4(18g-12)=12(6g-4)+4

Help me solve this please

The Bernoulli equation transforms into the linear equation using the substitution v=y¹⁻ⁿ or v=y¹⁻¹.

Given: Bernoulli equation dy/dx p(x)y=q(x)yn

Objective:

To prove that the substitution v=y1−n transforms the Bernoulli equation into the linear equation dy/dx (1−n)p(x)v(x)=(1−n)q(x)

Solution:

Given Bernoulli equationdy/dx p(x)y=q(x)yn ---(1)

Let v = y1−n

Taking derivative of v with respect to yv = y1−n

Taking derivative of v with respect to y and simplifying itv = (1-n)y⁻ⁿ

Substituting v into equation (1)dy/dx p(x)y=q(x)yn...(1)dy/dx p(x)(v¹⁻¹)ⁿ=q(x)(v¹⁻¹)

Now taking derivative of both sides with respect to x

Chain rule is used here(dy/dx)v = (dv/dx)y(dy/dx) = (dv/dx)(y¹⁻¹) or(dy/dx) = (dv/dx)(y¹⁻¹) ---(2)

Differentiating v = y1−n with respect to x will give(1-n)y⁻ⁿ(dy/dx) = (dv/dx) ...(3)

Substituting equations (2) and (3) in equation (1) will give

(dy/dx)(v) = (1-n)p(x)(y¹⁻¹)(dv/dx) = (1-n)q(x)(y¹⁻¹)v= y¹⁻ⁿ = y¹⁻¹(1-n) v = (y¹⁻¹)(y¹⁻ⁿ) v = (y¹⁻¹)(v)So v = y¹⁻¹ = y¹⁻ⁿ satisfies the linear equation dy/dx (1−n)p(x)v(x)=(1−n)q(x).

Therefore the Bernoulli equation transforms into the linear equation using the substitution v=y¹⁻ⁿ or v=y¹⁻¹.

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Answer:

Acceleration

\(a=\left(2t-\dfrac{3}{5}\right)\:\sf ms^{-2}\)

Part (A)

Velocity

\(\begin{aligned}\displaystyle v= \int a\:dt & =\int \left(2t-\dfrac{3}{5}\right)\:dt\\\\ & = t^2 -\dfrac{3}{5}t+C \end{aligned}\)

\(\begin{aligned} \textsf{As }\:v(0)=10 \implies (0)^2-\dfrac{3}{5}(0)+C & =10\\C & = 10 \end{aligned}\)

\(\implies v(t)=\left(t^2-\dfrac{3}{5}t+10\right)\: \sf ms^{-1}\)

Part (B)

Displacement

\(\begin{aligned}\displaystyle s= \int v\:dt & =\int \left(t^2-\dfrac{3}{5}t+10\right)\:dt\\\\ & = \dfrac{1}{3}t^3-\dfrac{3}{10}t^2+10t+C \end{aligned}\)

\(\begin{aligned} \textsf{As }\: s(0)=5 \implies \dfrac{1}{3}(0)^3-\dfrac{3}{10}(0)^2+10(0)+C & =5\\C & = 5\end{aligned}\)

\(\implies s(t)=\left(\dfrac{1}{3}t^3-\dfrac{3}{10}t^2+10t+5\right)\: \sf m\)

Part (C)

(i)  t = 2 s

\(v(2)=(2)^2-\dfrac{3}{5}(2)+10=\dfrac{64}{5}=12.8\: \sf ms^{-1}\)

\(s(2)=\dfrac{1}{3}(2)^3-\dfrac{3}{10}(2)^2+10(2)+5=\dfrac{397}{15}=26.47\: \sf m\:(2\:dp)\)

(ii) t = 5 s

\(v(5)=(5)^2-\dfrac{3}{5}(5)+10=32\: \sf ms^{-1}\)

\(s(5)=\dfrac{1}{3}(5)^3-\dfrac{3}{10}(5)^2+10(5)+5=\dfrac{535}{6}=89.17\: \sf m\:(1\:dp)\)

Answer:

7.6 g

Step-by-step explanation:

No: of boxes = 8

Grams of clay in each = 19

Total no: of grams = 19 x 8 = 152

No: of students = 20

Grams eah will get = 7.6

I hope im right!!

The average field strength in current carrying wire placed between the poles of a strong magnetic field is 1.46 T.

The formula to be used for calculation is -

B = F/(I×L×Sin theta), where B is magnetic field density, F is force, I is current and l is length.

Keep the values in formula -

Converting length to m. 1 m is 100 cm.

3.5 cm = 0.035 m

B = 2.17 / (42.5 × 0.035 × sin 90)

Performing multiplication on Right Hand Side of the equation

B = 2.17 / 1.49

Performing division on Right Hand Side of the equation

B = 1.46 T

Hence, the magnetic field is 1.46 T.

