Evaluate the indefinite integrals. (a) ∫ 4x 5 − 6 csc2 (x) + 10e x − 200 dx
Answers
∫ (4x^5 - 6csc^2(x) + 10e^x - 200) dx = (4/6)x^6 + 6cot(x) - 10e^x - 200x + C, where C is the constant of integration using indefinite integral.
We need to use the following integration rules:
∫csc2(x) dx = -cot(x) + C, where C is the constant of integration.
∫e^x dx = e^x + C, where C is the constant of integration.
Using these rules, we have:
∫(4x^5 - 6csc^2(x) + 10e^x - 200) dx
= (4/6)x^6 + 6cot(x) + 10e^x - 200x + C, where C is the constant of integration.
Therefore, the indefinite integral is:
(4/6)x^6 + 6cot(x) + 10e^x - 200x + C
where C is the constant of integration.
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Related Questions
pls give simple working out
due in 5 minsss
Answers
a) alternate- angle a is 60 degrees
b) corresponding- 75 degrees
c) corresponding- 108 degrees
the number of students enrolled at a college is 15 000 and grows 3% each tear. what will be the estimated population of the school in 6 yeears
Answers
The expected student population of the school will be N(t) = 15000*(1+3%)6=17910.78.
The term "population" refers to all citizens who are either permanently residing in a country or who are just passing through. Growth rates are the population changes that occur each year as a result of births, deaths, and net migration. The world population clock maintained by the US Census Bureau indicated that there were 7,922,312,800 people on the planet as of September 2022, and that number would rise to 8 billion by mid-November. China and India will have the two largest populations in the world in 2022, followed by the United States, the European Union, Indonesia, and Pakistan.
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The vertices of a square are A (-6, 4), B(-1, 6), C(1, 1), and D( -4, -1). How long is the diagonal?
1. √29 units
2. 2√29 units
3. √58 units
4. 2√58 units
Answers
Answer:
\( \sqrt{58} \)
Type the correct answer in the box. Use numerals instead of words.
For this item, if the answer is not a whole number, enter it as a fraction in simplest form using / as the fraction bar.
Isolde is stacking books. The stack of books forms a rectangular prism.
Each book is the same size. Isolde knows the area of the base of one book is 22 1/2 square inches and each book is 3/4 inch thick.
The volume of a stack of 9 books is cubic inches.
Answers
The volume of a stack of 9 books is 1368.75 cubic inches.
Volume of a book stackTo find the volume of a stack of 9 books, we first need to find the height of the stack. Since each book is 3/4 inch thick, the height of the stack is 9 times 3/4 inch, which is 6 3/4 inches.
Now we need to find the area of the base of the rectangular prism formed by the stack of books. Since each book has an area of 22 1/2 square inches, the total area of the base of the stack is 9 times 22 1/2 square inches, which is 202 1/2 square inches.
Therefore, the volume of the stack of 9 books is:
Volume = Area of base x heightVolume = (202 1/2 square inches) x (6 3/4 inches)Volume = 1368.75 cubic inchesMore on volume of stacked books can be found here: https://brainly.com/question/1058070
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Find the least number which must be subtracted from 3255 so as to get a perfect square. PLS ANSWER I NEED IT PLS.....................
Answers
Answer:
Step-by-step explanation:
to make 3255 a perfect square subtract 6 from 3255
3255 - 6 = 3249
3249 is a perfect square
For the following set of data, find the number of data within 1 population standarddeviation of the mean.68 68 70 61 67 71 63 67
Answers
68 68 70 61 67 71 63 67
Step 1: Write the formula of standard deviation
\(\text{Stanadard deviation = }\sqrt[]{\frac{Sum(x\text{ - }\mu)^2}{n}}\)\(\begin{gathered} \text{Where } \\ n\text{ = number of data } \\ \mu\text{ = mean} \end{gathered}\)n = 8
Step 2: Find the mean
\(\begin{gathered} \operatorname{mean}\text{ }\mu\text{ = }\frac{\sum ^{}_{\text{ }}x}{n} \\ \mu\text{ = }\frac{68\text{ + 86 + 70 + 61 + 67 + 71 + 63 + 67}}{8} \\ \mu\text{ = }\frac{535}{8} \\ \mu\text{ = 66.9} \end{gathered}\)Step 3: find the standard deviation
Next, substitute to find the standard deviation
\(\begin{gathered} \text{standard deviation = }\sqrt[]{\frac{sum(x\text{ - }\mu)^2}{n}} \\ =\text{ }\sqrt[]{\frac{78.88}{8}} \\ =\text{ }\sqrt[]{9.86} \\ =\text{ 3.14} \end{gathered}\)standard deviation = 3.14
Final answer
The number of data within the standard deviation of the mean = 5
Determine the algebraic degree of the following (7,7)-function, where a is a primitive element of F27. Is it linear, affine, quadratic or cubic? Explain your answer. (5%)
F(x) = alpha ^ 49 * x ^ 37 + alpha ^ 52 * x ^ 28 + alpha ^ 81 * x ^ 13 + alpha ^ 26 * x ^ 9 + alpha ^ 31 * x
Answers
The highest exponent of x in F(x) is 37, which means the algebraic degree of the function is 37.
