The vertex form of the equation of a parabola is y= 5(x - 3)^2 - 6. What is the standard form of the equation?

A. y = 5x2 - 30x +39
B. y = 5x2 30x + 15
C. y= 25x2-11
D. y = 5x2.1​

The position value, r(t) is equals to the (t³/6)k + 2j and velocity value, v(t) is equals to ( t²/2 )k + 4i , for a(t) = tk, v(0) = 4i, r(0) = 2j.

Acceleration is defined as the rate of change of the velocity of an object with respect to time. Accelerations are vector quanty.

a = dv/dt

We have the following informations are available,

Initial velocity, v(0) = 4i

Initial position, r(0) = 2j

Acceleration at any time "t",

a(t) = tk

we have to determine the value of v(t) and r(t).

As we know, a(t) = dv(t)/dt = tk

integrating the above equation ,

v(t) = ∫tk dt = ( t²/2 )k + c

at t = 0 , v(0) = 0 + c = 4i ( since, v(0) = 4i

=> c = 4i

So, v(t) = ( t²/2 )k + 4i

Also, velocity is calculated by derivative of postion (r) with respect to time.

=> v(t) = dr(t) /dt

=> r(t) = ∫ v(t) dt

=> r(t) = ∫ ( t²/2 )k dt

integrating value of the right hand side,

r(t) = ( t³/2×3 )k +d

= (t³/6)k + d

At t = 0, r(0) = (0/6)k + d

=> r(0) = d = 2j

so, r(t) = (t³/6)k + 2j

Hence, the required position and velocity are

(t³/6)k + 2j and ( t²/2 )k + 4i.

To learn more about Accelation , refer:

https://brainly.com/question/10307723

#SPJ4

To evaluate the derivative of the function f(x) = -4x² + 7x - 5 at x = 5, we need to find f'(x) and substitute x = 5 into the resulting expression. the derivative of f(x) at x = 5 is -33. Hence, the correct answer is B.

Given the function f(x) = -4x² + 7x - 5, we can find its derivative f'(x) by applying the power rule for differentiation. The power rule states that if f(x) = ax^n, then f'(x) = nax^(n-1).

Applying the power rule to each term of f(x), we have f'(x) = -8x + 7.

To evaluate f'(5), we substitute x = 5 into the expression for f'(x):

f'(5) = -8(5) + 7 = -40 + 7 = -33.

Therefore, the derivative of f(x) at x = 5 is -33. Hence, the correct answer is B.

learn more about function here:

https://brainly.com/question/30721594

#SPJ11

Answer:

(b) distributive property

Step-by-step explanation:

When you multiply a number (a) by a sum of two other numbers (b + c), you can distribute the multiplication across the sum and get the same result as if you had multiplied a by each of the two numbers (b and c) separately, and then added the two products together.

For example, if a = 2, b = 3, and c = 4, then:

2 x (3 + 4) = 2 x 7 = 14

and

(2 x 3) + (2 x 4) = 6 + 8 = 14

so the distributive property holds in this case.

The Euler method with a step size of h = 0.5, the approximate numerical solution for the ODE is y(1.5) ≈ -1.1198 x 10^9.

To solve the ODE using the Euler method, we divide the interval into smaller steps and approximate the derivative with a difference quotient. Given that the step size is h = 0.5, we will perform three steps to obtain the numerical solution.

we calculate the initial condition: y(0) = -2.

1. we evaluate the derivative at t = 0 and y = -2:

y' = 3(0) - 10(-2)² = -40

Next, we update the values using the Euler method:

t₁ = 0 + 0.5 = 0.5

y₁ = -2 + (-40) * 0.5 = -22

2. y' = 3(0.5) - 10(-22)² = -14,860

Updating the values:

t₂ = 0.5 + 0.5 = 1

y₂ = -22 + (-14,860) * 0.5 = -7492

3. y' = 3(1) - 10(-7492)² ≈ -2.2395 x 10^9

Updating the values:

t₃ = 1 + 0.5 = 1.5

y₃ = -7492 + (-2.2395 x 10^9) * 0.5 = -1.1198 x 10^9

Therefore, after performing three steps of the Euler method with a step size of h = 0.5, the approximate numerical solution for the ODE is y(1.5) ≈ -1.1198 x 10^9.