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The complete question is -

A wire carrying a 30.0-A current passes between the poles of a strong magnet that is perpendicular to its field and experiences a 2.16-N force on the 4.00 cm of wire in the field. What is the average field strength

Step-by-step explanation:

inversely means

y = k/x

therefore

30 = k/4

120 = k

y = 120/10 = 12

FYI :

directly would mean

y = kx

The value of y will be 12 when x is equal to 10.

The relationship between two variables known as "inverse variation" occurs when the value of one variable increases while the value of the other variable decreases.

Given that, y varies inversely with x.

Here, y∝1/x

y=k/x

xy=k

When x is 4, y is equal to 30, we get

k=4×30

k=120

When x=10, we get

10y=120

y=12

Therefore, the value of y will be 12 when x is equal to 10.

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надеюсь что объяснила точно и нормально

Answer:

bottom right hand corner is false

Step-by-step explanation:

Key word perpendicular, it just needs to have relectional symmetry across the line that goes across the figure

271,403.00000

Step-by-step explanation:

Answer:

300,000

Step-by-step explanation:

If you look at it the number seven before two by 3 so every thing below it not going to matter

let me give you another example like 54,555  rounded to the nearest ten thousand for this one you would take the number in the ten thousand palce(5) and look at the number before it and get 50,000

Answer:

4.5 yard width, 12 yard length

Step-by-step explanation:

Answer:

Solution given;

width [b]=1.5in=4.5yd

length[l]=4in=12yd

area =l×b=4.5×12=54yd² is actual area.

Answer:

1,250,250 gallons

Step-by-step explanation:

1.25 * 10^6 gallons = 1,250,000 gallons

1,250,000 gallons + 250 gallons = 1,250,250 gallons

Answer:

1.22

53.08

Step-by-step explanation:

4. We can find the quarter circle, we can find the whole triangle, lets do that

The circle is, 1/4*(1)^2*pi, which is 1/4pi

The triangle is, 2 * 2 divided by 2, which is 2

2 - 1/4pi gives us the shaded part or

2 - 1/4*3.14

2 - 0.785 = 1.215 rounded to 1.22

5. The area of a cylinder is pir^2h. r is 10, h is 1.2

12pi cm^3

we have 20 m^3 which is 2000 cm^3

Let's divide,

2000/37.68 = 53.078, rounded gives us 53.08

Three consecutives even integers are 42, 44, and 46.

The three consecutives even integers can be represented as x, x+2, and x+4. We can create an equation to solve for x, using the given information.

3(x+4) = 52 + x + (x+2)

3x + 12 = 54 + 2x

x = 42

Therefore, the three consecutives even integers are 42, 44, and 46. To explain this answer, we can use the equation we created. We know that the sum of the smaller two integers is 52 less than three times the largest. We can represent this as 3(x+4) = 52 + x + (x+2). We can then solve for x by subtracting 2x from both sides and adding 12 to both sides, resulting in x = 42. This means that the three consecutives even integers are 42, 44, and 46.

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The values of a, b, c are 152°, 28°, 152° respectively.

Angles around a point describes the sum of angles that can be arranged together so that they form a full turn.

The sum of angles at a point will give 360°.

This means that a + b + c + 28 = 360

c +28 = 180° ( angle on a straight line)

c = 180 -28

c = 152°

c = a( alternate angles are equal)

therefore the value of a = 152°

b = 28( alternate angles are equal)

therefore the value of b is 28

therefore the values of a, b, c are 152°, 28°, 152° respectively

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Therefore, the degree of the resulting polynomial is m + n when two polynomials of degree m and n are multiplied together.

What is polynomial?

A polynomial is a mathematical expression consisting of variables and coefficients, which involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. Polynomials can have one or more variables and can be of different degrees, which is the highest power of the variable in the polynomial.

Here,

When two polynomials are multiplied, the degree of the resulting polynomial is the sum of the degrees of the original polynomials. In other words, if the degree of the first polynomial is m and the degree of the second polynomial is n, then the degree of their product is m + n.

This can be understood by looking at the product of two terms in each polynomial. Each term in the first polynomial will multiply each term in the second polynomial, so the degree of the resulting term will be the sum of the degrees of the two terms. Since each term in each polynomial has a degree equal to the degree of the polynomial itself, the degree of the resulting term will be the sum of the degrees of the two polynomials, which is m + n.

