the sum of two numbers is 22, and their difference is 12. set up two equations to solve using elimination to help you find the numbers. enter the lesser of the two numbers here:

The solution to the differential equation (x^3 + y^3) dx − xy^2 dy = 0 is y/x^3 = Ce^(−(y/x)^3), where C is an arbitrary constant.

Substituting y = vx and dy = x dv + v dx, we get:

(x^3 + (vx)^3)dx − x(vx)^2(x dv + v dx) = 0

Simplifying and rearranging, we get:

x^2v dx + (x^3 + 3xv^2 − v^3x^2)dv = 0

Dividing both sides by x^2v and rearranging, we get:

dx/x + (1/v)dv + (3/xv - v^2)dv = 0

Integrating both sides, we get:

ln|x| + ln|v| + 3ln|v/x| − v^3 = C

Where C is an arbitrary constant. Simplifying, we get:

ln|vx/x^3| = C − v^3

Rearranging, we get:

vx/x^3 = Ce^(−v^3)

Finally, we can express this in terms of x and y as:

y/x^3 = Ce^(−(y/x)^3)

The solution to the differential equation (x^3 + y^3) dx − xy^2 dy = 0 is y/x^3 = Ce^(−(y/x)^3), where C is an arbitrary constant.

Learn more about equation here

https://brainly.com/question/29657992

#SPJ4

The given sequence appears to be an arithmetic sequence, as the common difference between consecutive terms is 4.

The nth term of an arithmetic sequence is given by the formula: a_n = a_1 + (n-1)d, where a_1 is the first term, d is the common difference and n is the nth term.

Given that the first term of the sequence is 2, the common difference is 4.

To find the 41st term of the sequence, we can use the formula:

a_41 = 2 + (41-1) * 4 = 2 + 40 * 4 = 2 + 160 = 162

Therefore, the 41st term of the sequence is 162.

Answer:

250u2

Step-by-step explanation:

The volume of a cube is found by multiplying LxWxH. 5x5x5-125, 125x2-250

Hope this helped :)

The picture explains it all. We use tangent rule to find out the measure of angle A.

The measure of angle unknown angle is 30°.

Use the concept of the triangle defined as:

A triangle is a three-sided polygon, which has three vertices and three angles which has a sum of 180 degrees.

Given that,

Side AC = 6 units

Side BC = 3 units

Let ∠BAC = θ

Since we know that,

Sin θ = opposite/Hypotenuse

Sin θ = BC/AC

Put the values,

Sin θ = 3/6

Sin θ = 1/2

Since we know that,

sin(π/6) = 1/2

Therefore,

Sin θ = sin(π/6)

Take the inverse of sin on both sides we get,

θ = π/6 or 30°

Hence,

The measure of angle unknown angle is 30°.

To learn more about the triangle visit;

brainly.com/question/1058720

#SPJ4

Answer:

2 1/2 + b = 4 2/3

Tom's monthly mortgage repayment will be an amount of $1,144.41.

To calculate Tom's monthly mortgage repayment, we can use the formula:

[tex]M = P [ i(1 + i)^n ] / [ (1 + i)^n -1 ][/tex]

Where:

M = monthly repayment

P = the principal amount (loan amount) = $300,000 - $30,000 = $270,000

i = monthly interest rate = 2%/12 = 0.02/12 = 0.0017

n = number of months = 25 years x 12 months/year = 300 months

Plugging in the values:

M = $270,000 [ 0.0017(1 + 0.0017)³⁰⁰ ] / [ (1 + 0.0017)³⁰⁰ – 1 ]

M = $1,144.41

Thus, his monthly mortgage repayment will be $1,144.41.

Learn more about mortgage repayment here:

https://brainly.com/question/15063865

#SPJ1

Answer:

A polynomial’s degree is the highest or the greatest power of a variable in a polynomial equation. The degree indicates the highest exponential power in the polynomial (ignoring the coefficients).

For example: 6x4 + 2x3+ 3 is a polynomial. Here 6x4, 2x3, 3 are the terms where 6x4 is a leading term and 3 is a constant term. The coefficients of the polynomial are 6 and 2.

