None of the equations in Problems 1 through 8 is exact, so they cannot be solved using the method of integration factors.
If an ODE is exact, it can be solved using the method of integration factors.
Here is the determination of whether each of the equations in Problems 1 through 8 is exact, and if it is, finding the solution:
1. (2x + 3) + ( 2y - 2)y' = 0
This equation is not exact.
2. (2x + 4y) + ( 2x - 2y)y' = 0
This equation is not exact.
3. (3x^2 - 2xy + 2) + ( 6y^2 - x^2 + 3) y' = 0
This equation is not exact.
4. dx/dt = bx + cy, dy/dt = ax - by
This system of ODEs is not exact.
5. dx/dt = bx - cy, dy/dt = ax + by
This system of ODEs is not exact.
6. (ye^(2x) -2e^(2x)x sin(2x)+2x)+(xe^(2x)y cos(2x) -3) y'=0
This equation is not exact.
7. (y/x+6x) +(In x - 2)y' = 0, x > 0
This equation is not exact.
8. (y^2)dy/dx + 0 = (x^2 + y^2)^(3/2)
This equation is not exact.
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ANWSER 1 AND 2 PLEASE!!!
1. Carter bought a jet pack, he flew for 17 miles at 2 miles per minute. How long did carter travel on his jet pack?
2. Aniya has just become the world champion of cartwheels. She is able to travel at 0.5 mph doing cartwheels. She went a distance of 0.1 miles. How long did Aniya do cartwheels?
Answer:
The trip took 2.5 hours
Step-by-step explanation:
Answer:
1. 8 minutes and 30seconds
Step-by-step explanation:
Divide 17*2= 8.5
Use a net of the square pyramid, if necessary, to find the surface area of the pyramid.
The surface area of the pyramid is 25 + 10h.
What is pyramid?A three-dimensional shape is a pyramid. A pyramid's flat triangular faces unite at a common point known as the apex and have a polygonal base. The bases are joined to the peak to create a pyramid. The lateral face is a triangle face formed by the connection of each edge of the base to the apex.
Given:
A pyramid with the square base.
The side of the base is 5 unit.
So, the surface area of the pyramid,
= base area + 1/2 x perimeter of base x slant height
= (5 x 5) + 1/2 x (4 x 5) + h
= 25 + 10h
Hence, surface area is 25 + 10h.
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A sales intern in a US metals company uses this graphic to follow industry trends and make informed business decisions. What graphic evidence best supports the claim that India is unlikely to be a strong competitor in the steel production industry in the future? India’s rate of steel production has gradually risen over China’s. India’s level of steel production in 2009 was much lower than that of all other countries. India’s total steel production and rate of production over a 30-year period has remained flat. China, Japan, and the US have had a much greater experience than India in producing steel
The graph backs up the assertion that India is unlikely to be a serious competitor in the steel production industry in the future because China, Japan, and the US have far more experience producing steel than India does.
What is an industry?A group of businesses or organisations that offer comparable goods or services is referred to as an industry. A few examples of the factors that can be used to define an industry include the kind of products or services they offer, their manufacturing procedures, the technology they use, or the customers they aim to serve. Development of industries was a result of the Industrial Revolution.
The graph shows that China, Japan, and the US all have a lot more experience making steel than India does, and India is not expected to become a significant competitor in the near future. Notwithstanding the nation's economic crisis, the industry—despite being one of the sectors that suffered the most—continues to play a vital role in the expansion of the economy.
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The government of Mexico declared blue sharks an endangered species.
They put tags on 36 blue sharks and release them. Later, they corral 130
blue sharks; among those blue sharks, 20 were tagged. Find the best
estimate for the blue shark population?
The best estimate for the blue shark population would be = 234.
How to calculate the estimate for blue shark population?The total number of blue sharks that was tagged and released = 36 blue sharks.
The total number of sharks that the government corral = 130.
