∫dF=F(x,y)=12ax2+bxy+12ℓy2+c=0 is the exact ode.
What is the exact equation?Specifically, an exact equation is a differential equation that can be solved instantly without the aid of any specialized methods. If the result of a straightforward differentiation, a first-order differential equation (of one variable) is referred to as an exact differential or exact differential. The equation
P(x, y)dy/dx + Q(x, y) = 0,
or in the equivalent alternate notation
P(x, y)dy + Q(x, y)dx = 0,
is exact if
∂P(x, y)/∂x = ∂Q(x, y)/∂y
In this instance, a function R(x, y) will exist whose partial x-derivative is Q and partial y-derivative is P, and whose equation R(x, y) = c (where c is constant) will implicitly establish a function y that will satisfy the initial differential equation.
An exact ODE is one where the equation can be written as dF=0 for some F(x,y). Expanding using chain rule, this means an equation of the form
∂1Fdx+∂2Fdy=0
Now if the second partials of F exist and are continuous, they must be equal due to Clairaut. So, given an equation
Mdx+Ndy=0
if we have
∂2M=∂1N
then there is an F such that
M=∂1F, N=∂2F
and hence that equation is exact, and the solution is simply
∫dF=0
We have
M=ax+by⇒∂2M=b
N=kx+ℓy⇒∂1N=k
so to be exact, we must have that b=k .
Then, integrating M and N , we have
F(x,y)=∫Mdx=12ax2+bxy+g(y)
F(x,y)=∫Ndy=bxy+12ℓy2+h(x)
and comparing these two, we can see that
∫dF=F(x,y)=12ax2+bxy+12ℓy2+c=0
is a solution to the equation for any a,b,c,ℓ . You can solve for y by quadratic methods.
To learn more about the, exact equation visit:
https://brainly.com/question/11935285
#SPJ4
I need this answer ASAP I will for real pay you just please help me out
The water level in Colorado river is 2.55 m below average. a large rainfall caused The water level to rise 0.8 m. what is the water level after the rainfall?
The water level after the rainfall in the Colorado River is 3.35 meters.
How is the water level determined?The water level after the rainfall can be determined using the mathematical operation of addition.
A mathematical operation changes the output value of some input values.
For instance, adding 0.8 to 2.55 results in 3.35 meters of the height of the Colorado River after the rainfall.
Data and Calculations:The average water level in the Colorado River = 2.55 m
Increase in water level following the large rainfall = 0.8 m
New water level after the rainfall = 3.35 M (2.55 + 0.8)
Thus, the water level after the rainfall in the Colorado River is 3.35 meters.
Learn more about mathematical operations at https://brainly.com/question/4721701
#SPJ1
how to write 0.5.5555.., 0.77777.., 0.288888… and 0.711111… as a fraction
Answer:
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation i2 = −1; every complex number can be expressed in the form a + bi, where a and b are real numbers. Because no real number satisfies the above equation, i was called an imaginary number by René Descartes. For the complex number a + bi, a is called the real part and b is called the imaginary part. The set of complex numbers is denoted by either of the symbols {\displaystyle \mathbb {C} }\mathbb {C} or C. Despite the historical nomenclature "imaginary", complex numbers are regarded in the mathematical sciences as just as "real" as the real numbers and are fundamental in many aspects of the scientific description of the natural world.[1][a]
Step-by-step explanation:
Answer:
iakajakakam kwokwmajsj kakajnsnsj wjjsjajsj sjsjjsjs
Step-by-step explanation:
let f(x)= 7x-2 and g(x)= sqrt (x) + 2x. what are (f+g)(x) and (f-g)(x)?
