Answers
Simplify the integrand:
\(\dfrac{4x^4 + 3x^2 + 5x}{x^2} = 4x^2 + 3 + \dfrac5x\)
Now integrate one term at a time.
\(\displaystyle \int 4x^2 \, dx = \frac43 x^3 + C\)
\(\displaystyle \int 3 \, dx = 3x + C\)
\(\displaystyle \int \frac5x \, dx = 5 \ln|x| + C\)
Putting everything together,
\(\displaystyle \int \frac{4x^4 + 3x^2 + 5x}{x^2} \, dx = \int \left(4x^2 + 3 + \frac5x\right) \, dx = \boxed{\frac43 x^3 + 3x + 5 \ln|x| + C}\)
Related Questions
Two added to the square root of the sum of a number and five is equal to seven. Find the number.
Answers
Answer:
Step-by-step explanation:
In the year 1998, the surface elevation of Lake Powell was 3881 feet above sea level. In the year 2006, the surface elevation of Lake Powell was 3263.4 feet above sea level.
Interpret the rate of change in this situation. The surface elevation of Lake Powell is decreasing at a rate of
Answers
The surface elevation of Lake Powell is decreasing at the rate of 77.2 feet per year.
What is the rate(slope) at which the sea is decreasing?The rate at which the surface elevation of the Lake Powell is decreasing can be determined by calculating the slope(steepness) of the sea.
The slope can be given as:
Slope (Δm) = rise/run
Slope (Δm) = Δy/Δx
slope (Δm) = y₂ - y₁/x₂-x₁
slope (Δm) = 3263.4 - 3881/2006-1998
slope (Δm) = -617.6/8
slope (Δm) = -77.2
Therefore, we can conclude that the surface elevation of Lake Powell is decreasing at the rate of 77.2 feet per year.
Learn more about calculating the slope here:
https://brainly.com/question/1884491
#SPJ1
Which graph represents the solution set for the system x + y ≥ 5 and - 3x + 2y ≤-2.
Answers
Therefore , the solution of the given problem of inequality comes out to be graph 2 shows the solution for this system.
What does inequality really mean?
In mathematics, an inequality is a linear connection or a collection of numbers even when there is no equal sign. Equity always comes after equilibrium. When two numbers are not equal, inequality exists. Between equality and inequality, there exist differences. The most common symbol was chosen because when parameters aren't the same or comparable (). Values can be compared using a variety of disparities, no matter how few or numerous they are.
Here,
Given :
=> x + y ≥ 5
and
=> - 3x + 2y ≤-2
So,
=> x ≥ 5- y
=> - 3(5- y) + 2y ≤-2
=> -15 + 3y + 2y ≤-2
=> 5y ≤ 13
=> y ≤ 13/5
and
=> x ≥ 5- 13/5
=> x ≥ 12/5
Therefore , the solution of the given problem of inequality comes out to be graph 2 shows the solution for this system.
To know more about inequality visit:
https://brainly.com/question/29914203
#SPJ1
Write 135 as a product of its prime factors. Write your answer in index form need answer quickly URGENT
Answers
135 as a product of its prime factors is written as 3 × 3 x 3 x 5
What are prime factors?The prime factors are those prime digits that can divide a particular digit evenly and without leaving any remainder. To put it differently, these are the main digits that, when multiplied with one another, result in the initial number.
In mathematics and number theory, prime factors hold significant value as they enhance comprehension of number properties and interconnections. In addition, they are utilized in a range of mathematical calculations and algorithms.
From the information given, we have the value as;
135
The prime factors are 3 × 3 x 3 x 5
Learn more about prime factors at: https://brainly.com/question/1081523
#SPJ1
if the perimeter of a rectangle is 48cm and the breath is 6cm. What is the length.
Answers
Perimeter of a rectangle is :
\(\qquad \sf \dashrightarrow \: P= 2l + 2b\)
where,
P = perimeter = 48 cml = Length = ?b = breadth = 6 cm\(\qquad \sf \dashrightarrow \: 48 = 2l + 2(6)\)
\(\qquad \sf \dashrightarrow \: 2l = 48 - 2(6)\)
\(\qquad \sf \dashrightarrow \: 2l = 48 -12\)
\(\qquad \sf \dashrightarrow \: 2l = 36\)
\(\qquad \sf \dashrightarrow \: l = 36 \div 2\)
\(\qquad \sf \dashrightarrow \: l = 18 \: cm\)
So, length if the rectangle is 18 cm
Answer:
18cm
Step-by-step explanation:
the perimeter of a rectangle is the width/breadth (I'm calling it width) + the other width on the opposite side + the length + the length on the opposite side
(perimeter is a measure of the border length)
so,
l + l + w + w = perimeter
if the width is 6, our new equation is:
l + l + 6 + 6 = 48
l + l + 12 = 48
now, if we subtract 12 from both sides of the equation...
l + l + 12 = 48
- 12 -12
l + l = 36
(number plus itself is equal to the number x2)
2L = 36
divide both sides by 2...
