount invested at 10%.
$6,446 is invested, part at 13 % and the rest at 11%.
This means that
x + y = 6,446
The formula for determining simple interest is expressed as
I = PRT/100
Where
I represents interest paid on the loan.
P represents the principal or amount taken as loan
R represents interest rate
T represents the duration of the loan in years.
Considering the amount invested at 13%,
P = x
R = 13%
T =1 year
I = (x × 13 × 1)/100 = 0.13x
Considering the amount invested at 10%,
P = y
R =10%
T = 1 year
I = (x × 10 × 1)/100 = 0.10y
If the interest earned from the amount invested at
13% exceeds the interest earned from the amount invested at
10% 10 % by $568.65, it means that
0.13x - 0.10y = 568.65,- - -- - - - - -1
Substituting x = 6,446 - y into equation 1, it becomes
0.13(6,446- y) - 0.10y =568.65
i.e. y= 1171
solving, we get,
x=5275
y= 1171
amount invested at 13%. is $5275
amount invested at 11%. is $1171
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Sunrise, a bed-and-breakfast hotel, charges a one-time deposit of $25 plus $95 per night. Another bed-and-breakfast hotel called Bright Eyes charges a flat rate of $110 per night. Amanda wants to book a hotel for 5 nights. Which hotel costs less to stay for 5 nights? How much less?
Answers
Answer:
Sunrise: 95x5+25 = 500
Bright Eyes: 110x5= 550
Sunrise Will be 50$ Cheaper
oops sorry did my math wrong
Answer: Sunrise Hotel is cheaper by $50
Step-by-step explanation:
First, you do $95 x 5 nights = $475, and then add $25 and get $500 per night (Sunrise).
Then multiply $110 and 5 nights and get $550 per night (Bright Eyes).
Lastly, subtract $550 and $500 and get $50.
A car covers a distance of 189km in 4.5 hours, what is the average speed
Answers
Step-by-step explanation:
The average speed is 42 km/hr.
To calculate the average speed, you divide the total distance by the time it took to travel that distance:
189 km / 4.5 hours = 42 km/hr
[tex]\texttt{speed}=\dfrac{d}{t}[/tex]
distance = 189 km
time = 4.5 hours
[tex]\texttt{speed}=\dfrac{189}{4.5}[/tex]
[tex]\fbox{speed = 42 km/hr}[/tex]
Please help will mark Brainly
Answers
Answer:
1
Step-by-step explanation:
Y intercept is 1
Y intercept is the point where the line crosses the y axis (point where x=0, you see the line crosses y axis at 1). Thus even if you put 0 in equation 9^x you will get 9^0 and anything power of 0 is 1.
A cookie recipe calls for 1.5 cups of sugar for two dozen cookies. How many cups of sugar are needed for one dozen cookies?? Plss help!!!
Answers
For a dozen cookies, 0.75 cups of sugar are needed in total.
What is ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
given, A cookie recipe calls for 1.5 cups of sugar for two dozen cookies.
Since,
For two dozen of cookies, there are a total of 1.5 cups of sugar required.
In 2 dozen cookies, required sugar = 1.5 cups
In 1 dozen cookies, required sugar = 1.5/2 cups
In 1 dozen cookies, required sugar = 0.75 cups
Therefore, The total number of cups of sugar required for one dozen cookies is 0.75.
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represent the shaded area in the drawing as a mixed number and also as an improper fraction
I got 1 3/4 & 3/5 but it is incorrect
Answers
Answer:
Mixed number: 1 3/8
Improper fraction: 11/8
Step-by-step explanation:
The first circle is 1 whole 1 = 8/8
The second circle is 3/8 *
8/8 + 3/8 = 11/8
----------------------
If you want to write a mixed number as improper fraction just multiply the whole number by the denominator and add the numerator's fraction.
1 3/8 Mixed number
1x8=8
8+3=11
11/8 Improper fraction
-----------------------
* the second circle is not divided into 4 parts. It is divided into 8 equal parts. Each part is 1/8. There are three shaded parts which means 3/8.
----------------------
I hope this helps!
PLEASE HELP!!!!!!!!!!!!!!
Answers
The required decimal that is greater than the decimals shown in the diagram are 0.5, 0.32, and 0.4. Options B, C, and D are correct.
What is decimal value?Decimal value is defined as showing the place value of the digits in a decimal number. If any proportion of the digit is lower than 1 it would be represented after the dot right to the absolute value,
here,
The decimal value is shown in the image,
= 31 / 100
= 0.31
From the options,
0.31 > 0.1
0.31 < 0.5
0.31 < 0.32
0.31 < 0.4
Thus, the required decimal that is greater than the decimals shown in the diagram are 0.5, 0.32, and 0.4. Options B, C, and D are correct.
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If you have 2 1/2 bags of grapes each bag of grapes weighs 1/2 pounds how many pounds of grapes do you have
Answers
2 1/2 bags * 1/2 pound/bag = 2.5 * 0.5 = 1.25 pounds.
So, you have 1.25 pounds of grapes
Consider the line y=7x-3.
Find the equation of the line that is parallel to this line and passes through the point (-4,-6).