Answer:
• [tex](f+g) (x)[/tex] = [tex]9x + \sqrt{x} -2[/tex]
• [tex](f-g)(x)[/tex] = [tex]5x - \sqrt x - 2[/tex]
Step-by-step explanation:
[tex]f(x) = 7x - 2[/tex]
[tex]g(x) = \sqrt{x} + 2x[/tex]
To calculate [tex](f+g) (x)[/tex] and [tex](f-g)(x)[/tex], we have to add and subtract [tex]f(x)[/tex] and [tex]g(x)[/tex] respectively:
• [tex](f+g) (x)[/tex]
⇒ [tex]f(x) + g(x)[/tex]
⇒ [tex]7x - 2 \: + \sqrt{x} + 2x[/tex]
⇒ [tex]9x + \sqrt{x} -2[/tex]
• [tex](f-g)(x)[/tex]
⇒ [tex]7x - 2 - (\sqrt x + 2x)[/tex]
⇒ [tex]7x - 2 - \sqrt x - 2x[/tex]
⇒ [tex]5x - \sqrt x - 2[/tex]
.How many gallons of hydrochloric acid must be added to
12 gallons of a 30% solution to obtain a 40% solution
Answer:
5.6
Step-by-step explanation:
.30*12+x=.40(12+x)
3.6+x=4.8+.40x
x-.40x=4.8-3.6
.6x=1.2
x=1.2/.6
x=2 gallons of acid needs to be added.
Proof:
.30*12+2=.4(12+2)
3.6+2=.4*14
5.6=5.6
Help! Multiply (3.25 x 10−9)(6.7 x 1015). Write the final answer in scientific notation.
21.775 x 10−135
2.1775 x 10−134
21.775 x 106
2.1775 x 107
Answer:
D. 2.1775 x 10^7
Step-by-step explanation:
I just finished the quiz and got it correct
Hope its not to late!
Answer:
2.1775 x 107
Step-by-step explanation:
Sophia finished 32 pages of a book. She calculated that she finished 90 more pages than she has yet to read. How long is her book?
Answer:
270
Step-by-step explanation:
From (1) and (2), we get,
> y + 90 = 2/3X
> 1/3 X + 90 = 2/3X
> 90 = 1/3 X
> X = 270
Therefore
An airplane leaves Los Angeles and travels 5 hours to New York City. The return trip travels along the same route and takes 6 hours and 15 minutes because the plane travels 99 mph slower due to a headwind. Find the distance the plane flies between the two cities.
The distance the plane flies between the two cities is 2,475 miles.
Given that, an aeroplane leaves Los Angeles and travels 5 hours to New York City. The return trip travels along the same route and takes 6 hours and 15 minutes because the plane travels 99 mph slower due to a headwind.
We need to find the distance the plane flies between the two cities.
How to find the distance with speed and time?To get the distance, multiply the speed by time. You may see these equations simplified as s=d/t, where s is speed, d is distance, and t is time.
Let the speed of an aeroplane while travelling from Los Angeles to New York City be x.
Then the speed of an aeroplane during the return trip will be x-99.
Now, Distance=Speed × Time
So, x × 5 = (x-99) × 6 1/4
⇒5x=25/4 (x-99)
⇒20x=25x-2475
⇒5x=2475
⇒x=495
The speed of an aeroplane is 495 mph.
Now, the distance = 5x =5 × 495
=2,475 miles
Therefore, the distance the plane flies between the two cities is 2,475 miles.
To learn more about speed, distance and time visit:
https://brainly.com/question/4978052.
#SPJ1
Answer: plane
Step-by-step explanation:
plane fliying in the sky it go fl y
-5/6x-(x-1)=1/4(-x+80)
Answer:
x = - 12
Step-by-step explanation:
- [tex]\frac{5}{6}[/tex] x - (x - 1) = [tex]\frac{1}{4}[/tex] (- x + 80) distribute parenthesis on left side by - 1
- [tex]\frac{5}{6}[/tex] x - x + 1 = [tex]\frac{1}{4}[/tex] (- x + 80)
multiply through by 12 ( the LCM of 4 and 6 ) to clear the fractions
- 10x - 12x + 12 = 3(- x + 80) ← distribute parenthesis by 3
- 22x + 12 = - 3x + 240 ( add 3x to both sides )
- 19x + 12 = 240 ( subtract 12 from both sides )
- 19x = 228 ( divide both sides by - 19 )
x = - 12
What is 8÷424.4 ? show your work.
Answer:
Step 1:
Start by setting it up with the divisor 8 on the left side and the dividend 424 on the right side like this:
8 ⟌ 4 2 4
Step 2:
The divisor (8) goes into the first digit of the dividend (4), 0 time(s). Therefore, put 0 on top:
0
8 ⟌ 4 2 4
Step 3:
Multiply the divisor by the result in the previous step (8 x 0 = 0) and write that answer below the dividend.