The number of sharks among the corral sharks that are tagged = 20
Since 130 = 20
X. = 36
Make X the subject of formula;
X = 130× 36/20
= 468/20
= 234.
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Pls help Im so confused
Answer:
57 ft
Step-by-step explanation:
Solution Given:
BC =40ft it also known as a.
<C=55°
<B=90°
<C=180-90-55=35°
height of the building =? also known as c
we have
law of sines
[tex]\frac{Sin A}{a} =\frac{Sin B}{b}=\frac{Sin C}{c}[/tex]
By inserting value[tex]\frac{Sin 35}{40} =\frac{Sin 55}{c}[/tex]
you can take any two what you want
doing criss cross multiplication
Sin 35*c=Sin55*40
we get
c=sin55 * 40 /Sin35
c=AB=57.12 ft in nearest 10 it is 57 ft
2) If r=9, b=5, g=-6 , what does (r+b-g)(b+g) equal? A)-20 B) -8 C)8 D)19 E)20
Work Shown:
(r+b-g)(b+g)
(9+5-(-6))(5-6)
(9+5+6)(5-6)
(20)(-1)
-20
A city engineer has estimated the annual toll revenues from a newly proposed highway construction over 20 years as follows: An ($2,000,000) (n) (1.06)" 1, n = 1,2, ..., 20. To validate the bond, the engineer was asked to present the estimated total present value of toll revenue at an interest rate of 6%. Assuming annual compounding, find the present value of the estimated toll revenue.
Answer:
get a life
Step-by-step explanation:
The present value of the estimated toll revenue for the proposed highway construction is approximately $31,333,333.33.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Now, Using the formula for the present value of an annuity, with a rate of 6% and 20 years, we get:
Present Value = $2,000,000 [ (1 - (1+0.06)⁻²⁰) / 0.06 ]
= $2,000,000 [ (1 - 0.312) / 0.06 ]
= $31,333,333.33
So, the present value of the estimated toll revenue for the proposed highway construction is approximately $31,333,333.33.
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What are all the factors of the number 16
Answer: 1,2,4,8,16
Step-by-step explanation: All of the factors of a number multiply to equal a certain number.
please help me with this question thank you
Question 3: Solve each of the following equations using completing the square
Write each answer in simplified surd form
(a) x² + 4x-3=0
The value of x is 0.645 and x= 4.645.
what is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
x² + 4x-3=0
Now, using Completing the Square method we have to half the coefficient of x and add and subtract the square.
then, x² + 4x-3=0
x² + 4x-3 + 2² - 2² =0
x² + 4x + 2² -3 - 2² =0
(x+ 2)² - 7 = 0
(x+ 2)² = 7
x+ 2= ±2.645
x= 0.645 and x= 4.645
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The bearing of a ship R from a lighthouse L is 220°
A canoe C is due North of R.
C is the same distance from the ship and the lighthouse.
What is the bearing of L from C?
The bearing of L from C is 50°.
How to solve for the bearing of lighthouse L from canoe CFirst we need to use the concept of transitive bearings. Given the bearing of the ship R from lighthouse L as 220°, and the fact that canoe C is equidistant from R and L,
we can set up a pair of complementary angles to find the bearing of L from C.
Since C is due North of R, the bearing of R from C is 90°. Then, the bearing of L from R is 90° + 220° = 310°.
To find the bearing of L from C, we subtract this angle from 180°.
Therefore, the bearing of L from C is 180° - 310° = 50°.
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using the following data on the observations 10, 13, 4, and 20, confirm that the complete linkage distance between the cluster containing {10, 13} and the cluster containing {4, 20} is 2.577 units as displayed in the dendrogram.
According to the dendrogram, the complete linkage distance between the cluster containing {10, 13} and the cluster containing {4, 20} is 2.577 units.
A dendrogram is a type of diagram that is used to represent the structure of a set of objects, where the objects are linked together in a hierarchy.
