6a-1÷7=4. . . . . . . . . . .. . . ​

To determine which differential equation(s) are linear, we need to examine the form of each equation. A linear differential equation is one that can be written in the form a(x)y" + b(x)y' + c(x)y = g(x), where a(x), b(x), c(x), and g(x) are functions of x.

The differential equation 2xy" - 5xy' + y = sin(3x) is linear. It can be written in the form a(x)y" + b(x)y' + c(x)y = g(x), where a(x) = 2x, b(x) = -5x, c(x) = 1, and g(x) = sin(3x).
The differential equation (v)² + xy = In(x) is not linear. It does not follow the form a(x)y" + b(x)y' + c(x)y = g(x) because it contains a term with (v)², where v represents the derivative of y with respect to x. This term does not have a linear coefficient.
The differential equation y' + sin(y) = e^(3x) is linear. It can be written in the form a(x)y' + b(x)y = g(x), where a(x) = 1, b(x) = sin(y), and g(x) = e^(3x).
The differential equation (x²+1)y" - 3y - 2x³y = -x - 9 is not linear. It does not follow the form a(x)y" + b(x)y' + c(x)y = g(x) because it contains a term with (x²+1)y", where the coefficient is a function of x.
The differential equation y' + xy = y" is linear. It can be written in the form a(x)y' + b(x)y = g(x), where a(x) = 1, b(x) = x, and g(x) = y".

Learn more about differential equation here
https://brainly.com/question/32524608



#SPJ11

y ( x) =  \(C_{1} e^{-2x} + C_{2} e^{-2x} + x^{2} - 5 x + \frac{9}{2}\) is the result of solving the subsequent differential equation with unknown coefficients.

One or more functions and [some of] their derivatives are connected by a differential equation. The [first] derivative of the function with respect to the variable is illustrated in the following example. Differentials are a term used to describe the and elements.

given

1/4 y'' + y' + y = x2 − 3x

The auxilary equation is

1/4 \(m^{2}\) + m + 1 = 0

\(m^{2}\) + m + 1 = 0

\(( m- 2)^{2}\) = 0

m = -2 , -2

= A =1 , 2A+ B = -3 , 1/2A + B = 0

A = 1 , B = - 5 , C = 9/ 2

Then the general solution is

y = yc + yp

y ( x) =  \(C_{1} e^{-2x} + C_{2} e^{-2x} + x^{2} - 5 x + \frac{9}{2}\) is the result of solving the subsequent differential equation with unknown coefficients.

To know more about differential equation visit :-

https://brainly.com/question/14620493

#SPJ4

The maximum burn rate ∣ΔM/Δt∣ that the engine could reach before the ship's acceleration exceeded 5 g and its human occupants began to lose consciousness is approximately 51.0 kg/s.

Acceleration is directly proportional to the force acting on an object. In simple terms, if the force on an object is greater, then it will undergo more acceleration. However, there are limitations to the acceleration that can be tolerated by the human body. At about 5 g (49.0 m/s2) for more than a few seconds, an average person starts to lose consciousness. Let's use this information to answer the given question.

Let the maximum burn rate |ΔM/Δt| that the engine could reach before the ship's acceleration exceeded 5 g be x.

Let the mass of the spaceship be m and the exhaust speed of the engine be v.

Using the formula for the thrust of a rocket,

T = (mv)e

After substituting the given values into the formula for thrust, we get:

T = (3.00 × 104)(2.50 × 103) = 7.50 × 107 N

Therefore, the acceleration produced by the engine, a is given by the formula below:

F = ma

Therefore,

a = F/m= 7.50 × 107/3.00 × 104= 2.50 × 103 m/s²

The maximum burn rate that the engine could reach before the ship's acceleration exceeded 5 g is equal to the acceleration that would be produced by a maximum burn rate. Therefore,

x = a/5g= 2.50 × 103/(5 × 9.8)≈ 51.0 kg/s

Therefore, the maximum burn rate ∣ΔM/Δt∣ that the engine could reach before the ship's acceleration exceeded 5 g and its human occupants began to lose consciousness is approximately 51.0 kg/s.