0
8 ⟌ 4 2 4
0
Step 4:
Subtract the result in the previous step from the first digit of the dividend (4 - 0 = 4) and write the answer below.
0
8 ⟌ 4 2 4
- 0
4
Step 5:
Move down the 2nd digit of the dividend (2) like this:
0
8 ⟌ 4 2 4
- 0
4 2
Step 6:
The divisor (8) goes into the bottom number (42), 5 time(s). Therefore, put 5 on top:
0 5
8 ⟌ 4 2 4
- 0
4 2
Step 7:
Multiply the divisor by the result in the previous step (8 x 5 = 40) and write that answer at the bottom:
0 5
8 ⟌ 4 2 4
- 0
4 2
4 0
Step 8:
Subtract the result in the previous step from the number written above it. (42 - 40 = 2) and write the answer at the bottom.
0 5
8 ⟌ 4 2 4
- 0
4 2
- 4 0
2
Step 9:
Move down the last digit of the dividend (4) like this:
0 5
8 ⟌ 4 2 4
- 0
4 2
- 4 0
2 4
Step 10:
The divisor (8) goes into the bottom number (24), 3 time(s). Therefore put 3 on top:
0 5 3
8 ⟌ 4 2 4
- 0
4 2
- 4 0
2 4
Step 11:
Multiply the divisor by the result in the previous step (8 x 3 = 24) and write the answer at the bottom:
0 5 3
8 ⟌ 4 2 4
- 0
4 2
- 4 0
2 4
2 4
Step 12:
Subtract the result in the previous step from the number written above it. (24 - 24 = 0) and write the answer at the bottom.
0 5 3
8 ⟌ 4 2 4
- 0
4 2
- 4 0
2 4
- 2 4
0
You are done, because there are no more digits to move down from the dividend.
The answer is the top number and the remainder is the bottom number.
Therefore, the answer to 424 divided by 8 calculated using Long Division is:
53
0 Remainder
Step-by-step explanation:
For which situations is it appropriate to use a sample? Select three options.
1What percentage of pick-up truck drivers want their next vehicle purchase to be another pick-up truck?
2What is the average number of rainbows each year in Honolulu?
3How many pedestrians would use a walkway built over a busy road?
4How many police cars are equipped with computers?
5What is the most popular car color in the teachers’ parking lot?
It is appropriate to use a sample at
What percentage of pick-up truck drivers want their next vehicle purchase to be another pick-up truck?How many pedestrians would use a walkway built over a busy road?How many police cars are equipped with computers?Options A, C, and D
This is further explained below.
What is the situation?Generally, Placement with respect to one's immediate environment; is the manner in which something is arranged. the whole physical, social, and psychocultural influences that operate upon a person to direct and control his or her conduct is referred to as an individual's environmental context.
In conclusion, It is OK to utilize a sample while answering the following question: What proportion of people who drive pick-up trucks want their next vehicle purchase to be another pick-up truck?
How many people do you think would utilize a walkway that was constructed over a major road? Alternatives A, C, and D
Read more about situations
https://brainly.com/question/15540434
#SPJ1
Tyrone biked 45 miles at an average speed of 18 miles per hour, without stopping. About how long did the ride take him? Use the formula t equals d over r
Answer: 2 1/2 hours
Step-by-step explanation: 45/18 = 2 1/2
The real estate agent's base salary is $21,000. They also receive 5% commission on total sales. How much in total sales do they have to make in order to earn $70,000 in one year?
======================================================
Work Shown:
x = amount of sales
0.05x = five percent of sales to represent commission earned
21,000+0.05x = add on the base salary to get total salary
21,000+0.05x = 70,000
0.05x = 70,000-21,000
0.05x = 49,000
x = (49,000)/(0.05)
x = 980,000
----------
Check:
If the real estate agent sold $980,000 worth of property, then s/he earned 5% of 980,000 = 0.05*980,000 = 49,000 dollars in commission.
The total salary for the year is 21,000+49,000 = 70,000 dollars. The answer is confirmed.
The segment shown is half of AB, where B(-5,1) is one endpoint of the segment and M(-3, 3) is the midpoint of the segment.
©2016 StrongMind. Created using GeoGebra.
What are the coordinates of point A?
Enter your answer as an ordered pair, formatted like this: (42, 53)
The coordinates of point A is(-1,5) of coordinate plane.