Now, let's take a closer look at the dendrogram that displays the complete linkage distance between the cluster containing {10, 13} and the cluster containing {4, 20}.
In this case, the maximum distance is
=> 20 - 4 = 16 units.
Next, we need to normalize the distance by dividing it by the square root of the number of data points in the two clusters. In this case, there are 4 data points in total, so the normalized distance is
=> 16 / √4 = 4.
Finally, we can use the formula for the complete linkage distance, which is given by
D = √2 * (1 - x),
where x is the normalized distance. Plugging in our values, we get
D = √2 * (1 - 4) = √2 * -3 = -2.236 units.
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the following are two points in a data set, find the euclidean distance between them. (1.0, 6.1) and (3.3, 8.7) round your answer to 1 decimal place.
The Euclidean distance between (1.0, 6.1) and (3.3, 8.7) is 3.48, rounded to 1 decimal place.
The Euclidean distance formula is used to calculate the distance between two points in a two-dimensional plane. The formula for Euclidean distance between two points (x1, y1) and (x2, y2) is given by:
[tex]d = √(x2-x1)2 + (y2-y1)2[/tex]
For our two points, (1.0, 6.1) and (3.3, 8.7), the Euclidean distance is:
[tex]d = √(3.3-1.0)2 + (8.7-6.1)2 \\ = √(2.3)2 + (2.6)2 \\ = √5.29 + 6.76 \\ = √12.05 \\ = 3.48[/tex]
Therefore, the Euclidean distance between (1.0, 6.1) and (3.3, 8.7) is 3.48, rounded to 1 decimal place.
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What is the product of 8.5\times 10^38.5×10 3 and 2.6 \times 10^32.6×10 3 expressed in scientific notation?
Answer:
8.468579573930919e+40
2.768574091477416e 41
Step-by-step explanation:
Linear equation that passes through the points of (3,4) and (0,5)
Answer:
y=-2/6+5
Step-by-step explanation:
At the sewing store, Olivia bought a bag of mixed buttons. She got 27 large buttons and 63 small buttons. What percentage of the buttons were large?
Answer: 80%
Step-by-step explanation:
Large Buttons=64
Small buttons = 16
64+16=80 (the total amount of buttons she got)
64/80 * 100%
0.8 * 100%
80%
Eva got an 80% of large buttons
Describe the possible echelon forms of the standard matrix for a lineartransformation T where T: R^4 --> R^3 is ontoGive some examples of the echelon forms. The leading entries, denoted , may have any nonzero value; the starred entries, denoted t, may have any value (including zero)
Possible echelon forms for matrix are:
[tex]\left[\begin{array}{ccc}Y&&\\0&Y&\\0&0&Y\\0&0&0\end{array}\right][/tex]
What exactly is a matrix?A collection of integers organised in rows and columns to form a rectangular array. The numbers are referred to as matrix elements or entries. Matrices are widely used in engineering, physics, economics, and statistics, as well as in many disciplines of mathematics. Matrices have also found usage in computer graphics, where they have been utilised to represent picture rotations and other transformations.
If there are m rows and n columns, the matrix is said to be an “m by n” matrix, written “m × n.” For example,
[tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\end{array}\right][/tex] its a 2×3 matrix.
The proof of the theorem proves that the columns, say, A and B must be independent.
In the matrix, there is linearity and the trivial solution would be [ 0, 0 , 0 , 0] for the matrix to exist. In other words, all the unknowns must be zero.
This establishes the fact that the matrix T needs to be independent for the matrix function, say T (x) to be one-to-one.
By definition, one-to-one is ker (T) = {0}
Thus, the null space is occupied only by the zero vector.
Note: if there was no linear independence in the vectors, the solution would not be zero in the vector.
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solve for x: [tex]2/3[/tex]x=6
Answer:
x = 9
Step-by-step explanation:
⅔x = 6
3/2 × ⅔x = 3/2×6
½ × 2 = 3×3
x = 9
PLEASE HELP!