The function F(x) is a cubic function.
Here, we have,
given function is:
F(x) = α⁴⁹ * x³⁷ + α⁵² * x²⁸ + α⁸¹ * x¹³ + α²⁶ * x⁹ + α³¹ * x
To determine the algebraic degree of the given (7,7)-function F(x), we need to find the highest exponent of x in the function.
F(x) = α⁴⁹ * x³⁷ + α⁵² * x²⁸ + α⁸¹ * x¹³ + α²⁶ * x⁹ + α³¹ * x
The algebraic degree of a polynomial function corresponds to the highest exponent of the variable in the function.
Linear functions have an algebraic degree of 1, affine functions have an algebraic degree of 1 or 0, quadratic functions have an algebraic degree of 2, and cubic functions have an algebraic degree of 3.
so, we get,
The highest exponent of x in F(x) is 37, which means the algebraic degree of the function is 37.
Therefore, the function F(x) is a cubic function.
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What is the formula for residential value
Answers
Residual Value = The percent of the cost you are able to recover from the sale of an item x The original cost of the item.
Answer:
i am not sure man
Step-by-step explanation:
3m + 4n = -135m + 6n = -19Solve the equation elimination method.
Answers
Answer:
m= 1, n = -4
Explanation:
Given the simultaneous equation
3m + 4n = -13 ...1 * 5
5m + 6n = -19....2 * 3
_______________________
15m + 20n = -65
15m + 18n = -57
Subtract the resulting equation:
20n - 18n = -65-(-57)
2n = -65+57
2n = -8
n = -8/2
n = -4
Substitute n = -4 into equation 1;
From1:
3m + 4n = -13
3m + 4(-4) = -13
3m - 16 = -13
3m = -13 + 16
3m = 3
m = 3/3
m = 1
Hence the value of m is 1
The solution to the system of equation (m, n) is (1, -4)
i need help on this (-4)²
help me
Answers
Answer:
Step-by-step explanation:
To have anything to a power is just multiplying the number as many times as it says to. ex. 2^3 is two times itself 3 times. 2 x 2 x 2= 8
In your case, you need to multiply -4 x -4 because the exponents tell you how many of the number you multiply.
-4 x -4 = 16
Hope this helps :)
What is the range of f(x) = ( 3/4)* - 4?
{yly>-4}
{yly> 3/4}
{yly<-4}
{yly< 3/4}
Answers
Answer:
the answer is {y | y> - 4}
Write the equation of the line with a slope of 5 and a y-intercept of (0, -3)
Answers
Answer:
y = 5x - 3
Step-by-step explanation:
equation of a straight line is y = mx + b where m=slope and b=y-intercept
in this case m=5 and b= -3
y = mx + b
y = 5x - 3
Would 2/3 produce a larger imagine? Scale factor
Answers
Answer:
no because 2/3 is 0.6666666667
Triangles A B C and L M N are shown. Angle B A C is 58 degrees. Angle M L N is 78 degrees. Sides A B and L M are congruent. Sides A C and L N are congruent.
Given AC = LN and BA = ML, which statement must be true?
BC < MN
BC > MN
BC = MN
BA = LN
Answers
Statement is true because the corresponding sides are congruent. The answer is: BA = LN.
What is Triangle?
A triangle is a closed, two-dimensional shape with three straight sides and three angles. It is one of the basic shapes in geometry and is used in many areas of mathematics, science, and engineering.
Since triangle ABC and triangle LMN have congruent corresponding sides, we know that they are similar triangles. This means that their corresponding angles are also congruent.