What is the short definition of a coordinate plane?
Two number lines combine to generate the two-dimensional surface known as the coordinate plane. The x-axis is a single horizontal number line. The y-axis is the name of the vertical number line that is the other number line. The origin is where the two axes come together. The coordinate plane can be used to graph points, lines, and other things.For point (x1,y1) and (x2,y2) on coordinate plane if m is the midpoint of these points, then coordinate of mid point is given by
(x1+x2)/2, (y1+y2)/ 2
Given point
B= (-5,1)
M = (-3,3)
we have to find point A, let it be (x,y)
using the above formula , midpoint m is
-3= (-5+x)/ 2 3= (1+y)/ 2
-3*2= -5+x 6= 1 +y
-6 +5 = x 6-1 =y
x = -1 y = 5
Thus, the coordinates of point A is(-1,5).
Learn more about coordinate plane
brainly.com/question/24134413
#SPJ9
Solve for a. Express your answer in simplest radical form if necessary.
Answer: =
√
شه دار
= 144
Answer:
12
Step-by-step explanation:
√144 = 12
The puppy shelter where Clara works is moving to a new building. The rooms in the new building are built to hold 6 puppies each. Clara needs to figure out how many rooms she'll need to house a total of 78 puppies.
Use an equation to find the number of rooms Clara needs.
Answer:
Equation: 6x = 78Rooms: 13Step-by-step explanation:
Let the number of rooms is x.
Each room is built to hold 6 puppies, so x rooms hold 6x puppies.
The equation for this is:
6x = 78x = 78/6x = 13And the solution is 13 rooms.
Rani is making rice pudding. She uses
cup
cup of white rice for every 2 cups
of milk. How many cups of rice does she need when she uses 3 cups of
milk?
Rani will use 3/2 cups of white rice for 3 cups of milk.
What is termed as unitary method?"It is a method in which we obtain the value of a single unit by subtracting the value of multiple units and thus the value of multiple units by subtracting the value of a single unit."
The value of several things is given in the unitary method, and we must either figure out the significance of more or lesser things. To do so, we must first determine the value of one item by division and then determine the value of ever more or fewer items by multiplication.Now, for the given question;
1 cup of white rice is required for every 2 cups of milk by Rani.
Thus,
2 cups of milk ------> 1 cup of white rice.
So, using unitary method. Divide both side by 2.
1 cups of milk ------> 1/2 cup of white rice.
Now, calculate for the 3 cups of milk.
multiplying both side by 3.
3 cups of milk ------> 3/2 cup of white rice.
Therefore, the 3/2 cups of white rice required for the 3 cups of milk.
To know more about unitary method, here
https://brainly.com/question/28540270
#SPJ9
Find the mode of the data set. 6.12 8.37 5.98 6.55 6.21 7.47 6.55 7.48 7.48 6.55 no mode 6.21
Answer:
Mode is 6.55
Step-by-step explanation:
To find the mode, you put the numbers in order from least to greatest and count how many times each number occurs. In this case its 6.55.
Answer: the mode set is 6.55
Step-by-step explanation:
First, order the data set:
5.88 6.12 6.21 6,55 6.55 6.55 7.47 7.48 7.48 8.37
The mode set is 6.55
What is the domain and range of the function below?
The process of measuring, analyzing, enhancing, and then controlling processes once they have been brought within the narrow six sigma quality tolerances or standards is referred to as the:______.
The process of measuring, analyzing, enhancing, and then controlling processes once they have been brought within the narrow Six Sigma quality tolerances or standards is referred to as the
Six Sigma process
What is Six Sigma?The phrase "Six Sigma" refers to a collection of quality-control methods that organisations can utilise to get rid of flaws and enhance operations so as to increase productivity and revenues. A scientist created it in the 1980s while he was employed by Motorola.
A statistical and data-driven technique called Six Sigma examines small errors or flaws. It places a focus on cycle-time gains while lowering manufacturing faults to no more than 3.4 incidents per million units or events. The fact that only 3.4 out of a million events along a bell curve will deviate by more than six standard deviations indicates that an error usually occurs with an event that deviates by six standard deviations from the mean.