The degree of the polynomial 6x4 + 2x3+ 3 is 4.

Answer:

(100/500) *200 =40%

Step-by-step explanation:

Answer:

Angle A = 83.59° (2 d.p.)

Angle C = 56.41° (2 d.p.)

Side a = 193.25 (2 d.p.)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Sine Rule} \\\\$\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c} $\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}[/tex]

Given:

Substitute the given values into the Sine Rule formula:

[tex]\implies \dfrac{\sin A}{a}=\dfrac{\sin 40^{\circ}}{125}=\dfrac{\sin C}{162}[/tex]

Solve for angle C:

[tex]\implies \dfrac{\sin 40^{\circ}}{125}=\dfrac{\sin C}{162}[/tex]

[tex]\implies \sin C=\dfrac{162\sin 40^{\circ}}{125}[/tex]

[tex]\implies C=\sin^{-1}\left(\dfrac{162\sin 40^{\circ}}{125}\right)[/tex]

[tex]\implies C=56.4136175...^{\circ}[/tex]

Interior angles of a triangle sum to 180°. Therefore:

[tex]\implies A+B+C = 180^{\circ}[/tex]

[tex]\implies A = 180^{\circ}-B-C[/tex]

[tex]\implies A = 180^{\circ}-40^{\circ}-56.4136175...^{\circ}[/tex]

[tex]\implies A = 83.5863824...^{\circ}[/tex]

Finally, to find a, substitute the found angles and sides into the Sine Rule and solve for a:

[tex]\implies \dfrac{\sin A}{a}=\dfrac{\sin B}{b}[/tex]

[tex]\implies \dfrac{\sin 83.5863824...^{\circ}}{a}=\dfrac{\sin 40^{\circ}}{125}[/tex]

[tex]\implies a=\dfrac{125\sin 83.5863824...^{\circ}}{\sin 40^{\circ}}[/tex]

[tex]\implies a=193.248396...[/tex]

The in-house production  amount costs per foot of cables A, B, and C are $6, $8, and $10, respectively.

1. The question states that a company produces three types of cables, A, B, and C.

2. The in-house production amount costs for each type of cable is given in the question. The cost per foot of cable A is $6, the cost per foot of cable B is $8, and the cost per foot of cable C is $10.

The company produces three types of cables, A, B, and C, and each type of cable has a different in-house production cost. Cable A has a cost per foot of $6, cable B has a cost per foot of $8, and cable C has a cost per foot of $10. This means that if the company produces 100 feet of cable A, the in-house production cost would be $600, whereas if they produce 100 feet of cable B, the in-house production cost would be $800, and if they produce 100 feet of cable C, the in-house production cost would be $1000.

Learn more about amount here

https://brainly.com/question/8082054

#SPJ4

The area above x axis is 12.6 sq units while the area under the y-axis is 42.443 sq units. The change in the average phone bill is 29.843 units.

a) Here we see that the graph is in the shape of a right-angled triangle above the x-axis

The area of a triangle = 1/2 X Base X Height

Here the base will be the measure of the distance of co-ordinates on the x-axis

The height is the distance between the coordinates on the axis for that triangle

= 1/2 X (16 - 8) X (3.15 - 0)

= 1/2 X 8 X 3.15

= 12.60 sq units

b)

Below the x-axis, the graph is a rectangle and a triangle

The area of the rectangle = length X width

Here length is the distance of the co-ordinates of the y-axis and width is the distance between the coordinates for the x-axis

Hence we get

(0 - (-5.14))(8 - 0)

= 5.14 X 8

= 41.12 sq units for the rectangle.

The area of the triangle will be

1/2 X (18 - 15.48) X (0 - (-1.05))

1/2 X 2.52 X 1.05

= 1.323 sq unit

Hence, the total area is

41.12 + 1.323

= 42.443 sq unit

c)

Since the area under the graph represents change,

Here we see that the change in the average cell phone bill will be

42.443 + 12.6

= 55.043

To learn more about Co-ordinate Geometry visit

https://brainly.com/question/14515991

#SPJ4

Complete Question

(Image Attached)

To get the initial mass, set t = 0.