Determine the terms and the coefficients of the terms for the
polynomial
x^2-3x+2
Complete the table for the polynomial
Terms Coefficients
X^2 ?
? -3
2 ?
Answer:
x^2=1
3x=+3
2=+2
Step-by-step explanation:
answers
1
3x
+2
hope it helps
The population of a colony started with 1,120 grows at an annual rate of 4.98%. How much more would you have, at the same time if you used continuous growth, compared to a growth rate when the continuous reaches 3,480?
The number of years its to make 3,480 is approximately 23 years.
What is population growth and population decrease formula?If a constant rate of growth be R% per annum, then population after n years = P(1+R/100)ⁿ.
Given that, the population of a colony started with 1,120 grows at an annual rate of 4.98%.
Here, A =3480
Now, 3480=1,120(1+4.98/100)ⁿ
(1+4.98/100)ⁿ=3480/1,120
(1.0498)ⁿ=3.107
Take the logarithm of both sides of the equation to remove the variable from the exponent.
Exact Form:
n=ln(3.107)/ln(1.0498)
Decimal Form:
n=23.32644715
Therefore, the number of years its to make 3,480 is approximately 23 years.
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At a basketball game, a team made 52 successful shots. They were a combination of 1- and 2-point shots. The team scored 89 points in all. Write and solve a system of equations to find the number of each type of shot.
Answer:
15 1-point shots37 2-point shotsStep-by-step explanation:
You want a system of equations and their solution for the number of shots of each type if the total number is 52 and the points from 1- and 2-point shots total 89.
SetupLet x and y represent the numbers of 1- and 2-point shots, respectively. The problem description tells of two relations:
x + y = 52 . . . . . . . total of shots is 52
x + 2y = 89 . . . . . . total of points is 89
SolutionSubtracting the first equation from the second, we get ...
(x +2y) -(x +y) - (89) -(52)
y = 37
Then the first equation tells us ...
x = 52 -y = 52 -37 = 15
The team made 15 1-point shots and 37 2-point shots.
Is he redoing the whole yard or just the front?
He's redoing the whole yard
How much topsoil does he need?
You will have to figure that out.
Remember he's putting a new 4 inch layer down over all the area currently covered by grass in the overhead picture above.
How big is the yard?
You can estimate it using the overhead schematic.
What kind of pickup truck does he drive?
A 2003 Ford F-150 XL.
How much can the pickup carry?
The truck bed is 80 inches long, 69
inches wide, and 20 inches tall.
How much is the delivery charge?
$30 per truckload on top of the soil cost. Each truckload can deliver up
to 18 cubic yards.
How much does the topsoil cost?
$18 per cubic yard (sold in 1/4 cubic
yard increments).
How far is the soil store?
It is 9 miles away. It takes about 20 minutes to drive there.
What gas mileage does the pickup truck get?
It averages 17 miles to the gallon.
What is the current gas cost?
Assume it's $3.79/gallon.
Using this information, figure out whether your neighbor will save money by picking up the soil himself. Use the results of your calculations to guide your decision: would you recommend that your neighbor pick up the soil himself, or pay for delivery?
Written Assignment: Write out your calculations with college level presentation and written statements that guide the reader through your process. Don't just fill the page with calculations. Label with headers what calculations you are performing for each part of your analysis. Clearly write out your final conclusions with your cost analysis using complete sentences. You need to submit your best work for evaluation, not a page of scratch paper.
1. How big is the area of the yard?
Area of the property:
Area of the house:
Area of the driveway:
Area of the yard (property – house – driveway):
2. How much topsoil will your neighbor need?
Convert 4 inches to feet:
Compute the cubic feet:
Convert cubic feet to cubic yards:
3. How much does the topsoil cost?
Amount of topsoil to be purchased:
Cost:
4. How much is the cost for delivery?
Number of truckloads:
Cost:
5. How much is the cost for your neighbor to pick up the topsoil himself?
Volume of the truck bed:
Convert cubic inches to cubic yards:
Number of trips:
Miles for number of trips:
Cost for gas:
He has to replace around 1775 square feet of yard, therefore after adding the 4 inches, he will require a total of 592 cubic feet of earth.