We are given that angle BAC is 58 degrees and angle MLN is 78 degrees. Since corresponding angles are congruent, this means that angle BAC is congruent to angle MLN.
Therefore, triangle ABC and triangle LMN are similar triangles with two pairs of corresponding congruent angles. This means that all corresponding sides are proportional.
Since AC = LN and BA = ML, we know that the ratio of the lengths of corresponding sides is:
AC / LN = BA / ML
Substituting the given values, we get:
1 = 1
This statement is true because the corresponding sides are congruent.
Therefore, the answer is: BA = LN.
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The sum of two numbers is 41. The larger number is one less than twice the smaller number. Find the numbers.
plz help
Answers
Answer:
14 and 17
Step-by-step explanation:
x+y=41
y=2x-1
x+(2x-1)=41
3x-1=41
3x=42
x=14
y=2(14)-1=27
Step-by-step explanation:
Step 1: Make a system of equation
The sum of two numbers is 41
x + y = 41
The larger number is one less than twice the smaller number.
x = 2y - 1
Step 2: Substitute x from the second equation into the first
\(x + y = 41\)
\((2y - 1) + y = 41\)
\(3y - 1+ 1 = 41 + 1\)
\(3y/3 = 42 / 3\)
\(y = 14\)
Step 3: Substitute y into the second equation
\(x = 2y - 1\)
\(x = 2(14) - 1\)
\(x = 28 - 1\)
\(x = 27\)
Answer: \(x = 27, y = 14\)
I kinda need help : /
Answers
Answer:
24 square units
Step-by-step explanation:
There are a couple of ways you can figure the area of the frame:
subtract the inner area from the outer areamultiply the width of the frame by the length of its centerline__
SubtractThe dimensions of the outer rectangle are twice the frame width plus the dimensions of the inner rectangle. That makes them 8 wide by 6 high. Then the difference of areas is ...
A = (8)(6) -(6)(4) = 48 -24 = 24 . . . . square units frame area
__
Width by LengthThe centerline of the frame is a rectangle with 1 unit greater length and width than the inner rectangle. It is 7 units by 5 units, so will have a perimeter of ...
P = 2(L+W) = 2(7+5) = 24 . . . . units
Then the area of the frame is this length multiplied by the width of the frame:
A = (24)(1) = 24 . . . . square units frame area
your cell phone company started a rewards club . for every three texts sent, you get 15 points. you need 1800 points for a price. How many texts do you need to send to get that prize?
Answers
Answer:
360 texts
Step-by-step explanation:
You get 15 points for each 3 texts.
That means you get 5 points per text.
1800/5 = 360
Answer: You need to send 360 texts.
4x^2-15x-4
factorise please
Answers
______________________________
1.) Change the equation using factored transformation: \(4x^2-15x-4=0\)- Quadratic polynomial can be factored using the transformation \(ax^2+bx+c=a(x-x_{1})(x-x_{2})\), where \(x_{1}\) and \(x_{2}\) are the solutions of the quadratic equation \(ax^2+bx+c=0\).
- This steps basically means change you current equation using the formula \(ax^2+bx+c=0\).
2.) Turn the factored form into the quadratic equation form:\(x=\frac{-(-15)\frac{+}{}\sqrt{(-15)^2-4\bold{x}4(-4)}}{2\bold{x}4}\)- All equations of the form \(ax^2+bx+c=0\) can be solved using the quadratic formula: \(\sqrt{\frac{-b\frac{+}{}\sqrt{b^2-4ac}}{2a} }\).
- The quadratic equation formula gives two solutions, one when \(\frac{+}{}\) is addition and one when it is subtraction.
3.) Square -15:\(-15^2=225\)
Equation at the end of Step 3:
\(x=\frac{-(-15)\frac{+}{}\sqrt{225-4\bold{x}4(-4)}}{2\bold{x}4}\)4.) Multiply −4 times 4:\(-4\) × \(4=-16\)Equation at the end of Step 4:
\(x=\frac{-(-15)\frac{+}{}\sqrt{225-16(-4)}}{2\bold{x}4}\)5.) Multiply −16 times −4:\(-16\) × \(-4=64\)Equation at the end of Step 5:
\(x=\frac{-(-15)\frac{+}{}\sqrt{225+64}}{2\bold{x}4}\)6.) Add 225 to 64:\(225+64=289\)Equation at the end of Step 6:
\(x=\frac{-(-15)\frac{+}{}\sqrt{289}}{2\bold{x}4}\)7.) Take the square root of 289:\(\sqrt{289}=17\)Equation at the end of Step 7:
\(x=\frac{-(-15)\frac{+}{}17}{2\bold{x}4}\)8.) Change -15 to positive 15:\(-15=15\)Equation at the end of Step 8:
\(x=\frac{15\frac{+}{}17}{2\bold{x}4}\)9.) Multiply 2 by 4:\(2\) × \(4=8\)Equation at the end of Step 9:
\(x=\frac{15\frac{+}{}17}8}\) 10.) Now Solve:Now solve the equation \(x=\frac{15\frac{+}{}17}8}\) when \(\frac{+}{}\) is plus.
