Answer:
[tex]\mathbf{6xe^xy+y^2e^x = C}[/tex] which implies that C is the integrating factor
Step-by-step explanation:
The correct format for the equation given is:
[tex]y(6x+y +6)dx +(6x +2y)dy=0[/tex]
By the application of the general differential equation:
⇒ Mdx + Ndy = 0
where:
M = 6xy+y²+6y
[tex]\dfrac{\partial M}{\partial y}= 6x+2y+6[/tex]
and
N = 6x +2y
[tex]\dfrac{\partial N}{\partial x}= 6[/tex]
∴
[tex]f(x) = \dfrac{1}{N}\Big(\dfrac{\partial M}{\partial y}- \dfrac{\partial N}{\partial x} \Big)[/tex]
[tex]f(x) = \dfrac{1}{6x+2y}(6x+2y+6-6)[/tex]
[tex]f(x) = \dfrac{1}{6x+2y}(6x+2y)[/tex]
f(x) = 1
Now, the integrating factor can be computed as:
[tex]\implies e^{\int fxdx}[/tex]
[tex]\implies e^{\int (1)dx}[/tex]
the integrating factor = [tex]e^x[/tex]
From the given equation:
[tex]y(6x+y +6)dx +(6x +2y)dy=0[/tex]
Let us multiply the above given equation by the integrating factor:
i.e.
[tex](6xy+y^2 +6y)dx +(6x +2y)dy=0[/tex]
[tex](6xe^xy+y^2 +6e^xy)dx +(6xe^x +2e^xy)dy=0[/tex]
[tex]6xe^xydx+6e^xydx+y^2e^xdx +6xe^xdy +2ye^xdy=0[/tex]
By rearrangement:
[tex]6xe^xydx+6e^xydx+6xe^xdy +y^2e^xdx +2ye^xdy=0[/tex]
Let assume that:
[tex]6xe^xydx+6e^xydx+6xe^xdy = d(6xe^xy)[/tex]
and:
[tex]y^2e^xdx +e^x2ydy=d(y^2e^x)[/tex]
Then:
[tex]d(6xe^xy)+d(y^2e^x) = 0[/tex]
[tex]6d (xe^xy) + d(y^2e^x) = 0[/tex]
By integration:
[tex]\mathbf{6xe^xy+y^2e^x = C}[/tex] which implies that C is the integrating factor
Can someone help me with this math homework please!
Answer:
The first answer
Step-by-step explanation:
Domain refers to the set of x values and range refers to the set of y values. Since x goes from 0 to 3, and does not exclude any values within those numbers, the first answer applies to that set.
Answer:
option 1
that is
{t| 0 <= t <= 3}
Step-by-step explanation:
as the graph plots height ove time
time will be the domain, taken on the x axis, with values ranging from 0 to 3.
so the domain is
{t| 0 <= t <= 3}
Clare has $150 in her bank account, She buys a bike for $200 whatsis Clare's balance now
Answer pls
Answer:
-50
Step-by-step explanation:
5 + 3bc =
9a + b =
cd + bc =
Answer:
You can't answer these questons
sorry
Hope This Helps!!!
Convert
[−1,∞) to inequality notation use the variable x.
Answer:
[tex]-1\leq x<\infty[/tex]
Step-by-step explanation:
We want to convert the interval [-1, ∞) to inequality notation using x as the variable.
The interval [-1, ∞) reads: "All real numbers between -1 and positive infinity."
In other words, it is all numbers greater than or equal to -1 and less than positive infinity.
Therefore:
[tex]-1\leq x<\infty[/tex]
Note that we do not use "or equal to" for the infinity as we can never really "equal" infinity.
Which equation represents the graphed function?
O-3x + 2 = y
0 x+2=y
ox-3=y
O 2x - 3= y
Answer:
y = 3/2x -3
Step-by-step explanation:
The general equation of a straight line is;
y = mx + b
where m is slope and b is the y-intercept
Here, we can see that the graph intercepts the y-axis at the point y = -3
So b = -3
To get m, we can substitute any other point values on the plot
We can select (2,0)
So we have;
y = mx -3
0 = 2m -3
2m = 3
m = 3/2
so;
y = 3/2x -3
Find the missing side. Round to the nearest tenth. (ITS DUE IN THE MORNING PLEASE HELP)
24.