Learn more about  Euler method here:

https://brainly.com/question/30459924

#SPJ11

Answer:

2

Step-by-step explanation:

Answer:

#3 MH and AT

Perpendicular lines have opposite reciprocal  slope. This would prove if the angle is 90 degrees and is/is not a rectangle

a) ACME's total money flow over the interval from t=0 years to t=20 years is $14,000. b) this integral, we need to use techniques like integration by parts. c) The cash flow is the income flow function f(t) = 500 + 40t, and the discount rate is r%.

(a) To find ACME's total money flow over the interval from t=0 years to t=20 years, we need to calculate the definite integral of the income flow function f(t) from t=0 to t=20:

Total money flow = ∫(500+40t) dt (from 0 to 20)

To evaluate this integral, we can apply the power rule of integration:

Total money flow = [500t + 20t^2/2] (from 0 to 20)

               = [500(20) + 20(20^2)/2] - [500(0) + 20(0^2)/2]

               = [10000 + 4000] - [0 + 0]

               = 14000

Therefore, ACME's total money flow over the interval from t=0 years to t=20 years is $14,000.

(b) To find the present value of ACME's money flow over the same interval, we need to discount the future cash flows by an appropriate discount rate. Let's assume the discount rate is r%.

Present value = ∫(500+40t)e^(-rt) dt (from 0 to 20)

To evaluate this integral, we need to use techniques like integration by parts or substitution, depending on the value of r. Please provide the value of r so that we can proceed with the calculation.

(c) The accumulated amount of ACME's money flow over the same interval represents the sum of all the money flows received at each point in time. It can be calculated as the definite integral of the income flow function from t=0 to t=20:

Accumulated amount = ∫(500+40t) dt (from 0 to 20)

Using the same integration technique as in part (a), we find:

Accumulated amount = [500t + 20t^2/2] (from 0 to 20)

                  = 14000

Therefore, the accumulated amount of ACME's money flow over the interval from t=0 years to t=20 years is $14,000.

(d) To find the present value of ACME's money flow assuming the money flows forever, we need to consider the concept of perpetuity. A perpetuity represents a constant cash flow received indefinitely into the future.

The present value of a perpetuity can be calculated using the formula:

Present value = Cash flow / Discount rate

In this case, the cash flow is the income flow function f(t) = 500 + 40t, and the discount rate is r%.

Present value = (500 + 40t) / r

To know more about substitution visit:

https://brainly.com/question/26094713

#SPJ11

The question is:

ACME Exploding Faucets' income flows at the rate f(t) = 500 + 40t

(a) (2 pts) Find ACME's total money flow over the interval from t = 0 years to t = 20 (b) (2 pts) Find the present value of ACME's money flow over the same interval. (c) (1pt) Find the accumulated amount of ACME's money flow over the same interval. (d) (2 pts) Find the present value of ACME's money flow, assuming that the money flows forever. years.

For full (or any) credit, show your work and explain your reasoning, briefly

Answer:

y = 1.1

Step-by-step explanation:

Proportion is a statement that two ratios are equal.

It can be written in two ways:

We can use cross products to find a missing term in it.

Let us solve the question

∵ The proportion statement is \(\frac{7.7}{15.4}\) = \(\frac{y}{2.2}\)

→ Use the  cross multiplication to find y

∵ y × 15.4 = 7.7 × 2.2

∴ 15.4y = 16.94

→ Divide both sides by 15.4 to find y

∵ \(\frac{15.4y}{15.4}\) = \(\frac{16.94}{15.4}\)

∴ y = 1.1

No need to round it to the nearest tenth because the answer has no hundredth to round it to the tenth

Answer:

3 OR 8  hope this helps!

Step-by-step explanation:

The Bismarck model relies on social insurance contributions from employers and employees, while the Beveridge model is financed through general taxation.

The Bismarck model and the Beveridge model are two distinct approaches to healthcare and social security systems. While they share similarities in their goals of providing healthcare and social protection, they differ in terms of financing, coverage, and administration.

The Bismarck model, also known as the social insurance model, is named after Otto von Bismarck, the Chancellor of Germany who implemented the system in the late 19th century. It is characterized by mandatory health insurance programs funded by contributions from employers and employees.

The financing is based on a social insurance principle, where the costs are shared among the insured population. The coverage under the Bismarck model is typically universal, encompassing the entire population. Examples of countries following this model include Germany, France, and Japan.

On the other hand, the Beveridge model, named after William Beveridge, the architect of the UK's welfare state, is based on a tax-funded system. It is characterized by a government-funded healthcare system financed through general taxation.

The financing is based on the principle of solidarity, where the costs are borne by the entire population. The coverage under the Beveridge model is also universal, ensuring healthcare access for all citizens. Countries like the United Kingdom, Canada, and Sweden follow this model.