Add 15 to 17:
\(15+17=32\)\(x=\frac{32}{8}\)Divide 32 by 8:
\(32\) ÷ \(8=4\)\(x=4\)Now solve the equation \(x=\frac{15\frac{+}{}17}8}\) when \(\frac{+}{}\) is minus.
Subtract 15 by 17:
\(15-17=-2\)\(x=\frac{-2}{8}\)Reduce the fraction to lowest terms by extracting and canceling out 2:
\(-2\) ÷ \(-2=-1\) \(8\) ÷ \(-2=-4\)\(x=-\frac{1}{4}\)11.) Factor the expression:Factor the original expression using \(ax^2+bx+c=a(x-x_{1})(x-x_{2})\). Substitute 4 for \(x_{1}\) and \(-\frac{1}{4}\) for \(x_{2}\):
\(4x^2-15x-4=4(x-4)(x-(-\frac{1}{4}))\)Simplify all the expressions of the form \(p-(-q)\) to \(p+q\):
\(4x^2-15x-4=4(x-4)(x+\frac{1}{4})\)Add \(\frac{1}{4}\) to x by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible:
\(4x^2-15x-4=4(x-4)\bold{x}(\frac{4x+1}{4})\)Cancel out 4, the greatest common factor in 4 and 4:
\(4x^2-15x-4=(x-4)(4x+1)\)______________________________
What are the first ten terms in the Fibonacci sequence
Answers
Answer:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34
Step-by-step explanation:
\(\Large \boxed{\sf 0, 1, 1, 2, 3, 5, 8, 13, 21, 34}\)
A series of integers known as the Fibonacci sequence begins with a zero, is followed by a one, another one, and then a series of increasing numbers. Each number in the series equals the sum of the two numbers before it. Every succeeding pair of Fibonacci numbers has a quotient resembling the golden ratio.
A binomial probability distribution with p = .3 is
a. bimodal
b. symmetrical
c. positively skewed
d. negatively skewed
Answers
A binomial probability distribution with p = 0.3 is c. positively skewed.
A binomial probability distribution with p = 0.3 is positively skewed. This means that the distribution is skewed to the right. In a binomial distribution, the skewness is determined by the value of p, which represents the probability of success in each trial. When p is less than 0.5, as in this case (p = 0.3), the distribution tends to be positively skewed.
The correct answer is c. positively skewed.
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Attachment Mathswatchhhh!!!!!!!!! answer only no explanation
Answers
Answer:
Option A is the correct answer
Step-by-step explanation:
Line is passing through the points (2, 0) and (0, - 3)
Gradient of line = (-3-0)/(0 - 2) = - 3/-2 = 3/2
Answer:
3/2
Step-by-step explanation:
3/2 is the gradient of the line
Estimate √200
Explain how you got your answer.
Answers
Answer:
√200 = √2×2×2×5×5= 2×5√2 = 10√2= 10×1.414= 14.14
the numbers from 1 to 8 are placed at the vertices of a cube in such a manner that thesum of the four numbers on each face is the same. what is this common sum?
Answers
The common sum is 18 as "the numbers from 1 to 8 are placed at the vertices of a cube in such a manner that the sum of the four numbers on each face is the same".
What is sum?A summation, also known as a sum, is the outcome of adding two or more numbers or quantities. There are always an even number of terms in a summation. There could be only two terms, or there could be one hundred, thousand, or a million. The outcome or conclusion we arrive at when we add two or more numbers is known as the SUM. Addends are the numbers that are added.
Here,
The sum of the numbers on one face of the cube is equal to the sum of the numbers on the opposite face of the cube; these 8 numbers represent all of the vertices of the cube.