To know more about Six Sigma, visit:
https://brainly.com/question/16180406
#SPJ4
Find the volume of the solid generated by revolving the region r bounded by y=e^-2x, y=0, x=0, x=ln9
The volume of the solid generated by revolving the region R bounded by
y = [tex]e^{-2x}[/tex], y = 0, x = 0, x = ln 9 around x-axis = 0.25 cubic units
Given the region R bounded by y = [tex]e^{-2x}[/tex], y = 0, x = 0, x = ln 9.
We will find the volume of the solid obtained by revolving this region around the x-axis through disc integration method.
The disc integration method is used to find the volume of a solid obtained by revolving a region around an axis parallel to x-axis.
Then, volume, V = [tex]\int\limits^0_{ln9} {y^2} \, dx[/tex]
= [tex]\int\limits^0_{ln9} {(e^{-2x})^2} \, dx[/tex]
= [tex]\int\limits^0_{ln9} {e^{-4x}} \, dx[/tex]
= [tex]\frac{e^{-4x}}{-4} |_{x=0\ to \ x=ln9}[/tex]
= [tex]\frac{e^{-4 ln9}}{-4} +\frac{1}{4}[/tex]
= [tex]\frac{9^{-4}+1}{4}[/tex] ≈ 0.25 cubic units
Learn more about disc integration method at https://brainly.com/question/24097453
#SPJ4
what is an equation of the line shown on the graph in the point-slope form, using the point(1,-1)
Please help in this questions there a pic for it.!
For 13 through 15 find the final answer
16 Just put final two answers, separate answers with a comma
Please help I really need it.
The amount of tax deductions in one payment period and one year based on a Social Security tax rate of 6.2% and Medicare tax rate of 1.45% are;
13. Kim's weekly Medicare deductions is $7.888
Her annual Medicare deductions is $410.176
14. Jeffrey's annual Social Security tax deductions is $3,517.0616
15. Kareem's annual Medicare tax deductions is $606.97
16. A. Parker's annual Social Security tax deductions is $4,836
B. His annual Medicare tax deductions is $1,131
Which method can be used to calculate the tax deductions?According to the accounting firm BGM website,in the year 2022, an employee is expected to pay a tax of 6.2% of the first $147,000 of wages, for Social Security, and a Medicare tax of 1.45% of the first $200,000
13. Kim's gross weekly salary is $544.
Given that 544 × 52 = 28,288 < 200,000, we have;
Kim's Medicare deduction for one pay period is 0.0145 × $544 = $7.888
Kim receives her payment weekly, therefore, multiplying by 52 gives;
Annual Medicare tax;
52 × $7.888 = $410.176
14. Jeffrey's semimonthly salary = $2,181.80
Jeffrey's tax deductions for Social Security for one pay period is therefore;
0.062 × $2,181.80 = $135.27160
The number of semimonthly payment periods in a year = 26
Jeffrey's annual Social Security tax deductions is therefore;
26 × $135.27160 = $3,517.061615. Kareem's gross biweekly salary is $1,610
Kareem's Medicare deductions per pay period is therefore;
0.0145 × $1,610 = $23.345
The number of biweekly pay periods in a year is 26
Kareem's total Medicare deductions for the year is therefore;
$23.345 × 26 = $606.9716. Parker's gross monthly salary is $6,500
A. Parker's Social Security deductions for one month is therefore;
0.062 × $6,500 = $403
The deductions in a year is therefore;
$403 × 12 = $4,836B. Parker's Medicare deductions for one month is given by the equation;
0.0145 × $6,500 = $94.25
Parker's Medicare deductions for one year is therefore;
12 × $94.25 = $1,131Learn more about tax deduction calculations here:
https://brainly.com/question/1775528
https://brainly.com/question/2317086
https://brainly.com/question/695693
#SPJ1
Ralph's grandmother was born in 1925. ralph was born in 1990. if both ralph and his grandmother took the intelligence quotient (iq) test, who would most likely get more items correct?
Ralph would most likely get more items correct than his Grandmother.
If both Ralph and his Grandmother took the Intelligence Quotient i.e., IQ test, then Ralph would most likely get more items correct than his Grandmother. This is due to Flynn Effect.
Flynn Effect refers to secular increase in population intelligence quotient observed throughout the 20th century. It demonstrates that the average of the IQ scores will change as varying generations have different thresholds for what intelligence is necessary.