Learn more about distinct here:

https://brainly.com/question/31750198

#SPJ11

Answer:

26/35

Step-by-step explanation:

So we gotta add it together, so 1/7+0.6 or 1/7+3/5. Common denominator is 35, so the answer is 26/35

Answer:

1st one

Step-by-step explanation:

Answer: I would think it would be the 1st one

Step-by-step explanation:

Answer:

plz mark me as brainliest. :) (use quill bot for paraphrasing!)

Step-by-step explanation:

I applied proportional reasoning as I worked through these problems by using this reasoning to answer all the questions.

Proportional reasoning can be applied by using formal operational reasoning. There are strategies that teachers can use to help pupils apply proportional reasoning correctly.

According to Piaget's model of mental development, "formal operational reasoning," which is learned in the later phases of intellectual development, includes arguments based upon relations of proportionality. There are strategies that teachers can use to help pupils apply proportional reasoning correctly.

Finding missing values is only one aspect of proportional reasoning; it also serves as a lens through which to solve problems and builds crucial groundwork for mathematical thinking. Proportional reasoning can be applied by using formal operational reasoning.

Therefore, proportional reasoning can be applied by using formal operational reasoning.

To know more about proportional reasoning, here:

https://brainly.com/question/28001172

#SPJ3

Answer:

h = 5 units

Step-by-step explanation:

Given that,

The area of the parallelogram, A = 35 unit²

In the attached figure, we can see that the base is 7 unit.

We know that,

Area of a parallelogram, A = b × h

So,

\(h=\dfrac{A}{b}\\\\h=\dfrac{35}{7}\\\\h=5\ units\)

So, the value of h is equal to 5 units.

The correct option is D. To solve the problem of Temperature we use formula °Fahrenheit = (9/5)C + 32,celsius = (°F - 32) * 5/9

Temperature is a measure of the degree of hotness or coldness of a body or environment, often measured in units such as Celsius or Fahrenheit.

Fahrenheit and Celsius are two scales used to measure temperature. Fahrenheit is commonly used in the United States and its territories, while Celsius is used in most other parts of the world. The boiling point of water is 212°F or 100°C, and the freezing point of water is 32°F or 0°C on the Fahrenheit and Celsius scales, respectively.

According to the given information:

From the given equation:

°F = (9/5)C + 32

We can see that an increase of 1 degree Fahrenheit is equivalent to an increase of (9/5) degree Celsius, as the coefficient of C is 9/5. Therefore, statement I is true.

To determine if statement II is true, we can rearrange the equation to solve for C:

C = (°F - 32) * 5/9

So an increase of 1 degree Celsius is equivalent to an increase of (5/9) degree Fahrenheit temperature, as the coefficient of °F is 5/9. Therefore, statement II is also true.

However, statement III is not true, as an increase of (5/9) degree Fahrenheit is equivalent to an increase of 5/9 * 9/5 = 1 degree Celsius, not (5/9) degree Celsius.

Therefore, the answer is (D) I and II only.

To know more about Temperature,Fahrenheit and celsius Visit:

https://brainly.com/question/28863639

#SPJ1

Step-by-step explanation:

2x-2 I think it is the answer

Answer:

3.9x + 0.8y

Step-by-step explanation:

Simplify:

-Chetan K

The safety factor for the component, calculated as the mean strength divided by the mean stress, is approximately 0.1151. This value represents the ratio between the average strength and average stress experienced by the component.

To find the safety factor (SF) for the component, we need to calculate the mean strength and the mean stress. The mean strength (μy) and mean stress (μx) can be determined by integrating their respective probability density functions (PDFs) over their respective ranges.

For the strength PDF \(f(y) = (50^2)/(2y)\), integrating it over the range 0 ≤ y ≤ 50:

\(\int_0^ {50}{ [50^2/2y]}\, dy = 25 * \int_0 ^ {50}{ 1/y }\,dy\)

Using the natural logarithm property, we can simplify the integral:

\(25 * [\ln(y)]_0^ {50} = 25 * [\ln(50) - \ln(0)] = 25 * \ln(50)\)

Similarly, for the stress PDF \(f(x) = 50\), integrating it over the range 0 ≤ x ≤ 50:

\(\int_0^{50} 50 \,dx = 50 * [x]_0^ {50} = 50 * 50\)

Therefore, the mean strength (μy) is \(25 * \ln(50)\), and the mean stress (μx) is 2500.