Learn more about maximum burn rate

https://brainly.com/question/29328145

#SPJ11

Answer:

3 and a fourth amount of bathces

The completed statements with regards to the compound interest of the amount in the account are;

If the account has a 5% interest rate and is compounded monthly, you have $101.655 million money after 2 years

If the account has a 5% interest rate compounded continuously, you would have $106.096 million money after 2 years

Compound interest is the interest calculated based on the initial amount and the accumulated interests accrued from the periods before the present.

The compound interest formula indicates that we get;

\(A = P\cdot (1 + \frac{r}{n}) ^{n\cdot t}\)

Where;

P = The principal amount invested = $92 million

r = The interest rate = 5% monthly

n = The number of times the interest is compounded per annum = 12

t = The number of years = 2 years

Therefore; \(A = 92\cdot (1 + \frac{0.05}{12}) ^{12\times 2}\approx 101.655\)

The amount in the account after 2 years is therefore about $101.655 million

The formula for the amount in the account if the principal is compounded continuously, we get;

A = \(P\cdot e^{(r\cdot t)}\)

Therefore, we get;

\(A = 96 \times e^{0.05 \times 2} \approx 106.096\)

The amount in the account after 2 years, compounded continuously therefore, is about $106.096 million

Learn more on compound interest here: https://brainly.com/question/21487182

#SPJ1

The translation from y = \(4^x\) to y = \(4^x\) + 3 - 1 are:

- Translating vertically 3 units up.

- Translating vertically 1 unit down.

It is the movement of the shape in the left, right, up, and down directions.

The translated shape will have the same shape and shape.

There is a positive value when translated to the right and up.

There is a negative value when translated to the left and down.

We have,

y = \(4^x\) and y = \(4^x\) + 3 - 1

Now,

y = \(4^x\)

Translating vertically 3 units up we get,

y = \(4^x\) + 3

Again,

Translating vertically 1 unit down we get,

y = \(4^x\) + 3 - 1

Thus,

The translation from y = \(4^x\) to y = \(4^x\) + 3 - 1 are:

- Translating vertically 3 units up.

- Translating vertically 1 unit down.

Learn more about translation here:

https://brainly.com/question/12463306

#SPJ1

Answer:

45 days

Step-by-step explanation:

Step 1:  Determine how long it will last

(9 cups) * (5 days / cup)

45 days

Answer: 45 days

ANSWERS

A. AB ≅ FG

B. ∡C≅ ∡H

EXPLANATION

A. To use SAS theorem, we have to know if one more side is congruent to the corresponding side of the other triangle. SAS is side-angle-side. The angle must be included between the two sides. Therefore the missing side is AB congruent to FG:

B. To use ASA Theorem we have to know one more angle. Since ASA is angle-side-angle, the side must be between two angles. Therefore, the missing angle is angle C congruent to angle H:

6x=55y

9x=188y

sure it is concurent equation

Answer:

\(x = \frac{5}{3} , \ \ y = -1\)

Step-by-step explanation:

6x + 5y = 5     -----(1)

9x - 4y = 19     -----(2)

Multiply (1) by 9 :  54x + 45y = 45   ------(3)

Multiply (2) by 6 : 54x - 24y = 114    -------(4)

(3) - (4) ==> 69y = -69

                 y = -1

Substitute y = -1 in (1)

               6x + 5(-1) = 5

               6x - 5 = 5

               6x = 5 + 5

              6x = 10

               \(x =\frac{10}{6} = \frac{5}{3}\)

Answer:

9

Step-by-step explanation:

I said so

No, the ratios 10:12 and 1:21 are not form a proportion.

A relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

The ratios are,

⇒ 10 : 12 and 1 : 21

We know that;

Two ratio are form a proportional when both are in same quantity or in a a same ratio.

