given that the absolute value of the difference of the two roots of $ax^2 + 5x - 3 = 0$ is $\frac{\sqrt{61}}{3}$, and $a$ is positive, what is the value of $a$?

Step-by-step explanation:

if the value of f(x) =7-4x

then the value of (-5)

= substituting the value

= 7-4x

or, 7-4*(-5)

or, 7(-4*-5)

or, 7*(+20)

or, 7*20

or, 140 Answer.

Answer:

Choice B. 20

Explanation:

The Pythagoras theorem gives

the left hand side simplifies to give

This means we are considering only a part of the ellipse that is centered at the point (0,0) and moves in the direction of the hands of a clock.

The given question is asking about a portion of an ellipse centered at the origin and oriented clockwise. Let's break down the question and provide a clear and concise answer.

An ellipse is a curved shape that looks like a stretched-out circle. It has two main properties:

a major axis and a minor axis. The major axis is the longer distance across the ellipse, and the minor axis is the shorter distance.

In the given question, we are specifically talking about a portion of the ellipse. This means we are considering only a part of the entire ellipse.

When we say the portion is centered at the origin, it means that the center of the portion lies at the point (0,0) on the coordinate plane.

Now, let's talk about the orientation. Clockwise orientation means that if you were to walk along the portion of the ellipse, you would move in the direction of the hands of a clock.

To summarize, the given question is asking about a portion of an ellipse centered at the origin and oriented clockwise.

This means we are considering only a part of the ellipse that is centered at the point (0,0) and moves in the direction of the hands of a clock.

To know more about ellipse refer here:

https://brainly.com/question/12043717

#SPJ11

Answer:

It is 9

Step-by-step explanation:

Answer:

ur answer is 4

Step-by-step explanation:

10 nickels = $0.50

10 dimes = $1.00

So- 10 nickels + 10 dimes = $1.50

(a) The equation connecting t and s in the proportionality question is t = 300/s .

(b) The minimum number of staff that must be working so that the time taken is under 60 minutes is 20 staff.

Inversely proportional means that the two quantities behave opposite in nature.

(a) To find the equation connecting t and s we use the inverse proportionality technique

From the question,

To remove the proportionality sign, we intoduce a constant (k)

Given:

Substite these values into equation 1

Therefore the equation connecting t and s is

(b) To calculate the minimum number of staff that must be working so that time take is under 60 minutes, we substite the value of t = 60 into the equation above

Hence, the equation is t = 300/s and the minimum number of staff is 20 staff.

Learn more about inverse proportion here: https://brainly.com/question/28054205

#SPJ1

The time taken for the water level in the tank to drop from 3 to 0.5 meters above the bottom cannot be determined without additional information.

To calculate the time taken, we need to know the flow rate or discharge rate of the water from the tank. This information is not provided in the question. The time taken to drain the tank depends on factors such as the diameter of the outlet pipe, the pressure difference, and any restrictions or obstructions in the flow path.

If we assume a known discharge rate, we can use the principles of fluid mechanics to calculate the time. The volume of water that needs to be drained is the difference in the volume of water between 3 meters and 0.5 meters above the bottom of the tank. The flow rate can be determined using the pipe diameter and other relevant factors. Dividing the volume by the flow rate will give us the time taken.

However, since the discharge rate is not given, we cannot perform the calculation and determine the time taken accurately.

Without knowing the discharge rate or additional information about the flow characteristics, it is not possible to calculate the time taken for the water level in the tank to drop from 3 to 0.5 meters above the bottom.