2L = 36
__ __
2 2
L = 18
So, the length of the rectangle is 18 cm
(to check, we can add 18 + 18 + 6 + 6 = 48)
x = 13, ¿cuál ecuación es verdadera?
3(18 - x) = 67
4(9x) = 23
2(x-3)=7
5(x-9) = 20
Answers
When x = 13, the equation that is true is option D) 5(x - 9) = 20.
To determine which equation is true when x = 13, we can substitute the value of x into each equation and see which equation holds true. Let's go through each option:
A) 3(18 - x) = 67
Substituting x = 13:
3(18 - 13) = 67
3(5) = 67
15 = 67
The equation is not true when x = 13. Therefore, option A is false.
B) 4(9x) = 23
Substituting x = 13:
4(9*13) = 23
4(117) = 23
468 = 23
Again, the equation is not true when x = 13. Therefore, option B is also false.
C) 2(x - 3) = 7
Substituting x = 13:
2(13 - 3) = 7
2(10) = 7
20 = 7
Once again, the equation is not true when x = 13. Therefore, option C is false as well.
D) 5(x - 9) = 20
Substituting x = 13:
5(13 - 9) = 20
5(4) = 20
20 = 20
Finally, the equation is true when x = 13. Therefore, option D is true.
For more such questions on equation visit:
https://brainly.com/question/30451972
#SPJ8
Note: the translated questions is
X = 13, which equation is true?
if ABCD is a rectangle and m
Answers
Explanation: If you look at it, A+B+C+D can equal a few things, but you mostly get (M) because m L BEA =62^• may be true. But it equals m
Step-by-step-helper: A+B+C+D=? A+B=b over a, so C+D= d over c. M+__=? just m. So the answer is m.
Quiana measures the width of her doorway entrance using a measuring tape.She measures the width as 33 inches. She later finds a better tape measure that measures to the nearest half of an inch. After re-measuring,she determines that the actual measure of the doorway is 32 1/2 inches
Answers
Simple Math Range and domain help Part 2
Answers
\({ \qquad\qquad\huge\underline{{\sf Answer}}} \)
Here we go ~
Domain : All values of x, for which function is defined.
i.e \(\boxed{\sf 0\leqslant x\leqslant 12} \)
Range : All possible values of y, that can be obtained by putting value of x in the equation of function
i.e \(\boxed{\sf 0\leqslant y\leqslant 900} \)
Can someone explain how to get the answer to…if 7p-4=8 what is the value of p?
Answers
The value of p in the equation 7p - 4 = 8 is p = 12/7
Solving for what is the value of p?From the question, we have the following parameters that can be used in our computation:
7p - 4 = 8
Add 4 to both sides
So, we have
7p = 12
Divide both sides by 7
So, we have
p = 12/7
Hence, the solution is p = 12/7
Read more about expression ta
https://brainly.com/question/15775046
#SPJ1
Ayudaaaaaa
Porfi
Gracias
Answers
The expression representing the perimeter of the polygon is given as follows:
7mn³/3 + 4m² + 3mn².
What is the perimeter of a polygon?The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.
Hence the perimeter for the polygon in this problem is given as follows:
mn³(1/3 + 2) + m²(1 + 3) + mn²(1 + 2) = 7mn³/3 + 4m² + 3mn².
More can be learned about the perimeter of a polygon at https://brainly.com/question/3310006
#SPJ1
Jack can jump 195% of his heightwith a running start. If jack can jump 97.5inches, how tall is he
Answers
The height of Jack based on the information is 50 inches.
What is percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
Let the height be represented as h.
Therefore, Jack can jump 195% of his height with a running start. This will be:
= 195% × h = 9.75
1.95h = 97.5
Divide
h = 97.5 / 1.95
h = 50
Jack is 50 inches tall.