Here, The ratios are,

⇒ 10 : 12 and 1 : 21

Clearly, We get;

10 / 12 = 5 / 6

1 / 21 = 1  21

Thus,

1 / 21 ≠ 5 /6

1 : 21 ≠ 10 : 12

Therefore, The ratios 10:12 and 1:21 are not form a proportion.

Learn more about the proportion visit:

https://brainly.com/question/870035

#SPJ9

Answer:

number is 2

Step-by-step explanation:

let the number be n then 7 times the number is 7n and 12 less than 13 times the number is 13n - 12

equating the 2 expressions

7n = 13n - 12 ( subtract 13n from both sides )

- 6n = - 12 ( divide both sides by - 6 )

n = 2

that is the number n is 2

The answer is:

the number is 2

Work/explanation:

I am going to start by letting b be the number.

Seven times b is 7b.

13 times the same number means 13 times b: 13b

12 less than 13b: 13b - 12

Thus, the equation is 7b = 13b - 12

Now to solve!

Add 12 on each side

7b + 12 = 13b

Subtract 7b on each side

12 = 13b - 7b

12 = 6b

Divide each side by 12

2 = b

The equation for the hyperbola with foci (0,±5) and asymptotes y=± 3/4 x is:

y^2 / 25 - x^2 / a^2 = 1

where a is the distance from the center to a vertex and is related to the slope of the asymptotes by a = 5 / (3/4) = 20/3.

Thus, the equation for the hyperbola is:

y^2 / 25 - x^2 / (400/9) = 1

or

9y^2 - 400x^2 = 900

The center of the hyperbola is at the origin, since the foci have y-coordinates of ±5 and the asymptotes have y-intercepts of 0.

To graph the hyperbola, we can plot the foci at (0,±5) and draw the asymptotes y=± 3/4 x. Then, we can sketch the branches of the hyperbola by drawing a rectangle with sides of length 2a and centered at the origin. The vertices of the hyperbola will lie on the corners of this rectangle. Finally, we can sketch the hyperbola by drawing the two branches that pass through the vertices and are tangent to the asymptotes.

Know more about equation for the hyperbola here:

https://brainly.com/question/30995659

#SPJ11

2. The equation is given as follows: x + 4x = 25.

3. The constrains are given as follows: 0 ≤ x ≤ 25, 0 ≤ y ≤ 75.

The time spent running is given by:

Running = 4x.

The time spent walking is one-fourth of the time spent walking, hence it is given by:

Walking = 4x/4 = x.

The total time is the sum of the times spent running and walking, hence the expression is presented as follows:

x + 4x = 25.

The variables are given as follows:

You can accept at most 25 out-of-state hires, hence:

0 ≤ x ≤ 25

(as the number cannot be negative).

The company plans to have three times as many in-state hires, hence:

0 ≤ y ≤ 75.

As:

More can be learned about equations and constraints at https://brainly.com/question/18435162

#SPJ1

Answer:

B

Step-by-step explanation:

it's (m+n-1) √p

hope this helps

We will investigate how to use ratios to determine the actual distance between cities as per defined scale.

We are given a scale conversion ( ratio ) at which distances are scaled down:

We will use the given scale ratio to determine the actual distance between two citites. The scale distance between Hawthorne and Doyelstown can be read.

Now utilize the scale conversion ratio to determine the actual distance:

Therefore, the distance between Hawthorne and Doylestown is:

Answer:

46,200 cm³

Step-by-step explanation:

The volume of a rectangular prism: length * width * height

Multiply:

The units are cm * cm * cm  or cm³

\(\boxed{\text{The volume is 46,200 cm}^3}\)

-Chetan K

The volume that can be held by the aquarium is 46,200 cm³

Volume can be regarded as scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface.