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Answer:

20

Step-by-step explanation:

just divide 600 by 30

20. because 600 divided by 30 is 20.

a. The linear equation that models the temperature T as a function of the number of chirps per minute N is: T(N) = (1/9)N + 60

b. If the crickets are chirping at 155 chirps per minute, the estimated temperature is approximately 77.22 degrees Fahrenheit.

a. Let's first find the slope of the line using the formula:

slope (m) = (y2 - y1) / (x2 - x1)

where (x1, y1) = (117, 73) and (x2, y2) = (180, 80).

slope = (80 - 73) / (180 - 117)

= 7 / 63

= 1/9

Now, let's use the point-slope form of a linear equation:

y - y1 = m(x - x1)

Using the point (117, 73):

T - 73 = (1/9)(N - 117)

Simplifying the equation:

T - 73 = (1/9)N - (1/9)117

T - 73 = (1/9)N - 13

Now, let's rearrange the equation to solve for T:

T = (1/9)N - 13 + 73

T = (1/9)N + 60

Therefore, the linear equation that models the temperature T as a function of the number of chirps per minute N is: T(N) = (1/9)N + 60

(b) If the crickets are chirping at 155 chirps per minute, we can estimate the temperature T using the linear equation we derived.

T(N) = (1/9)N + 60

Substituting N = 155:

T(155) = (1/9)(155) + 60

T(155) = 17.22 + 60

T(155) ≈ 77.22

Therefore, if the crickets are chirping at 155 chirps per minute, the estimated temperature is approximately 77.22 degrees Fahrenheit.

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Answer:

Step-by-step explanation:

24: the domain is the set of all values of x, and the range are the input y

{(–5, 8), (–5, 2), (–3, 3), (–3, 1), (0, 4), (0, 5), (–5, 7), (–3, 6)}

Answer:

z = 33

Step-by-step explanation:

\(1 \frac{4}{11} \times z = 45 \\ \\ \frac{1 \times 11 + 4}{11} \times z = 45 \\ \\\frac{11 + 4}{11} \times z = 45 \\ \\\frac{15}{11} \times z = 45\\ \\z = \cancel{ 45} \: \: \red{ \bold{3}} \times \frac{11}{ \cancel{15}} \\ \\ z = 3 \times 11 \\ \\ z = 33\)

The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.

To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model. The model assumes that the value of a stock is equal to the present value of all its expected future dividends.

First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:

Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17

Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40

Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65

Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92

Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22

After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.

The present value of the dividends can be calculated as follows:

PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n)

where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.

In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value:

PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)

PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5

PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59

PV ≈ $16.22

Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.

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The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.

To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model.
The model assumes that the value of a stock is equal to the present value of all its expected future dividends. First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:

Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17
Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40
Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65
Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92
Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22

After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.
The present value of the dividends can be calculated as follows:
PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n) where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.

In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value: PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)
PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5
PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59
PV ≈ $16.22
Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.

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Answer:

The answer is (0, 2)

Step-by-step explanation:

Ive also had this question and viewed iver it and said it was right this was some time ago but im glad to help :)

We are given the following equation

We are asked to solve the equation for y.

Solving for y means that we have to separate the variable y.

Step 1:

Subtract 3x from both sides of the equation

Answer:

Yes

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

40 is 100

32 is x

100*32/40=80

Answer:

125 percent

hope it help

The equation for the translated function is:

g(x)  =-3x + 1

Remember that a vertical translation of N units can be written as:

g(x) = f(x) + N

If N > 0, the translation is up.

if N < 0, the translation is down.

Here the translation is of 9 units up, then we need to write:

g(x) = f(x) + 9

Replacing f(x) we will get:

g(x) = -3x - 8 + 9

g(x)  =-3x + 1

That is the translated function.

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Answer:

1

Step-by-step explanation:

To translate f(x) = -3x - 8, 9 units up, we simply add 9 to the function: g(x) = -3x - 8 + 9 = -3x + 1. Therefore, g(x) is equal to -3x plus one. The slope of g(x) is -3 and the y-intercept is 1.

So, √121 belongs to the set of natural numbers, whole numbers, integers, and real numbers.

The number √121 is the square root of 121. The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, the square root of 121 is 11 because 11 * 11 = 121.

Since the question asks for the subset(s) of real numbers to which the number belongs, we can say that √121 belongs to the set of natural numbers, whole numbers, integers, and real numbers.

- Natural numbers: These are the counting numbers starting from 1 and going to infinity. Since 11 is a positive whole number, it is a natural number.
- Whole numbers: These are the natural numbers, including 0. Since 11 is a positive whole number, it is also a whole number.

- Integers: These are the positive and negative whole numbers, including 0. Since 11 is a positive whole number, it is also an integer

- Real numbers: These are all the numbers on the number line, including both rational and irrational numbers. Since 11 is a whole number, it is also a real number.

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Answer:

10

Step-by-step explanation:

The value of linear equation which representing the relationship between x, the number of months of service, and y, the total amount paid in dollars by an customer is,

⇒ y = 150x

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

For new customers, there is an additional one-time $150 service fee.

Now, Let the number of months of service = x

And, the total amount paid in dollars by an customer = y

Hence, The correct linear equation is,

⇒ y = 150x

Thus, The value of linear equation which representing the relationship between x, the number of months of service, and y, the total amount paid in dollars by an customer is,

⇒ y = 150x

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