A) 14.2
C) 13.8
B) 9.2
D) 15.7.
25.
A) 37.6
B)30.8
C) 45.1
D)5.5
Answer:
24. A)14.2
25. D)5.5
Step-by-step explanation:
I hope it help for you keep safe
You wish to purchase a new car and can afford monthly repayments of up to $250 per month. You see a car you like for $12,000 and are offered financing to secure the purchase. The loan lasts for 5 years and the annual interest rate is 17.9%. Can you afford to purchase the car on finance?
Answer:
Since the finance’s monthly required payment of $304.07 is greater than the $250 monthly that you can afford, this implies that you CANNOT afford to purchase the car on finance.
Step-by-step explanation:
The monthly required payment of the finance can be calculated using the formula for calculating the present value of an ordinary annuity as follows:
PV = M * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)
Where;
PV = Present value or finance amount = $12,000
M = Finance’s monthly required payment = ?
r = Monthly interest rate = Annual interest rate / 12 = 17.9% / 12 = 0.179 / 12 = 0.0149166666666667
n = number of months = Number of years * 12 = 5 * 12 = 60
Substitute the values into equation (1) and solve for M, we have:
$12,000 = M * ((1 - (1 / (1 + 0.0149166666666667))^60) / 0.0149166666666667)
$12,000 = M * 39.464764662266
M = $12,000 / 39.464764662266 = $304.07
Since the finance’s monthly required payment of $304.07 is greater than the $250 monthly that you can afford, this implies that you CANNOT afford to purchase the car on finance.
8
6471 sq. in.
25671 sq. in.
1,02471 sq. in.
Answer:
102471 sq .in the land answer Teri ma ki bosra
Answer:
=256 pi
Step-by-step explanation:
The surface area of a sphere is
SA = 4pi r^2
SA = 4 pi (8)^2
= 4 * pi *64
=256 pi
the temperature is -3 at 6am but it rises to 12 at the afternoon what is the temperature In the afternoon
Answer:
1cm divided by 17 = 32 then subtract the 32 into 17
The volume of air inside a rubber ball with radius r can be found using the function V(r)= 4/3pier^3 what does V(5/7) represent?
Answer:
Step-by-step explanation:
I can tell you what it represents, but not what it means. Or maybe the units.
V(5/7) means that wherever you see an r on the right hand side, you put in 5/7 where the R is.
V = 4/3 * pi * r^3
V(5/7) = 4/3 * 3.14 * (5/7)^3
V(5/7) = 4/3 * 3.14 * 125 / 343
V(5/7) = 4/3 * 3.14 * 0.3644
V(5/7) = 1.526 cubic units (of whatever the units of 5/7 were to begin with)
A rectangle has a perimeter of 46 cm with a length of 12 cm. What is its width
Answer:
11 cmStep-by-step explanation:
Given:
Perimeter = 46 cm
Length = 12 cm
To Find:
Width = ?
Solution:
Perimeter of Rectangle = 2( l + b)
We know the value of length
So, we can express this as a linear equation,
[tex]2(l + b) = 46 \\ 2(12 + b) = 46 \\ 24 + 2b = 46 \\ 2b = 46 - 24 \\ 2b = 22 \\ b = \frac{22}{2} \\ b = 11[/tex]
So therfore, the width/breadth of the rectangle is 11.
Express the polynomial −g + 3g + 2g2 in standard form and then classify it.
cubic binomial
quadratic binomial
cubic trinomial
quadratic trinomial
Answer:
quadratic binomial
[tex]{ \boxed{ \bf{a {x}^{2} + bx + c }}} \\ 2 {g}^{2} + 3g - g[/tex]
The graph below shows the solutions to which inequality?
Which equation can be used to determine the reference angle
Answer:
2nd option
Step-by-step explanation:
[tex]\frac{7\pi }{12}[/tex] is an angle in the second quadrant
Thus to find the reference angle, subtract from π , that is
r = π - θ
Which statements are true about the result of simplifying this polynomial?
+ (8 + 9t) – (t2 + 4)(+2 – 3t)
The simplified expression has four terms.