To know more about water level visit:

https://brainly.com/question/30015643

#SPJ11

Answer:

432

Explanation:

If the lumberjack follows Jim's instruction and cuts the log of wood into 24 parts the first time, the log of wood has 24 parts

If the lumberjack follows John's instruction to further cut the log of wood already cut into 24 parts then we would have 24×18= 432 parts of the log of wood

Answer:

C. 10 units

Step-by-step explanation:

Distance formula sqrt( (y1 - y2)^2 + (x1 - x2)^2 )

sqrt( (3-3)^2 + (-7 - 3)^2)

sqrt ( 10^2)

10 units

Answer:

50 grams

Step-by-step explanation:

Let t = maximum daily sugar value

From the question, we know that : 92% of the daily value is 46 grams

this equation can be formed

0.92 x t = 46 grams

to find t, divide both sides of the equation by 0.92

t =46/0.92= 50 grams

Answer:

495km

Step-by-step explanation:

180 km in 4 hours means x km in 11 hours.

Cross multiply and you'll find x as 495 km

If you want to solve for y, then you would get y = -2x-9

This is the result after subtracting 2x from both sides. This is so we can undo the +2x that happens to the y variable.

Answer:

Infinitely many solutions (If its solved by systems of equations)

y = -2x - 9 (if you ONLY want to solve for y)

Step-by-step explanation:

Well you can solve this is 2 ways. Substitution and Elimination

SUBSTITUTION

2x + y = -9

2x+y=-9

Step 1: Solve 2x+y =−9 for y:

2x+y=−9

2x+y+−2x=−9+−2x(Add -2x to both sides)

y=−2x−9

Step: Substitute −2x−9 for y in 2x+y=−9:

2x+y=−9

2x+−2x−9=−9

−9=−9(Simplify both sides of the equation)

−9+9=−9+9(Add 9 to both sides)

Final answer -----> 0=0

ELIMINATION

2x + y = -9

2x+y=-9

Step 1: Multiply the second equation by -1, then add the equations together.

(2x + y = -9)

-1(2x+y=-9)

Which then becomes:

2x + y = -9

-2x - y = 9

Step 2: Add these equations to eliminate x:

Final answer -----> 0 = 0

\(\\ \rm\hookrightarrow \dfrac{BC}{AB}=\dfrac{CE}{ET}\)

\(\\ \rm\hookrightarrow \dfrac{4}{7}=\dfrac{8}{x}\)

\(\\ \rm\hookrightarrow 4x=56\)

\(\\ \rm\hookrightarrow ET=x=14\)

Answer:

XW = 134

Step-by-step explanation:

The fact that YZ bisects VW means that the angles VX and XW are supplementary, that is, they add to 180º. So

VX + XW = 180

We have that VX = 46. So

46 + XW = 180

XW = 134

We have the expression for the height H of the rock in function of the time r, when it falls from a height of 20 meters:

When r = 1 second, we have:

When r = 1.1 seconds, we have:

When r = 1.2 seconds, we have:

To know the time for each height, we have to work with the equation like this:

Then, we can calculate at which time the height is 15 meters:

When the height is 10 meters, r is:

When the height is 5 meters, r is:

The rock hits the ground when H=0. This happens when r is:

To approximate the solution and maximize the given objective function we need to find the steepest ascent direction and iteratively update the values of x₁ and x₂ to approach the maximum value of z.

The method of steepest ascent involves finding the direction that leads to the maximum increase in the objective function and updating the values of the decision variables accordingly. In this case, we aim to maximize the objective function z = -(x₁ - 3)² - (x₂ - 2)².

To find the steepest ascent direction, we can take the gradient of the objective function with respect to x₁ and x₂. The gradient represents the direction of the steepest increase in the objective function. In this case, the gradient is given by (∂z/∂x₁, ∂z/∂x₂) = (-2(x₁ - 3), -2(x₂ - 2)).

Starting with initial values for x₁ and x₂, we can update their values iteratively by adding a fraction of the gradient to each variable. The fraction determines the step size or learning rate and should be chosen carefully to ensure convergence to the maximum value of z.

By repeatedly updating the values of x₁ and x₂ in the direction of steepest ascent, we can approach the solution that maximizes the objective function z. The process continues until convergence is achieved or a predefined stopping criterion is met.