A(0) = 621 (1/2)0/30 g = 621 (1) g = 621 g

To get the mass after 100 years, just plug t = 100 into A(t) and evaluate.

A(100) = 621 (1/2)100/30 g = ? g

To learn more about  International System of Units (SI) refer to:

https://brainly.com/question/14288881

#SPJ1

The class width of the histogram is 5

A histogram is a visual representation of statistical data that makes use of rectangles to illustrate the frequency of data points over a range of successive numerical intervals of equal width called the class width.

The independent variable and dependent variable are plotted along the horizontal axis and the vertical axis, respectively, in the most common type of histogram.

The class width is plotted in the x - direction. this is the difference between the two consecutive values in the boundary.

class width = 100.5 - 95.5 = 5

class width = 85.5 - 80.5 = 5

learn more about class width at:

https://brainly.com/question/14378469

#SPJ1

Answer: Since the company is running short of cash they have failed or late to pay the shareholders' share of the profit which is the dividend.

The equation of the straight line would be -

y = 4x + 5.

Given is that a line y = mx + 5 that passes through the point (1, 6) and is parallel to y = 4x + 6.

       y = mx + c

Equation of the line is -

y = mx + 5

It is parallel to -

y = 4x + 6

Then -

m = 4  {slopes of || lines are equal)

So, we get the equation as -

y = 4x + 5

Therefore, the equation of the straight line would be -

y = 4x + 5.

To solve more questions on algebraic expressions, visit the link below -

brainly.com/question/1041084

#SPJ1

your solution

4+13x=57

x=53÷4 = 13.25

Answer:

this is a little typical

Slope is y is -1x + 1.

To enter data and find the equation's solution, we can utilize the equation's point-slope form.

use the point ( 2, 3) and the slope of 1.

m \s= \s− \s1

x \s1 \s= \s− \s2

y \s1 \s= \s3

In the point-slope formula,

y \s− \sy \s1 \s= \sm \s( \sx \s− \sx \s1 \s)

the values into the plug

y \s− \s3 \s= \s− \s1 \s( \sx \s− \s( \s− \s2 \s) \s)

symbol reduction

Distribute the 1 according to y 3 = 1 (x + 2).

Use additive inverse to find the y in the equation y = 3 = 1 x 2

y \s− \s3 \s+ \s3 \s= \s− \s1 \sx \s− \s2 \s+ \s3

simplify

y \s= \s− \s1 \sx \s+ \s1.

To learn more about Slope refer to:

https://brainly.com/question/3493733

#SPJ1

Answer:

5.92

Step-by-step explanation:

Set up a proportion

cups/mg = cups/mg

[tex]\frac{1.5}{148}[/tex] = [tex]\frac{6}{x}[/tex]

1.5 x 4 = 6,

so 1.48 x 4 = 5.92

The general solution with the initial condition y(-1)=C is y=-(1+x)/(6+x)=-2/7.

The general solution to the differential equation -6y = 1+x+y+xy is y = -(1+x)/(6+x). To apply the initial condition, we can substitute x=-1 and y=C into the above equation and solve for C. We get C=-(2/7). Therefore, the general solution to the differential equation with the initial condition y(-1)=C is y=-(1+x)/(6+x)=-2/7.

Substituting x=-1 and y=C into the equation:

-6C = 1-1+C+(-1)C

-7C = 1

C = -1/7

Therefore, the general solution with the initial condition y(-1)=C is y=-(1+x)/(6+x)=-2/7.

Learn more about differential equation here:

https://brainly.com/question/14620493

#SPJ4

Consequently, x∈R denotes that x belongs to the set of Real numbers. This means that x is a real number.

Hence, As a result, the symbol x∈R indicates that x is a member of the Real number set. Thus, x must be a real number.