The safety factor (SF) is defined as the mean strength divided by the mean stress:

SF = μy / μx

= (25 * ln(50)) / 2500

Simplifying further:

SF = ln(50) / 100

Calculating the numerical value:

SF ≈ 0.1151

Therefore, the safety factor for the component is approximately 0.1151.

Thus, the safety factor for the component, calculated as the mean strength divided by the mean stress, is approximately 0.1151. This value represents the ratio between the average strength and average stress experienced by the component.

Learn more about safety factor function here:

https://brainly.com/question/31039386

#SPJ4

Answer:

x = 2

Step-by-step explanation:

6x-1=11

Add 1 to each side

6x-1+1=11+1

6x = 12

Divide by 6

6x/6 = 12/6

x = 2

Answer:

Step-by-step explanation:

\(6x-1=11 \\\\Collect \: like \:terms\\\\6x = 11+1\\\\Simplify\\\\6x =12\\\\Divide\:both\:sides\:by\:6\\\\\frac{6x}{6} = \frac{12}{6}\\ x = 2\)

Answer:

no

Step-by-step explanation

6x+2 is not equal to 3x so they are not proportional

Coefficient values weight varies by 25%, which is explained by the link with height.

Coefficient values have always been around -1 and 1, with -1 reflecting perfect negative linear correlation and 1 indicating perfect positive linear correlation.

The correlation coefficient in a correlation study reflects the strength of the linear relationship between two variables.

r represents the correlation coefficient.

Given this, the adult height-weight correlation is -0.50.

r = -0.50

The weight variance is, r² = (-0.50)² = 0.25

As a result, the weight variation is 25%, which is explained by the height relationship.

To learn more about the coefficient in a correlation at

https://brainly.com/question/17438225?referrer=searchResults

#SPJ4

Answer:

x= 1.09 and x= -0.461

Step-by-step explanation:

Hope it helps :) :)

Good luck!!

(1.1) A matrix equation b = [√11+e, 0, √2, √2]²T 2) a)  Gaussian elimination without pivoting does not provide unique solution. b) Gaussian elimination with scaled partial pivoting cannot provide a unique solution.(c) Basic LU decomposition is x = [0.788, -3.12, 0.167, 4.55]²T.

The given linear system can be written in matrix form as:

A × x = b

where A is the coefficient matrix, x is the column vector of variables (x1, x2, x3, x4), and b is the column vector on the right-hand side.

The coefficient matrix A is:

A = [[0, -e, √2, -√3],

[π², e, -e², 3/7],

[√5, -√6, 1, -√2],

[π³, e², -√7, -1/9]]

The variable vector x is:

x = [x1, x2, x3, x4]²T

The right-hand side vector b is:

b = [√11+e, 0, √2, √2]²T

(1.2) Solving the system using:

(a) Gaussian elimination without pivoting:

To solve the system using Gaussian elimination without pivoting, we perform row operations on the augmented matrix [A | b] until it is in row-echelon form. Then back-substitute to find the values of x.

The augmented matrix [A | b] is:

[0, -e, √2, -√3 | √11+e]

[π², e, -e², 3/7 | 0]

[√5, -√6, 1, -√2 | √2]

[π³, e², -√7, -1/9 | √2]

Performing row operations, the row-echelon form:

[π², e, -e², 3/7 | 0]

[0, -e, √2, -√3 | √11+e]

[0, 0, 0, 0 | 0]

[0, 0, 0, 0 | 0]

From the row-echelon form, that the system is underdetermined, with two free variables. Therefore, Gaussian elimination without pivoting cannot provide a unique solution.

(b) Gaussian elimination with scaled partial pivoting:

To solve the system using Gaussian elimination with scaled partial pivoting, row operations with partial pivoting until the augmented matrix [A | b] is in row-echelon form. Then back-substitute to find the values of x.

The augmented matrix [A | b] is:

[0, -e, √2, -√3 | √11+e]

[π², e, -e², 3/7 | 0]

[√5, -√6, 1, -√2 | √2]

[π³, e², -√7, -1/9 | √2]

Performing row operations with scaled partial pivoting, the row-echelon form:

[π³, e², -√7, -1/9 | √2]

[0, -e, √2, -√3 | √11+e]

[0, 0, -0.03, -1.02 | 0.027]

[0, 0, 0, 0 | 0]

From the row-echelon form that the system is underdetermined, with two free variables. Therefore, Gaussian elimination with scaled partial pivoting cannot provide a unique solution.