Learn more about fraction here:

https://brainly.com/question/10354322

#SPJ11

using the sum of the first 10 terms, the approximation for the sum of the series ∑(1/(3n)) from n = 1 to infinity is approximately 18.33333.

To approximate the sum of the series ∑(1/(3n)) from n = 1 to infinity using the sum of the first 10 terms, we can calculate:

s ≈ ∑(1/(3n)) from n = 1 to 10

s ≈ 1/3(1) + 1/3(2) + 1/3(3) + ... + 1/3(10)

s ≈ (1/3)(1 + 2 + 3 + ... + 10)

To find the sum of the arithmetic series 1 + 2 + 3 + ... + 10, we can use the formula:

Sum = (n/2)(first term + last term)

Sum = (10/2)(1 + 10)

Sum = 5(11) = 55

Substituting this value back into the original equation:

s ≈ (1/3)(55)

s ≈ 55/3 ≈ 18.33333

To know more about equation visit:

brainly.com/question/29538993

#SPJ11

The sandwich with the largest mean in the distribution of types of sandwiches ordered is the roast beef sandwich. This is because the roast beef sandwich has the highest number of orders, followed by the ham sandwich and the vegetarian sandwich.

The distribution of types of sandwiches ordered is as follows:

Roast beef: 40 orders

Ham: 30 orders

Vegetarian: 20 orders

As you can see, the roast beef sandwich has the highest number of orders, followed by the ham sandwich and the vegetarian sandwich. This means that the roast beef sandwich has the largest mean in the distribution of types of sandwiches ordered.

The manager should take this into account when placing the next order for food supplies. They should order more roast beef sandwiches than ham sandwiches or vegetarian sandwiches.

Visit here to learn more about distribution:

brainly.com/question/17284266

#SPJ11

The sandwich with the largest mean in the distribution of types of sandwiches ordered is the roast beef sandwich. This is because the roast beef sandwich has the highest number of orders, followed by the ham sandwich and the vegetarian sandwich.

The distribution of types of sandwiches ordered is as follows:

Roast beef: 40 orders

Ham: 30 orders

Vegetarian: 20 orders

As you can see, the roast beef sandwich has the highest number of orders, followed by the ham sandwich and the vegetarian sandwich. This means that the roast beef sandwich has the largest mean in the distribution of types of sandwiches ordered.

The manager should take this into account when placing the next order for food supplies. They should order more roast beef sandwiches than ham sandwiches or vegetarian sandwiches.

Visit here to learn more about distribution:

brainly.com/question/17284266

#SPJ11

Answer:

Check your question well

Step-by-step explanation:

U didn't ask to draw angle p so how can we get the angle r

Answer:

3:5

Step-by-step explanation:

The simplest ratio of circles to squares is 3/5.

Here,

Given that there are 15 squares and 9 circles.

We have to find, the simplest ratio of circles to squares.

What is Simplest ratio?

A ratio is said to be is the simplest form or in the lowest term if two quantities of a ratio have no common factor other than 1.

Now,

There are 15 squares and 9 circles.

Hence,  the simplest ratio of circles to squares = \(\frac{9}{15}\)

                                                                        = \(\frac{3}{5}\)

So, The simplest ratio of circles to squares is 3/5.

Learn more about the simplest ratio visit:

https://brainly.in/question/50875797

#SPJ2

The table mentioned in the question is not provided. However, we can use the following formula to find the probability of two independent events occurring together:

P(A and B) = P(A) x P(B)

Here, A represents the event of the coin landing heads up, and B represents the event of the pointer landing on either 1, 2, or 4.

Assuming that the spinner has equal sections, the probability of the pointer landing on either 1, 2, or 4 is 3/8 (since there are three out of eight possible sections on the spinner).

The probability of flipping a fair coin and getting heads is 1/2.