Flynn Effect is documented by Flynn in a study on intelligence quotient. As Ralph's grandmother was born on 1925 and Ralph was born in 1990, so they have a generation gap of almost six decades. That is why Ralph will have a higher IQ than his grandmother.
Know more about Flynn Effect:
brainly.com/question/10607327
#SPJ4
Which is the first error that Tomas made?
Answer:
on what nothing there
Step-by-step explanation:
a 2 yard piece of aluminum wire cost $16.44 what is the price per foot?
Answer: The price per foot will be 2.74$
Step-by-step explanation:
what is the relation between yard and foot?
The value of one yard is equal to3 feet.
That is given by ,
1 yard =3 feet.
we have 2 yards piece of aluminium wire
Firstly,we have to find the cost of 2 pieces of aluminium wire.
2×3=6
The cost is 16.44
16.44/6=2.74.
Therefore the price per foot will be $2.74.
To learn more about the unit conversion
visit; https://brainly.com/question/13016492
Answer:2.74
Step-by-step explanation ; firstly we have to find the cost for 2 pieces of wire . 2×3≈6. the cost is 6. 16.44÷6=2.74. therefore the price per foot will be 2.74.Help me, please?????
Answer: The equation is true
Step-by-step explanation:
Since x=3 and y= 5
Substitute the values for x and y
y=2x-1
5=2(3)-1
5=6-1
5=5
⇒The equation is true
The difference of two natural number is 2. The sum of their squares is 100.Find the numbers.
The required two numbers are 6 and 8.
Let us denote the required numbers by c and d.
Given that the difference between two natural numbers is 2.
If we assume d > c, then d – c = 2
⇒ d = 2 + c → equation 1.
Also given that the sum of their squares is 100.
⇒ c² + d² = 100
⇒ c² + (2 + c)² = 100 (using the value of d from equation 1)
⇒ 2c² + 4c + 4 = 100
⇒ 2c² + 4c = 96
⇒ 2c(c+2) = 96
⇒ c(c+2) = 48
Using the factorization for 48, we get 6 × 8 = 48
⇒ c = 6
⇒ c+2 = 8
⇒ d = 8
Therefore, the required two numbers are 6 and 8.
Learn more at:
https://brainly.com/question/10005040
#SPJ9
help please
15 points
need by the end of today
9. Enrique would earn $7. 50 per hour. Option B
10. The number of girls that were at the assembly is 1390 . Option J
11. 40% of 60 is 24 . Option C
12. The simple interest is $72. 00 . Option F
13. The factory produces 1080 shoes on Tuesday. Option D
How to determine the value9. From the information given, we have;
He earns $420He works a total of 56 hoursHe would earn;
= 420/ 56
= $7. 50 per hour
10. We have that;
There are 1200 boys at the assemblyRatio of boys to girls is 20: 23The number of girls at the assembly would be;
= 23/ 20 × 1200
= 1. 15 × 1200
= 1380
11. Let the number be x
40% of x = 24
40/ 100x = 24
0. 4 x = 24
Make 'x' the subject
x = 24/ 0. 4
x = 60
12. The formula for simple interest is expressed as;
Simple interest = PRT / 100
Simple interest = 300 × 4 × 6/ 100
Simple interest = 7200/ 100
Simple interest = $72. 00
13. We have that;
Monday's production = 900 shoes
Tuesday's production = 900 + 900 × 20% = 900 × 20/ 100 = 18000/ 100 = $900 + 180
= $1080
Thus, the total amount Enrique earns per hour is $7. 50 .Option B
Learn more about word problem here:
https://brainly.com/question/13818690
#SPJ1
k) pq (r² + 1) - r (p² + q²)
Answer:
pqr²−p²r−q²r+pq
Step-by-step explanation:
Let's simplify step-by-step.
pq(r²+1)−r(p²+q²)
Distribute:
=(pq)(r²)+(pq)(1)+−p²r+−q²r
=pqr²+pq+−p²r+−q²r
=pqr²−p²r−q²r+pq
what is 2 -x/15=-3 pls give in step by step explatorn or do work in paper
Answer:
2 + -x/15 = -3 the answer is x = 75Step-by-step explanation:
2+-x15 = -3
15.2 2 /15 -x =3
30 -x /15 = -3 x= 75