What is area?An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The square unit, which is frequently expressed as square inches, square feet, etc., is the accepted unit of area.
My calculations show that my Neighbour would save $20 by collecting the soil themselves. According to my calculations, he has to replace around 1775 square feet of yard, therefore after adding the 4 inches, he will require a total of 592 cubic feet of earth.
On the other hand, the man's truck can hold 110,400 cubic inches of dirt, and we know that we need 1,023,000 cubic inches of dirt, so we did a cubic feet to cubic inches calculation and found that it will take us 10 loads to get all the dirt. The shipping company charges $30 to deliver 18 cubic yards of dirt, but our neighbour needs about 22 cubic yards, so they will need to take 2 trips totaling $60 to get all the dirt. Since the store is 9 miles away, it will take 18 miles to transport each load of dirt.
With a total distance of 180 miles to travel and my neighbor's truck getting 17 miles per gallon, our estimated gas consumption is 10.6 gallons. At $3.79 per gallon, the 10.6 gallons of gas we'll need will cost us about $40. This indicates that we will save $20 by picking up the dirt ourselves rather than having it delivered.
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What is equivalent to 9+7x-3y
Answer:
16-3y
Step-by-step explanation:
9+7= 16
16-3y. first u do the ones that the same and don't have a letter after them. then you do the letter which in this case u just put the minus sign befor and it cokes out to 16-3y.
5x+3y=-7 6x-7y=-8. Substitution method
The solution of the system is X = -73/53 and Y = -2/53.
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.
Given:
System of equations,
5X + 3Y = -7 {equation 1}
6X - 7Y = -8 {equation 2}
From equation 1,
Y = (-7-5X)/3
Substituting the value to the equation 2,
6X - 7{(-7-5X)/3} = -8
18X + 49 + 35X = -24
53X = -24 - 49
53 X = -73
X = -73/53
And Y = -2/53
Therefore, X = -73/53 and Y = -2/53.
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Solve the inequality for x.
-5x + 20 < 5
A x < 3
B x > 5
C x > -5
D x < -5
E x > 3
Answer: E. x > 3
Step-by-step explanation:
Step 1: Subtract 20 from both sides.
−5x +20 − 20 < 5 − 20
−5x < −15
Step 2: Divide both sides by -5.
−5x/−5 < −15/−5x
x > 3
On a number line, it would look like this:
Find the future value of the loan. Round your answer to the nearest cent. P= 1250, r= 3.31 t= 2 years==The future value of the loan is $
The future value of the loan is $1,333.86
What is Simple interest?A quick and easy method of calculating the interest charge on a loan is called a Simple interest.
Given that;
Values are,
P = 1250, r = 3.31 and t = 2 years
Now, We know that;
⇒ Amount = P (1 + r)ⁿ
Substitute all the values we get;
⇒ Future value = 1250 (1 + 3.31/100)²
⇒ Future value = 1250 (1 + 0.033)²
⇒ Future value = 1250 (1.033)²
⇒ Future value = 1250 × 1.067
⇒ Future value = $1,333.86
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Scientific notation
The Scientific notation of [tex]$0.09 \cdot\left(9 \times 10^{-4}\right)$[/tex] be 0.000081.
What is meant by Scientific notation?Very big or very small numbers can be written using scientific notation. Once a number between 1 and 10 has been multiplied by a power of 10, it is then expressed in scientific notation.
Simple numerical writing is what scientific notation is. Because it is shorter and more efficient and indicates magnitude very easily, it is particularly helpful for expressing very large or very small values. Every real number can be expressed as the product of two parts: an integer power of ten and a decimal part.