Therefore, the probability of the coin landing heads up and the pointer landing on either 1, 2, or 4 is:

P(A and B) = P(A) x P(B) = (1/2) x (3/8) = 3/16

So, the probability of the coin landing heads up and the pointer landing on either 1, 2, or 4 is 3/16.

The probability of the coin landing heads up and the pointer landing on either 1, 2, or 4 is 3/16.

Probability denotes the possibility of the outcome of any random event. The meaning of this term is to check the extent to which any event is likely to happen.

Given that, a spinner is spined and coin is flipped,

P(A and B) = P(A) x P(B)

Here, A represents the event of the coin landing heads up, and B represents the event of the pointer landing on either 1, 2, or 4.

Assuming that the spinner has equal sections, the probability of the pointer landing on either 1, 2, or 4 is 3/8 (since there are three out of eight possible sections on the spinner).

The probability of flipping a fair coin and getting heads is 1/2.

Therefore, the probability of the coin landing heads up and the pointer landing on either 1, 2, or 4 is:

P(A and B) = P(A) x P(B) = (1/2) x (3/8) = 3/16

So, the probability of the coin landing heads up and the pointer landing on either 1, 2, or 4 is 3/16.

Learn more about probability click;

https://brainly.com/question/30034780

#SPJ1

The method of reduction of order is a technique used to find a second solution to a homogeneous linear differential equation when one solution is already known.

However, it cannot be directly used for nonhomogeneous linear differential equations. In nonhomogeneous equations, the method of undetermined coefficients or variation of parameters is typically used to find a particular solution.

Therefore, the statement "the method of reduction of order can also be used for the nonhomogeneous equation" is false. It is important to understand the different techniques for solving differential equations, and to choose the appropriate method based on the type of equation and boundary conditions given.

To know more about homogeneous linear differential equation visit:

https://brainly.com/question/31129559

#SPJ11

Answer:

10m + 16

-5y + 15

Step-by-step explanation:

-3m + 16 - (-13m) =

= -3m + 16 + 13m

= 10m + 16

15y - 20y + 15 =

= -5y + 15

By using the volume formula for a cone and the definition of rate of change, the depth of the cone is changing at a rate of approximately 0.062 feet per minute.

The volume of a cone (V), in cubic feet, is represented by the following formula:

V = (π / 3) · R² · h    (1)

Where:

In addition, the radius and the height have following relationship:

h / R = 7 / 10

h = (7 / 10) · R      (2)

h' = (7 / 10) · R'     (3)

The rate of change of the cone is found by means of first derivatives:

V' = (2π / 3) · R · h · R' + (π / 3) · R² · h'

V' = (π / 3) · R · (2 · h · R' + R · h')        (4)

Where:

By (2) and (3) in (4):

V' = (π / 3) · (10 / 7) · h · [2 · h · (10 / 7) · h' + (10 / 7) · h · h']

V' = (10π / 21) · h · [(30 / 7) · h · h']

V' = (300π / 147) · h² · h'

If we know that h = 5 ft and V' = 10 ft³ / min, then the rate of change for the depth of the cone is:

10 = (300π / 147) · 5² · h'

h' ≈ 0.062 ft / min

The depth of the cone is changing at a rate of approximately 0.062 feet per minute.

To learn more on rates of change: https://brainly.com/question/11606037

#SPJ1

Answer:

h = height s = slant height a = side length P = perimeter of base e = lateral edge length r = a/2 V = volume L = lateral surface area B = base surface area A = total surface area

A  = 72.17 m2

Step-by-step explanation:

hope this helped!

Navier Stokes For Blood Clot region - Velocity Profile and Net Momentum loss.

The Navier-Stokes equation is a set of equations in fluid mechanics that represents the conservation of mass, momentum, and energy. It's a complicated set of nonlinear partial differential equations that describe fluid motion in three dimensions. The flow of blood is a complex fluid flow that is affected by numerous factors, including flow velocity, blood vessel wall properties, and fluid viscosity.