The simplified expression is a polynomial.
The simplified expression has a constant term.
The simplified expression is cubic.
a
The simplified expression is a trinomial.
Answer:
The simplified expression has four terms.
The simplified expression has a constant term.
The simplified expression is cubic.
The simplified expression is a trinomial.
The statements that are true about the result of simplifying this polynomial are:
b. The simplified expression is a polynomial.
c. The simplified expression has a constant term.
What are polynomials?Sums of terms of the form k x xⁿ, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. A description of polynomials.
All other options are false. As it is not cubic because it is degree 4, and it does not have four terms as it has five terms. And it is not trinomial as it has five terms, not three.
The full solution is;
t³(8 + 9t) - (t² + 4)(2 - 3t)
8t³ + 9t⁴ - (2t² - 3t³ + 8 - 12t)
8t³ + 9t⁴ - 2t² + 3t³ - 8 + 12t
9t⁴ + 11t³ - 2t² + 12t - 8
Therefore, the correct options are a, and b.
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Solve the solution of this inequality 4/9x-10>x/3-12
The volume of a cuboid is 975cm3.
The length is 15cm and the width is 130mm.
Work out the height of the cuboid in cm
Answer:
Solution given:
Volume of cuboid=975cm³
length[l]=15cm
width[w]=130mm=13cm
height [h]=?
we have:
Volume of cuboid=l*w*h
975=15*13*h
h=[tex]\frac{975}{195}=5cm[/tex]
The height of the cuboid is 5cm.
Using the unit circle, what is the exact value of tan pi/6?
Answer:
1/root(3)
Step-by-step explanation:
the steps are in the pic above.
The value of tan pi/6 is 0.5773502.
What are trigonometric functions?The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others.
Given that, what is the exact value of tan pi/6,
To find the value of tan π/6 using the unit circle:
Rotate ‘r’ anticlockwise to form pi/6 angle with the positive x-axis.
The tan of pi/6 equals the y-coordinate(0.5) divided by the x-coordinate(0.866) of the point of intersection (0.866, 0.5) of unit circle and r.
Hence, the value of tan pi/6 = y/x = 0.5774 (approx)
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Triangle ABC has an Area of 4 3/8 square feet. If the length of AC IS 1 2/3 feet, what is the length of BC?
Answer:
length of BC = 5 1/4 feet
Step-by-step explanation:
Area of a triangle = 1/2×base×height
Area = 4 3/8 square feet
Base = AC= 1 2/3 feet
Height = BC = ?
Area of a triangle = 1/2×base×height
4 3/8 = 1/2 × 1 2/3 × height
35/8 = 1/2 × 5/3 × height
35/8 = 5/6 × height
Height = 35/8 ÷ 5/6
= 35/8 × 6/5
= (35 × 6) / (8 × 5)
= 210 / 40
= 5 1/4 feet
Height = BC = 5 1/4 feet
length of BC = 5 1/4 feet
Recall how the sorceress's twin
brother converts blueberries by
adding 9 to the number of
blueberries given to him and then
doubling it. Find the output if he is
given zero blueberries.
The wizard returns blueberries.
Answer:
18 blueberries
Step-by-step explanation:
also nice zoro profile pic
Question
The quotient of a number and 5 has a result of 2. What is the number
Answer:
Probably 10
Step-by-step explanation:
10/5=2
Alice bought a (k) kg of pork and (i) kg of chicken. how many kg of meat did alice buy??
Write the solutions and explanation with algebraic expression
Answer:
(k)kg+(l)kg=kg
Step-by-step explanation:
I just looked at letters. it's definitely wrong but I typed something so I could get points and get my answers. idc tbh but good luck ig
The Marked price of an article was fixed to Rs 1380 by increasing 15% on its actual price. Find the actual price.
Answer:
The actual price of the article was Rs. 1200.
Step-by-step explanation:
mp (marked price)
ap (actual price)
[tex]mp = 1380[/tex]
[tex]mp = ap + 15\%(ap)[/tex]
[tex]1 380 = ap + \frac{15}{100} ap[/tex]
[tex]1380 = \frac{100}{100} ap + \frac{15}{100} ap[/tex]
[tex]1380 = \frac{115}{100} ap[/tex]
[tex]1380 \div \frac{115}{100} = ap[/tex]
[tex]1380 \times \frac{100}{115} = ap[/tex]
[tex] \frac{138000}{115} = ap[/tex]
[tex]1200 = ap[/tex]
The actual price of the article is given by the equation A = $ 1,200
What is an 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.