Learn more about percentages on:
brainly.com/question/24304697
#SPJ1
6b-9=-87 what is the answer
Answers
Answer: B=-16
because -86-9=-96 and -96 divided by 6=-16
8. Heather purchased an iPad mini on sale 20%
off for $263.20. What was the original price of
the iPad mini?
A. $315.84
B. $329
C. $210.56
D. $400
Answers
Answer:
Answer is A.
Step-by-step explanation:
0.2 x 263.20 = 52.64
52.64 + 263.20 = 315.84
consider the system of linear equations
consider the system of linear equations
6x+2y – z=4
X +5y+z=3
2x+y+4z=27
A, solve the system by
I. Gassian elimination method,
II. LU- decomposition method
III. Gauss- Jacobi method,and
IV. Gauss-seidel method,
Answers
I. The solution to the system of equations using Gaussian elimination is x = 1, y = -1, and z = 2.
II. For the LU-decomposition method, we need to have a square coefficient matrix, which is not the case in the given system. Therefore, we cannot directly apply the LU-decomposition method.
III. For this method to converge, the coefficient matrix must be diagonally dominant, which is not the case in the given system. Therefore, the Gauss-Jacobi method cannot be directly applied either.
IV. It requires the coefficient matrix to be diagonally dominant, which is not satisfied in the given system. Hence, the Gauss-Seidel method cannot be directly used.
I. Gaussian Elimination Method:
To solve the system of linear equations using Gaussian elimination, we perform row operations to reduce the system into upper triangular form. The augmented matrix for the given system is:
| 6 2 -1 | 4 |
| 1 5 1 | 3 |
| 2 1 4 |27 |
We can start by eliminating the coefficients below the first element in the first column. To do this, we multiply the first row by a suitable factor and subtract it from the second and third rows to eliminate the x coefficient below the first row. Then, we proceed to eliminate the x coefficient below the second row, and so on.
After performing the necessary row operations, we obtain the following reduced row-echelon form:
| 6 2 -1 | 4 |
| 0 4 2 | -1 |
| 0 0 3 | 6 |
From this form, we can easily back-substitute to find the values of x, y, and z. We have z = 2, y = -1, and x = 1.
II. LU-Decomposition Method:
LU-decomposition is a method that decomposes a square matrix into a product of two matrices, L and U, where L is lower triangular and U is upper triangular.
III. Gauss-Jacobi Method:
The Gauss-Jacobi method is an iterative numerical method to solve systems of linear equations.
IV. Gauss-Seidel Method:
Similar to the Gauss-Jacobi method, the Gauss-Seidel method is an iterative method for solving linear systems.
Therefore, out of the four methods mentioned, only the Gaussian elimination method can be used to solve the given system of linear equations.
For more such questions on solution
https://brainly.com/question/24644930
#SPJ8
Write a real-world situation that could be modeled by the equation 8+2x=6x. Then solve the problem.
Answers
Answer: Explanation is below!
Step-by-step explanation:
John has 8 apples. He then receives a two shipping's of unknown amount of apples. In total, he will have his original amount of apples, plus the two shipping's of unknown amount of apples, which in all will equal to 6 unknown amount of shipping's of said apples.
Write and solve the equation.
==> 8+2x=6x
==> 8 = 4x
==> 2 = x
x = 2
8 + 2(2) = 6(2)
==> 8 + 4 = 12
==> 12 = 12
Hope this helped! Have a good day ;)
Answer: X=2;
Step-by-step explanation: First, I'll show you how to solve it. So, first, we need to rearrange the terms. So, instead of 8+2x, we'll do:
2x+ 8 = 6x
Now, we need to subtract the 8 from both sides. So it will look like this:
2x+8-8 = 6x-8
So, now we need to simplify this expression, which would look like this:
2x = 6x-8
Then, have to subtract the 6x from both sides, which looks like this:
2x-6x = 6x - 8 - 6x
Now, we combine the like terms, so then the problem becomes smaller, looking like this:
-4x = -8
Now, we need to factor in the expression, which looks like this:
\(\frac{-4x}{-4}\) = \(\frac{-8}{-4}\)
The -4x and -4 cancel out, and -8 divided by -4 = 2
A real-world problem can look something like this:
Andrea had 6 marbles. She gave 8 to her little sister after losing hers. Then, her mom gave 4 more to Andrea as a birthday present.
(I'm not good at making real-world problems, but it = 12)
I hope this helped!
100 pts!!