To learn more about Real numbers, refer to:

https://brainly.com/question/17201233

#SPJ4

The linear equation in two variables is -5X + 10 = Y

A linear equation in mathematics is an equation that may be written as follows: Y = aX + b where a and b are the coefficients, which are frequently real numbers, and X and Y are the variables (or unknowns). As long as they don't contain any of the variables, the coefficients can be thought of as equation parameters and can be arbitrary expressions. The coefficients must not all be 0 in order to produce a meaningful linear equation.

A linear polynomial over a field, from which the coefficients are taken, can also be equalised to zero to produce a linear equation.

Such an equation's solutions are the values that, when used as placeholders for the unknowns, result in the equality being true.

Let us assume that given equation as  linear equation in two variables

Y = aX + b

Also, from the given table, the value which satisfy the equations are

X =3, Y = -5 and X = 4, Y = -10

using these values we have

-5 = 3a +b and -10 = 4a +b

subtracting both the equations we get,

-5 = a

Now putting this value in an equation we get

b = 10

so the general equation is -5X + 10 = Y

To learn more about linear equation from the given link

https://brainly.com/question/11897796

#SPJ1

Answer:

pie/8, 3pie/8

Or

B

The number of handshakes altogether exists 45.

In mathematics, there are two alternative methods for dividing up a collection of components into subsets: combination and permutation. The subset's components can be arranged in any sequence when used together. The components of the subset are arranged in a particular order in a permutation.

A combination in mathematics is a choice of elements from a set with distinct members, where the order of the choices is irrelevant.

Combinations are a mathematical method for calculating the number of alternative arrangements in a collection of objects where the order of the selection is irrelevant. You are free to choose any combination of the things.

Given:

Number of people in the conference = 10

Each person shakes hands with others.

The total number of handshakes [tex]$={ }^n \mathrm{C}_2$[/tex]

Total number of handshakes [tex]$={ }^{10} C_2=(10 \times 9) / 2=45$[/tex] handshakes.

The complete question is:

At the end of a meeting all the ten people present shake hands with each other once. The number of handshakes altogether is

To learn more about combinations refer to:

https://brainly.com/question/295961

#SPJ4

Answer:

   C

Step-by-step explanation:

2.52/4 =0.63/1

Answer:

Here is your answer. Hope this helps.

A) r(t) =[tex]c_{1}[/tex]×e^(∧×t)[tex]v_{1}[/tex]+ [tex]c_{2}[/tex] × e^(∧²×t)[tex]v_2[/tex]  ; B) r(t) = X×e^(∧×t)c ; C) [tex]r_1[/tex](t) = [tex]c_{1}[/tex](-1×[tex]e^{3t}[/tex])×cos(t) -1×[tex]e^{3t}[/tex]×sin(t) -4×[tex]e^{3t}[/tex], [tex]r_2[/tex](t) =  [tex]c_2[/tex](-1×[tex]e^{3t}[/tex]×cos(t) -1×[tex]e^{3t}[/tex]×sin(t) + 4i×[tex]e^{3t}[/tex].

A) The solution to the linear equation in eigenvalue/eigenvector form:

r(t) = [tex]c_{1}[/tex]×e^(∧×t)[tex]v_{1}[/tex]+ [tex]c_{2}[/tex] × e^(∧²×t)[tex]v_2[/tex]

B) The solution to the linear equation in fundamental matrix form:

 r(t) = X×e^(∧×t)c

C) As two equations: The solution to the linear system can also be written as two equations as follows:

 [tex]r_1[/tex](t) = [tex]c_1[/tex] ×e^(∧²×t)[tex]v_1[/tex] = [tex]c_{1}[/tex](-1×[tex]e^{3t}[/tex])×cos(t) -1×[tex]e^{3t}[/tex]×sin(t) -4×[tex]e^{3t}[/tex]

 [tex]r_2[/tex](t) = [tex]c_2[/tex]×e^(∧² ×t)[tex]v_2[/tex] = [tex]c_2[/tex](-1×[tex]e^{3t}[/tex]×cos(t) -1×[tex]e^{3t}[/tex]×sin(t) + 4i×[tex]e^{3t}[/tex]

To learn more about eigenvalues and eigenvectors:

brainly.com/question/15423383

#SPJ4