Find the equation of the line that is perpendicular to this line and passes through the point (-4, -6).
Answers
The equation of the line that is parallel to this line and passes through the point (-4,-6) is y = 7x + 22
The equation of the line that is perpendicular to this line and passes through the point (-4,-6) is y = -(1/7)x - 46/7
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.
The slope intercept form of a line is:
y = mx + b
where m is the slope and b is the y intercept
Two lines are parallel if they have the same slope and are perpendicular if the product of their slope is -1.
Given the line:
y = 7x - 3
The slope is 7. The line parallel to this line would also have a slope of 7, while the line perpendicular have a slope of -1/7
The equation of the line that is parallel to this line and passes through the point (-4,-6) is:
y - (-6) = 7(x - (-4))
y = 7x + 22
The equation of the line that is perpendicular to this line and passes through the point (-4,-6) is:
y - (-6) = (-1/7)(x - (-4))
y = -(1/7)x - 46/7
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7. 23% of the class was unhappy. 19 students were unhappy. How many students were in the class? Round to the nearest student.
Answers
The total number of students in the class given the percentage of unhappy students is 263 students.
How many students were in the class?Percentage of unhappy students= 7.23%
Number of unhappy students= 19
Total number of students in class= x
Number of unhappy students = Percentage of unhappy students × Total number of students in class
19 = 7.23% × x
19 = 0.0723 × x
19 = 0.0723x
divide both sides by 0.0723
x = 19/0.0723
x = 262.7939142461964
Approximately,
x = 263 students
Therefore, there are 263 students in the class.
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The graph below shows an exponential function and a quadratic function.
mc012-1. Jpg
How do the functions compare over the interval mc012-2. Jpg?
The exponential grows at approximately half the rate of the quadratic.
The exponential grows at approximately the same rate as the quadratic.
The exponential grows at approximately twice the rate of the quadratic.
The exponential grows at approximately four times the rate of the quadratic.
Answers
The exponential grows at the same rate as the quadratic in the interval
0 ≤ x ≤ 1.
What is the Average Rate of Change function?The average Rate of Change function is defined as the average rate at which one quantity is changing with respect to something else changing. In simple terms, an average rate of change function is a process that calculates the amount of change in one item divided by the corresponding amount of change in another.
The average rate of change of a function A = [tex](f(a) - f(b))/(b-a)[/tex]
Given an exponential function, say f(x), such that f(0) = 1 and f(1) = 2.
A quadratic function, say g(x), such that g(0) = 0 and g(1) = 1.
The rate of change of a function f(x) over an interval a ≤ x ≤ b is given by
[tex](f(a) - f(b))/(b-a)[/tex].
Thus, the rate of change (growth rate) of the exponential function, f(x) over the interval 0 ≤ x ≤ 1 is given by
= (2-1)/1 = 1
Similarly, the rate of change (growth rate) of the quadratic function, g(x) over the interval 0 ≤ x ≤ 1 is given by
=(1 - 0)/1 = 1
Therefore, the exponential grows at the same rate as the quadratic in the interval 0 ≤ x ≤ 1.
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Answer:
B
Step-by-step explanation:
This is the sketch of a graph of y=(x-1)(x-3)
Question is below
Answers
From the graph, the coordinates of the points of the equation y=(x-1)(x-3): (1,0) (4,0), P(0,3) and turning point (2.5,2)
How to find the coordinates?You should know that these are possible reading from the graph
The scale of the graph is [laced at 1 com to 1 unit on both axes
From the graph, the coordinates of A are (1, 0) This is where x=1 and y=0
The coordinates of B = (4, 0) This is where x=4 and y=0
b) The coordinates of point P are (0,3) This is where x=0 and y= 3
c) The coordinates of the turning point are (2.5, 2) This is the minimum value of the curve
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53) Jim drove 180 miles in 5 hours. If he can keep the same pace, how long will it take him to drive 900 miles?
Answers
The total number of hours for Jim to drive 900 miles is given by the proportion A = 25 hours
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the number of hours for Jim to drive 900 miles be A
Now , the number of hours = 5 hours
The total distance traveled by Jim in 5 hours = 180 miles
Now , the distance traveled by Jim = 900 miles
And , the proportion will be
A / 900 = 5 / 180
Multiply both sides of the equation by 900 , we get
A = ( 5 x 900 ) / 180
On simplifying the equation , we get
A = 5 x 5
A = 25 hours
Hence , the number of hours is 25 hours
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Equivalent to 28 to the second power-3
Answers
Answer:
13 since the second power (-3) is doubled.
which is greater 4 4/10 or 32/10
Answers
44/10 > 32/10
Answer:
4 4/10 is greater.
Step-by-step explanation:
4 = 40/10
then:
4 4/10 = 4 + 4/10 = 40/10 + 4/10 = (40+4)/10 = 44/10
Then:
44 > 32
44 is greater.
What is the slope-intercept form of this equation?
3x + 9y = 18
please help :)
Answers
Answer:
Below
Step-by-step explanation:
Solve the given equation for y
3x+9y = 18
9y = -3x + 18 divide by 9
y = - 1/3 x + 2 done