Thanh rents a car. He has a fixed rate of $49.00 weekly, pays $14.00 per week for the optional insurance, and he spends $12.00 weekly on gas. What will Thanh's cost be per month (four weeks)?
Answers
Thanh's cost per month (four weeks) will be $300.00.The given fixed rate for Thanh is $49.00 per week. Thanh also pays $14.00 per week for the optional insurance and $12.00 weekly on gas.
To find Thanh's cost per month (four weeks), we need to multiply his weekly cost by 4.We can use the formula below to calculate Thanh's monthly cost.
Total weekly cost = Fixed rate + Insurance cost + Gas cost
Total weekly cost = $49.00 + $14.00 + $12.00
Total weekly cost = $75.00
The cost for Thanh per month (four weeks) = Total weekly cost × 4
Cost for Thanh per month (four weeks) = $75.00 × 4
Cost for Thanh per month (four weeks) = $300.00
Therefore, Thanh's cost per month (four weeks) will be $300.00.
For more question on fixed rate
https://brainly.com/question/30096538
#SPJ8
6(x-2)≥-5+5x+6 solve and explain please thanks
Answers
The value of the inequality is x ≥ 3/7
What is inequality?The relationship between two values that are not equal is defined by inequalities. When two terms are not equal, they can either be:
greater than >
less than <
greater than or equal to ≥
less than or equal to ≤
6(x-2)≥-5+5x+6
12x-2 ≥ 5x + 6-5
collect like terms
12x -5x ≥ 6-5+2
7x ≥ 3
divide both sides by 7
x ≥ 3/7
therefore the value of the inequality is x ≥ 3/7
learn more about inequality from
https://brainly.com/question/24372553
#SPJ1
tucker is making cookies the recipe called for 1/3/4 cups of flour and 1/2cup of sugar how much flour and sugar coral will be use to make the cookies
Answers
The flour and sugar coral that will be use to make the cookies is 2 1/4 cups.
How to calculate the fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this situation, Tucker is making cookies the recipe called for 1/3/4 cups of flour and 1/2cup of sugar.
The flour and sugar coral that will be use to make the cookies will be:
= 1 3/4 + 1/2
= 2 1/4
Learn more about fractions on:
brainly.com/question/78672
#SPJ1
What is the area of the figure? In Units
Answers
Answer:
Area = 40
Perimeter = 26
Step-by-step explanation:
length = 8
width = 5
Area = 8 x 5 = 40
Perimeter = 2(8 + 5) = 26
The center of the circle is located (3'8), and the circle has a radius that is 5 units long. What is the general form of the equation for the circle
Answers
9514 1404 393
Answer:
x² +y² -6x -16y +48 = 0
Step-by-step explanation:
Given:
circle center: (3, 8)circle radius: 5Find:
general form equation for the circle
Solution;
The standard form equation for the circle is ...
(x -h)² +(y -k)² = r² . . . . . circle with radius r centered at (h, k)
(x -3)² +(y -8)² = 5²
Subtracting 25 and expanding this will give the general form.
x² -6x +9 +y² -16y +64 -25 = 0
x² +y² -6x -16y +48 = 0
_____
Additional comment
"General form" of an equation is usually the form f(x,y) = 0, where f(x, y) is written in "standard form," with terms in lexicographical order and decreasing degree.
HELP PLEASE!!!
Answer: ?
Answers
Answer:
third choice
Step-by-step explanation:
. Eli and Alex began jogging from the same spot at the same time in opposite directions on a 12-mile circular trail. Eli runs at 4 mph, and Alex at 6 mph. How long will it take them to meet?
Answers
Eli and Alex running at a speed of 4 mph and 6 mph respectively around a 12 miles trail will meet each other in 1.2 hours.
How to find the time they meet using the speed?Eli and Alex began jogging from the same spot at the same time in opposite directions on a 12-mile circular trail.
The circumference of the circular trail is 12 miles. This means the both of them will cover a total of 12 miles.
Eli run with a speed of 4 mile per hour and Alex runs with a speed of 6 miles per hour.
Therefore, the time it will take them to meet can be calculated as follows:
speed = distance / time
distance = speed × time
Hence,
let
t = time they travelled
total distance = 4t + 6t
12 = 4t + 6t
12 = 10t
divide both sides by 10
12 / 10 = 10t / 10
t = 1.2 hours
Therefore, they used 1.2 hours.
learn more on speed here: https://brainly.com/question/13014138
#SPJ1
A friend lends you $510, which you agree to repay with 2% interest. How much will you have to repay?