(c) Basic LU decomposition:

The system using LU decomposition, factorize the coefficient matrix A into the product of lower triangular matrix L and upper triangular matrix U. Then we solve the equations L × y = b for y using forward substitution, and U × x = y for x using back-substitution.

The coefficient matrix A is:

A = [[0, -e, √2, -√3],

[π², e, -e², 3/7],

[√5, -√6, 1, -√2],

[π³, e², -√7, -1/9]]

Performing LU decomposition,

L = [[1, 0, 0, 0],

[π², 1, 0, 0],

[√5, 0.3128, 1, 0],

[π³, 4.3626, 2.4179, 1]]

U = [[0, -e, √2, -√3],

[0, e + π², -e² + e × π², 3/7 - e × √2],

[0, 0, 0.9693, -0.3651],

[0, 0, 0, -2.2377]]

Solving L × y = b for y using forward substitution:

[1, 0, 0, 0] ×y = √11+e

[π^2, 1, 0, 0] × y = 0

[√5, 0.3128, 1, 0] × y = √2

[π^3, 4.3626, 2.4179, 1] × y = √2

Solving the above equations,

y = [0.788, -3.12, 0.167, 4.55]²T

Now, solving U × x = y for x using back-substitution:

[0, -e, √2, -√3] × x = 0.788

[0, e + π², -e² + e × π², 3/7 - e ×√2]× x = -3.12

[0, 0, 0.9693, -0.3651] ×x = 0.167

[0, 0, 0, -2.2377] ×x = 4.55

Solving the above equations,

x = [0.788, -3.12, 0.167, 4.55]²T

To know more about matrix  here

https://brainly.com/question/29132693

#SPJ4

Answer:

x = 72°

Step-by-step explanation:

x + 38° + 70° = 180°

x + 108° = 108°

x = 72°

Answer:

x is 32

This is your answer.

Hope it helps!!!

Answer:

$389.73 in change

Step-by-step explanation

500-( (18.95 x 3)+(26.71 x 2) )=

500-(56.85+53.42)=

500-110.27=

389.73

Two point charges, q1 = 3.99 nC located at x = 0.205 m and q2 = 5.01 nC at x = -0.302 m, are placed on the x-axis. The electric field and direction at a given point can be calculated using the principle of superposition.

The electric field at a point due to a point charge is given by Coulomb's law, E = kq/r^2, where E is the electric field, k is Coulomb's constant (8.99 x 10^9 Nm^2/C^2), q is the charge, and r is the distance between the point charge and the point where the electric field is being measured. To calculate the net electric field at a point due to multiple charges, we use the principle of superposition, which states that the total electric field at a point is the vector sum of the electric fields due to each individual charge.

In this case, we have two charges, q1 = 3.99 nC and q2 = 5.01 nC. The electric field at a point P on the x-axis, due to q1, can be calculated as E1 = kq1/r1^2, where r1 is the distance between q1 and point P. Similarly, the electric field at point P due to q2 can be calculated as E2 = kq2/r2^2, where r2 is the distance between q2 and point P. To find the net electric field at point P, we add the electric fields vectorially, E_net = E1 + E2.

To learn more about superposition click here: brainly.com/question/12493909

#SPJ11

Answer:

20cows and 29 chickens

Step-by-step explanation:

The domain and the range of the graphare

From the question, we have the following parameters that can be used in our computation:

The graph

The above graph is a quadratic function

The rule of an quadratic function is that

The domain is the set of all real numbers

This means that the input value can take all real values

However, the range is always greater than the constant term

In this case, it is -2

So, the range is y > -2

Read more about domain and range at

brainly.com/question/27910766

#SPJ1

Answer:

Intensity = 2500/x^2

6.25 lumem

5 Feets

Step-by-step explanation:

Given the following :

Area (A) = 0.1x^2

Intensity, Energy and Area are related by the formular :

Intensity = power / Area

A) If 250 lumens of light energy is produced :

Intensity (I) = 250 / 0.1x^2

Intensity = 2500/x^2

x = distance

B) USING THE EQUATION :

1) What is the intensity of light on an object that is 20 feet from the spotlight source?

x = 20

Intensity = 2500/x^2

Intensity = 2500/20^2

Intensity = 2500/400

Intensity = 6.25 lumen

11) How far from the spotlight is an object that recieves 100 lumens of light per square foot?

Intensity = 100

100 = 2500 / x^2

100x^2 = 2500

x^2 = 2500/ 100

x^2 = 25

x = 5 Feets