Let the equation be [tex]$0.09 \cdot\left(9 \times 10^{-4}\right)$[/tex]
Apply exponent rule: [tex]$\quad a^{-b}=\frac{1}{a^b}$[/tex]
[tex]$=9 \times 0.09 \times \frac{1}{10^4}$$[/tex]
Multiply fractions: [tex]$\quad a \times \frac{b}{c}=\frac{a \times b}{c}$[/tex]
[tex]$=0.09 \times \frac{1 \times 9}{10^4}[/tex]
[tex]$& \frac{1 \times 9}{10^4}=\frac{9}{10000} \\[/tex]
simplifying the above equation, we get
= 0.09 × 9/10000
Multiply fractions: [tex]$\quad a \times \frac{b}{c}=\frac{a \times b}{c}$[/tex]
= 9 × 0.09/10000
= 0.81/10000
Divide the numbers: 0.81/10000 = 0.000081
= 0.000081
Therefore, the Scientific notation of [tex]$0.09 \cdot\left(9 \times 10^{-4}\right)$[/tex] be 0.000081.
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Question content area top Part 1 Suppose the average yearly salary of an individual whose final degree is a master's is $44 thousand less than twice that of an individual whose final degree is a bachelor's. Combined, two people with each of these educational attainments earn $121 thousand. Find the average yearly salary of an individual with each of these final degrees. Question content area bottom Part 1 The average yearly salary for an individual whose final degree is a bachelor's is $ enter your response here thousand and the average yearly salary for an individual whose final degree is a master's is $ enter your response here thousand.
The average yearly salary of an individual with each of these final degrees is,
Master's individual earns average of $66,000 while the Bachelor's individual earns $55,000.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The average yearly salary of an individual whose final degree is a master's is $44 thousand less than twice that of an individual whose final degree is a bachelor's.
And, Combined, two people with each of these educational attainments earn $121 thousand.
Now, The total amount earned by a Bachelor's person be $x:
And, amount earned by a masters person will be; $(2x - 44)
Hence, Total amount earned by the two individuals will be;
⇒ x + (2x - 44) = 121
Solve for x as;
⇒ x + 2x - 44 = 121
⇒ 3x - 44 = 121
⇒ 3x = 121 + 44
⇒ 3x = 165
⇒ x = 165/3
⇒ x = 55
And, (2x - 44) = 2 × 55 - 44
= 110 - 44
= 66
Therefore we conclude that; master's individual earns average of $66,000 while the Bachelor's individual earns $55,000.
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13. ABCD is
a. Congruent
b. Similar
c. Neither
to A'B'C'D'.
Answer:
a
Step-by-step explanation:
Congruent shapes are shapes that are exactly the same. The corresponding sides are the same and the corresponding angles are the same. To do this we need to check all the angles and all the sides of the shapes. as you can see they are exactly the same
Answer:
Step-by-step explanation:
Similar
The brain volumes (cm³) of 50 brains vary from a low of 906 cm³ to a high of 1498 cm³. Use the range rule of thumb to estimate the standard deviations and compare the result to the exact standard deviation of 171 cm³, assuming the estimate is accurate if it is within 15 cm³.
The estimated standard deviation is
Answer:
Step-by-step explanation:
The range of the brain volumes is:
Range = highest value - lowest value = 1498 cm³ - 906 cm³ = 592 cm³
According to the range rule of thumb, the standard deviation can be estimated as:
Standard deviation ≈ Range / 4
Standard deviation ≈ 592 cm³ / 4 ≈ 148 cm³
The estimate of the standard deviation is within 15 cm³ of the exact standard deviation of 171 cm³, so it can be considered accurate according to the given criteria. However, note that the range rule of thumb is a very rough estimate and may not be very accurate in all cases.
Answer:
The range rule of thumb suggests that the estimated standard deviation is approximately 18.2 cm³. This estimate is within 15 cm³ of the exact standard deviation of 171 cm³, indicating that it is accurate.