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 data ,
Let the actual price of the article be A
Now , the equation will be
The marked price of the article be = $ 1380
The percentage of increase from the actual price = 15 %
So , the equation is
The actual price + percentage of increase from the actual price = 1380
Substituting the values in the equation , we get
A + ( 15/100 )A = 1380 be equation (1)
( 115/100 ) A = 1380
Multiply by 100 on both sides of the equation , we get
115A = 138000
Divide by 115 on both sides of the equation , we get
A = $ 1200
Therefore , the value of A is $ 1200
Hence , the actual price of the article is $ 1200
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Find the area of the rectangle whose dimensions are 5 cm x 9 cm.
Answer:
45 square cm
Step-by-step explanation:
To find the area you multiply the length by the width. 5 times 9 is 45
Cual de las siguientes fracciones es equivalente a 6/18
1/3
2/3
3/18
3/6
Answer:
the answer is going to be 1/3
The students at Southern Junior High School are divided into four homerooms. Benjamin just moved into the school district and will be randomly assigned to one homeroom.
Which methods can be used to simulate this situation? Select three options..
Flip a coin 4 times, once for each homeroom, with heads up representing being assigned to the homeroom represented by that flip.
Draw a marble from a bag containing 5 white marbles, 5 black marbles, 5 red marbles, and 5 green marbles, with each color representing a different homeroom.
Use a random number generator with 1, 2, and 12 representing the first homeroom, 7, 9, and 10 representing the second homeroom, 3, 8, and 11 representing the third homeroom, and 4, 5, and 6 representing the fourth homeroom.
Roll a number cube with 1 representing the first homeroom, 2 representing the second homeroom, 3 representing the third homeroom, and any other outcome representing the fourth homeroom.
Spin a spinner with 8 congruent sections with 2 sections assigned to each homeroom.
Step-by-step explanation:Spin a spinner with 8 congruent sections with 2 sections assigned to each homeroom.
4c = 3c + 4
my answer :
4c = 4 - 3c
4c = 1c
c = 4/1
c= 4
just checking, Is this Correct?
Answer:
c = 4
See explanation
Step-by-step explanation:
Given:
4c = 3c - 4
Your calculation:
4c = 3c + 4
4c = 4 - 3c
4c = 1c
c = 4/1
c= 4
Correct calculation:
4c = 3c + 4
Collect like terms by subtracting 3c from both sides
4c - 3c = 3c + 4 - 3c
c = 4
Check:
4c = 3c + 4
4(4) = 3(4) + 4
16 = 12 + 4
16 = 16
Therefore,
Your final answer is correct but your method of calculation is not correct
Choose the appropriate word or phrase from the drop down menu to complete the sentences: The mean of the quantitative variable of interest in the population is called the [ Select ] . The mean of the quantitative variable of interest in the sample is called the [ Select ] . The standard deviation of the quantitative variable of interest in the population is called the [ Select ] . The standard deviation of the quantitative variable of interest in the sample is called the [ Select ] .
Answer:
1. Population mean
2. Sample mean
3. Population standard deviation
4. Sample standard deviation
Step-by-step explanation:
Required
Complete the gaps
The answer is self-explanatory.
All you need to do in this question is to look for the keywords (mean/standard deviation) and (population/sample).
In addition, the symbol of the parameters are:
1. Population mean [tex]\mu[/tex]
2. Sample mean [tex]\bar x[/tex]
3. Population standard deviation [tex]\sigma[/tex]
4. Sample standard deviation [tex]\sigma_x[/tex]
9. Solve the system of equations using substitution.
3y = -5x+2.
y = -x + 9
Answer:
y=43/2
Step-by-step explanation:
The value of -9 is __ than the value of -12 because -9 is to the __of -12 on the number line.
Less
Or
Greater
Answer:
Step-by-step explanation:
-9 is greater than the value of -12 because -9 is to the right of -12 on the number line.