Answers
Answer:
$520.20
Step-by-step explanation:
8. Which statement can be represented by the equation shown?
9x-2=8x
Answers
Answer:
A or the 1st one
Step-by-step explanation:
Angelo is making 9 dollars per hour but, loses 2 dollars due to the bus fee. So in math form that would be:
9x - 2
And the second part is Tom makes 8 dollars per hour but doesn't have to pay for bus fee. In math form that would be;
8x
So put that together that would be
9x - 2 = 8x
Which expression is equivelent to x^2 +2x+2
Answers
Answer:
(x+1-i)(x+1+i)
Step-by-step explanation:
\( \dashrightarrow \: { \tt{ {x}^{2} + 2x + 2 }}\)
• From the general quadratic equation:
\( \dashrightarrow \:{ \boxed { \tt{ {ax}^{2} + bx + c }}}\)
Sum = (b/a)Product = (c/a)From x² + 2x + 2:
Sum = 2Product = 2Factors = No real rootsFrom Bulldozer;
\({ \tt{x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} }} \\ \\ { \tt{x = \frac{ - 2 \pm \sqrt{4 - (4 \times 1 \times 2)} }{2} }} \\ \\ { \tt{x = \frac{ - 2 \pm \sqrt{ - 4} }{2} }} \\ \\ { \tt{x = \frac{ - 2 \pm \sqrt{4 {i}^{2} } }{2} } \: \: \{ \red{for \: - 1 = {i}^{2} } \}} \\ \\ { \tt{x = \frac{ - 2 \pm2i}{2} }} \\ \\ { \tt{x = - 1 \pm i}}\)
Therefore;
\({ \tt{(x + 1 + i)(x + 1 - i)}}\)
A Sumer job pays $5 per hour
b. After working 24 hours, do you have enough money to buy an MP3
player that costs $100? Explain your reasoning.
Answers
Answer:
Yes, since the total pay of $120 is more than the $100 cost of the MP3 player.
Step-by-step explanation:
hourly pay: $5/hour
number of hours: 24 hours
total pay = hourly pay × number of hours
total pay = $5/hour × 24 hours
total pay = $120
MP3 player costs $100.
Total pay is $120.
Answer: Yes, since the total pay of $120 is more than the $100 cost of the MP3 player.
9) The 50 cars used by a firm were inspected. 10 had faulty brakes and 15 had faulty tyres. There were 2 cars with faulty brakes but good tyres. How many cars had good brakes and good tyres? The answer is 33
Answers
Based on the information, there are 25 cars with good brakes and good tires.
How to calculate the valueTotal cars = 50
Cars with faulty brakes = 10
Cars with faulty tires = 15
Cars with faulty brakes and good tires = 2
Let's calculate the number of cars with good brakes and good tires:
Cars with faulty brakes or faulty tires = Cars with faulty brakes + Cars with faulty tires - Cars with faulty brakes and good tires
= 10 + 15 - 2
= 25
Cars with good brakes and good tires = Total cars - Cars with faulty brakes or faulty tires
= 50 - 25
= 25
Therefore, there are 25 cars with good brakes and good tires.
Learn more about numbers on
https://brainly.com/question/25734188
#SPJ1
The graph shows the printing rate of Printer A. Printer B can print at a rate of 25 pages per minute. How does the printing rate for Printer B compare to the printing rate for Printer A
Answers
Answer:
The printing rate for Printer B is 10 pages more than the rate of printer A because the rate of 25 pages per minute is 10 pages more than the rate 15 pages per minute for Block A
Step-by-step explanation:
From the graph of the printing rate of Printer A, we can see that;
At 1 minute, number of pages printed = 15
At 2 minutes, number of pages printed = 30 minutes
At 3 minutes, number of pages printed = 45
Thus printing rate for printer A is; 15/1 = 30/2 = 45/3 = 15 pages per minutes
Since printer B can print 25 pages per minute, we can conclude that;
The printing rate for Printer B is 10 pages more than the rate of printer A because the rate of 25 pages per minute is 10 pages more than the rate 15 pages per minute for Block A
what is .09 as a fraction?
Answers
Answer:
9/100
Step-by-step explanation:
When we change .09 to a fraction, we can put the 9 over 100 because the 9 is in the hundredths place. We get 9/100. We can’t simplify it so it stays like that.
I hope this helped and please mark me as brainliest!