                                      To investigate blood flow, the Navier-Stokes equation may be used. The velocity profile and net momentum loss are then determined using the Navier-Stokes equation. The following is the detailed answer for this question:Velocity Profile:Velocity is a vector quantity that represents the rate of motion in a particular direction. Blood flow velocity is a critical indicator of vascular health.

                                      The velocity profile in the Navier-Stokes equation is determined by determining the velocity at various points in a given fluid. This is accomplished by solving a set of differential equations that take into account the fluid's viscosity, density, and other physical properties.Net Momentum Loss:When a fluid flows through a blood vessel, it exerts a force on the vessel walls. This is referred to as a momentum transfer.

The momentum transfer rate, which is the rate at which momentum is transferred to the vessel walls, is determined using the Navier-Stokes equation. The momentum transfer rate is determined by integrating the fluid's momentum flux over the vessel's cross-sectional area. The net momentum loss can be calculated by subtracting the momentum transfer rate from the initial momentum of the fluid.

Learn more about Navier-Stokes equation

brainly.com/question/29181204

#SPJ11

Statement is true because the corresponding sides are congruent. The answer is: BA = LN.

What is Triangle?

A triangle is a closed, two-dimensional shape with three straight sides and three angles. It is one of the basic shapes in geometry and is used in many areas of mathematics, science, and engineering.

Since triangle ABC and triangle LMN have congruent corresponding sides, we know that they are similar triangles. This means that their corresponding angles are also congruent.

We are given that angle BAC is 58 degrees and angle MLN is 78 degrees. Since corresponding angles are congruent, this means that angle BAC is congruent to angle MLN.

Therefore, triangle ABC and triangle LMN are similar triangles with two pairs of corresponding congruent angles. This means that all corresponding sides are proportional.

Since AC = LN and BA = ML, we know that the ratio of the lengths of corresponding sides is:

AC / LN = BA / ML

Substituting the given values, we get:

1 = 1

This statement is true because the corresponding sides are congruent.

Therefore, the answer is: BA = LN.

Learn more about Triangle

https://brainly.com/question/17335144

#SPJ1

In order to advise the tire manufacturer on their advertising effectiveness and allocation, we need to calculate the marginal return to sales for each region, assess the impact of additional advertising expenditure, determine where the additional money should be spent, and consider the reallocation of current advertising expenditures.

To find the marginal return to sales for each region, we differentiate the sales equation with respect to x. For Region 1, ds_1/dx = 36 - 2.6x, and for Region 2, ds_2/dx = 19 - 1.2x. If $10 million is being spent on TV advertising in each region, we substitute x = 10 into the respective equations to find the marginal return to sales. In Region 1, ds_1/dx = 36 - 2.6(10) = 11, and in Region 2, ds_2/dx = 19 - 1.2(10) = 7. Hence, the marginal return to sales is $11 million in Region 1 and $7 million in Region 2.

To determine which region would benefit more from additional advertising expenditure, we compare the marginal returns. Since the marginal return in Region 1 is higher ($11 million) compared to Region 2 ($7 million), Region 1 would benefit more from additional advertising expenditure.

If additional money is made available for advertising, it should be spent in Region 1 as it has the higher marginal return. Increasing the advertising expenditure in Region 1 would likely result in a greater increase in sales revenue compared to Region 2.

To reallocate money already being spent to produce more sales revenue, we should compare the coefficients of the quadratic term (x^2) in the sales equations. In Region 1, the coefficient is -1.3, and in Region 2, it is -0.6. Since the coefficient in Region 1 is larger in absolute value, reallocating some advertising expenditure from Region 2 to Region 1 would likely lead to a larger increase in sales revenue overall.

Therefore, based on the analysis, the tire manufacturer should focus on increasing advertising expenditure in Region 1, as it has a higher marginal return, and consider reallocating some advertising funds from Region 2 to Region 1 to optimize sales revenue.

Learn more about marginal return  here:

https://brainly.com/question/3116739

#SPJ11