Using the formula

Volume= (length * width * height)

=(50 * 28 * 33)

=46,200 cm³

Learn more about Volume at:

https://brainly.com/question/23963432

Answer:

Step-by-step explanation:

Given equation:

Multiply all terms by (x - 3)(x - 2):

Compare this to the given form to get:

Correct choice is A

On solving

x=4±√3

So

a=4 and b=3

Answer:

A

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

-9-(-9)+5=5

Mr. and Mrs. Bill traveled 12.5 miles when they met up with each other.

Let's start by converting the 15 minutes delay of Mr. Bill's departure into hours:

15 minutes = 15/60 = 0.25 hours

Next, we can use the formula:

distance = speed x time

to calculate the distance traveled by each person before they meet up.

For Mr. Bill, the distance he traveled before meeting his wife is:

distance = speed x time

distance = 50 mph x 0.25 hours

distance = 12.5 miles

For Mrs. Bill, we need to account for the 15 minutes head start Mr. Bill had. So, her time traveled will be slightly longer than Mr. Bill's:

time = distance / speed

time = (12.5 miles) / (52 mph)

time = 0.24 hours

Her distance traveled will be:

distance = speed x time

distance = 52 mph x 0.24 hours

distance = 12.48 miles

To find the total distance traveled when they met up, we add the distances traveled by each person:

total distance = distance traveled by Mr. Bill + distance traveled by Mrs. Bill

total distance = 12.5 miles + 12.48 miles

total distance = 24.98 miles

Rounding to the nearest tenth of a mile, we get that Mr. and Mrs. Bill traveled 12.5 miles when they met up with each other.

For more questions like Distance click the link below:

https://brainly.com/question/15172156

#SPJ11

The six trigonometric identities are:

Trigonometry is the branch of mathematics that deals with the relationships between the angles and sides of triangles. In trigonometry, there are six basic functions, sine, cosine, tangent, cosecant, secant, and cotangent, each of which is represented by a specific letter. These functions are related to each other through a set of identities known as the trigonometric identities.

The six trigonometric identities listed above, are the most commonly used identities, and provide the relationships between the six trigonometric functions and each other. They are useful for solving trigonometric equations, simplifying trigonometric expressions, and solving problems in geometry, physics, engineering and other sciences.

The Pythagorean identity states that the sum of the squares of the sine and cosine of an angle is equal to 1, which is a fundamental relationship between the two functions. The reciprocal identities state that the reciprocal of the sine and cosine of an angle is equal to the cosecant and secant of that angle respectively.

The quotient identities state that the tangent of an angle is equal to the sine of that angle divided by the cosine of that angle, and the cotangent of an angle is equal to the cosine of that angle divided by the sine of that angle.

It's important to note that these identities are valid for all values of the angle, and are true in any angle measurement system (degrees or radians).

To know more about  trigonometric identities on the link below:

https://brainly.com/question/24377281#

#SPJ11

Answer:

Step-by-step explanation:

25, i think

The equations of the parabolas are: (a) (x + 5)^2 = 8(y + 6)    (b) (y - 6)^2 = 4(x - 0)

(c) (y - 0)^2 = 16(x + 1/43)   (d) (y + 6.4)^2 = 4y

(a) To find the equation of a parabola with directrix x = 4 and focus at (-6, -5), we can use the formula: (x - h)^2 = 4p(y - k), where (h, k) is the vertex and p is the distance between the vertex and the focus. In this case, the vertex is (-6, -5), and p is the distance from (-6, -5) to the directrix x = 4, which is 10 units. Plugging in the values, we get (x + 6)^2 = 8(y + 5).

(b) For a parabola with directrix y = 2 and focus at (3, 10), we use the formula: (y - k)^2 = 4p(x - h). The vertex is (3, 10), and the distance between the vertex and the directrix y = 2 is 8 units. Plugging in the values, we get (y - 10)^2 = 32(x - 3).