=(1+2+3+4+5+6+7+8)/2
=18
Since "the numbers from 1 to 8 are placed at the vertices of a cube in such a manner that the sum of the four numbers on each face is the same," the common sum is 18.
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Speedometer readings for a motorcycle at 12-second intervals are given in the table.
t (s) 0 12 24 36 48 60
v (ft/s) 30 28 25 21 25 27
(a) Estimate the distance traveled by the motorcycle during this time period using the velocities at the beginning of the time intervals.
ft
(b) Give another estimate using the velocities at the end of the time periods.
ft
(c) Are your estimates in parts (a) and (b) upper and lower estimates? Explain.
O (b) is a lower estimate and (a) is an upper estimate since v is a decreasing function of t.
O (a) and (b) are neither lower nor upper estimates since v is neither an increasing nor decreasing function of t.
O (a) is a lower estimate and (b) is an upper estimate since v is an increasing function of t.
Answers
(a) The distance traveled by motorcycle is 1548 ft.
(b) The distance traveled by motorcycle is 1512 ft.
(c) (b) is a lower estimate and (a) is an upper estimate since v is a decreasing function of t.
What is velocity?
The primary indicator of an object's position and speed is its velocity. It is the distance that an object travels in one unit of time. The displacement of the item in one unit of time is the definition of velocity.
Given table is:
t (s) 0 12 24 36 48 60
v (ft/s) 30 28 25 21 25 27
The distance traveled by motorcycle during this time period using the velocities at the beginning of the time intervals is:
12(30 + 28 + 25 + 21 + 25)
=12 × 129
= 1548 ft
The distance traveled by motorcycle during this time period using the velocities at the end of the time intervals is:
12(28 + 25 + 21 + 25 + 27)
=12 × 126
= 1512 ft
The distance traveled by motorcycle at the end of the time intervals is greater than the distance traveled by motorcycle at the beginning of the time intervals.
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Dina pays $875 each month for rent. She has been in her apartment for 9 months. How much
she paid for rent in all?
A. $7,875
B. $7,525
C. $7.275
D. $7,235
Answers
Answer:
$7,875
Step-by-step explanation:
\(875 \times 9\)
If the coordinates of two points are A (-3,5) and B (-9, -6), then find the value of (abscissa of A) + (ordinate of B)
Answers
Answer:
abscissa of A = -3
ordinate of B = -6
A+B = -3+(-6)= -3-6=
-9
Help is appreciated!
Answers
1) Answer: The answer is Table B.
Explanation: The explanation is in the image.
2) Answer: The answer is 12.
There are 157 newly built homes in a subdivision 68 gallons of paint and 13 paint brushes were used for each house about how many gallons of paint we use for the new homes
Answers
About 10,676 gallons of paint were used to paint the 157 newly built homes in the subdivision, assuming each house required exactly 68 gallons of paint and 13 paint brushes.
How to solve this statement problem?The statement problem states that there are 157 newly built homes in a subdivision, and that 68 gallons of paint and 13 paint brushes were used for each house. This means that each house required 68 gallons of paint and 13 paint brushes.
To find the total amount of paint used for all 157 houses, we need to multiply the amount of paint used per house (68 gallons) by the number of houses (157):
Total amount of paint = 68 gallons/house x 157 houses
Total amount of paint = 10,676 gallons
Therefore, approximately 10,676 gallons of paint were used for the 157 newly built homes in the subdivision.
It's worth noting that this calculation assumes that each house required exactly 68 gallons of paint and 13 paint brushes. In reality, there may be some variation in the amount of paint and brushes used for each house, so the actual total may be slightly different.
However, this calculation provides a reasonable estimate of the total amount of paint used
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damien has enough red paint to cover an area of 24 square meters . the surface area of the playground tunnel he must make has a radius of r of 3 meters. Find the length of the tunnel demien can paint. round your answer to nearest decimal points if necessary
Answers
The required length of the tunnel that Damien can paint is 1.72 meters.
Let the tunnel is a cylinder with a radius r = 5 m and length l.
The formula for the surface area of the playground tunnel is:
S = 2πrl
S = 2π×5×l
S = 10πl
And we also know that the area of the tunnel is S = 54 m²
⇒ 10πl = 54
⇒ π = 3.14
⇒ 10×3.14×l = 54
Apply the multiplication operation, and solve for l
⇒ l = 1.72 m
Thus, the required length of the tunnel that Damien can paint is 1.72 meters.
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Need answer fast!!!!