(c) To find the equation for a parabola with focus at (-3, 2) and directrix y = 6, we can use the formula (y - k)^2 = 4p(x - h). The vertex is the midpoint between the focus and the directrix, which is (-3, 4). The distance between the vertex and the focus (or directrix) is the value of p, which is 2 units. Plugging in the values, we get (y - 4)^2 = 16(x + 1/43).

(d) For a parabola with vertex at the origin and focus at (0, -6.4), we can use the formula (x - h)^2 = 4p(y - k). The vertex is (0, 0), and the distance between the vertex and the focus (or directrix) is the value of p, which is 6.4 units. Plugging in the values, we get (y - 0)^2 = 4(6.4)y, which simplifies to y^2 = 4(6.4)y.

Learn more about Parabola here: brainly.com/question/11911877

#SPJ11

The total cost of repayment over 5 years is $23,300.

A loan repayment refers to the act of paying back money previously borrowed from a lender.

To get total cost of repayment, we must principal amount, the interest rate and the duration of the loan.

The formula to get total cost of repayment is given by \(Total Cost of Repayment = Principal + Interest\)

Interest = Principal * Interest Rate * Time

Given:

Principal amount is $20,000

Interest rate is 3.3%

Duration is 5 years.

Interest = $20,000 * 0.033 * 5

Interest = $3,300

Total Cost of Repayment = Principal + Interest

= $20,000 + $3,300

= $23,300.

Read more about repayment

brainly.com/question/25696681

#SPJ1

Answer:

a /4+-3=15?

Step-by-step explanation:

Answer:

\(({2x}^{2} )^{3} \times ( - {x}^{4} )\)

\( {2x}^{6} \times ( - {x}^{4} )\)

\( - {2x}^{6 + 4} \)

\( - {2x}^{10} \)

hope it helps you :)

Answer:

4/3

hope this helped :)

a.. F'(x) = 6/5 is the derivative function for the expression f(x) = (6/5)x + 3. b. y - (9/5) = (6/5)(x + 1) is the equation of the tangent line to the graph of f at (-1, f(-1)).

a. The power rule for derivatives can be used to determine the derivative function f'(x) for the function f(x) = (6/5)x + 3. The power rule states that the derivative of a function \(f(x) = ax^n\) is given by \(f'(x) = nax^{(n-1)\).

Applying the power rule to f(x), we have:

\(f'(x) = (6/5)(1)x^{(1-1) }= (6/5)x^0 = 6/5\)

Therefore, the derivative function f'(x) for f(x) = (6/5)x + 3 is f'(x) = 6/5.

b.We must ascertain the slope of the tangent line at that location in order to ascertain the equation of the line tangent to the graph of f at (a, f(a)) for a = -1.

We are aware that the derivative of the function at that location determines the slope of the tangent line. The slope of the tangent line is also 6/5 because we discovered in part (a) that f'(x) = 6/5.

The equation of the tangent line can be expressed using the point-slope form of a linear equation as follows:

y - f(a) = m(x - a)

Plugging in the values a = -1, f(a) = f(-1), and m = 6/5, we have:

y - f(-1) = (6/5)(x - (-1))

To find f(-1), substitute x = -1 into the original function f(x):

f(-1) = (6/5)(-1) + 3 = -6/5 + 3 = 9/5

Now we can rewrite the equation of the tangent line:

y - 9/5 = (6/5)(x + 1)

This equation is in point-slope form and represents the line tangent to the graph of f(x) = (6/5)x + 3 at the point (-1, 9/5).

Learn more about derivative here: https://brainly.com/question/32963989

#SPJ11

Answer:

\(\angle BAC=180^{\circ}-\frac{13\sin 23^{\circ}}{6}\)

Step-by-step explanation:

\(\frac{\sin(\angle BAC)}{13}=\frac{\sin 23^{\circ}}{6} \\ \\ \sin \angle BAC=\frac{13\sin 23^{\circ}}{6} \\ \\ \angle BAC=180^{\circ}-\frac{13\sin 23^{\circ}}{6}\)