Mathematics College

The points (-7, r) and (-3, 14) lie on a line with slope 3. Find the missing coordinate r.

Answers

Answer 1

The value of the missing coordinate, r as required to be determined from the given information is; r = 2.

What is the value of the missing coordinate, r?

It follows from the task content that the value of the missing coordinate, r is to be determined from the task content.

On this note, since the given points are; (-7, r) and (-3, 14) and the slope of the line through them is; 3.

It follows from the slope formula;

m = (y₂ - y₁) / (x₂ - x₁) that;

3 = ( 14 - r ) / ( -3 -(-7) )

-9 + 21 = 14 - r

r = 14 + 9 - 21

r = 2.

On this note, the required value of the missing coordinate, r is; 2.

Related Questions

given sales for the year of $218,000, cash expenses of $92,000 and depreciation expense of $23,000, net cash flow for the year is blank . multiple choice question. $195,000 $126,000 $103,000 $218,000

Answers

Answer:

$126,000

Step-by-step explanation:

The net cash flow for the year is $103, 000.

What is Net cash flow?

After all debts have been settled, net cash flow can represent either a gain or a loss in money over a time period. A company is said to have positive cash flow if, after paying all of its operational expenses, it still has cash left over.

We have,

Sales for the year = $ 218, 000

Cash expenses = $92, 000

Depreciation Expenses = $23, 000

So, the Net cash flow is

= 218,000 - (92, 000 + 23, 000)

= $ 103, 000.

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take the van der pol equation . (a) set and . convert the above second order differential equation to a two dimensional system of differential equations:

Answers

The van der Pol equation which is a second-order differential equation is given by

d²x/dt² - μ(1 - x²)dx/dt + x = 0

Here we are asked to convert it to a two-dimensional system.

Here we need to set y = dx/dt, where y represents the system's velocity.

Hence we will rewrite it as

d²x/dt² = μ(1 - x²)y + x

Now if we set the derivatives of x and y with respect to time to be equal to different variables we get

dx/dt = y

dy/dt = μ(1 - x²)y + x

Hence we get the above systems of equations as the 2-dimensional representation of the Van der Pol equation where x and y represent the system's position and velocity respectively.

If we set μ = 1 and x = 0, then we get

dx/dt = y

dy/dt = y

Hence we get the system of differential equations representing the behavior of the van der Pol equation with μ = 1 and x = 0 in two dimensions.

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Please help me with this question

Answers

Answer:

y = -1/2 x - 1

Step-by-step explanation:

A (-2,0)

B (0,-1)

slope = (-1-0)/(0-(-2)

-1/2

y intercept = -1

y = -1/2 x - 1

Answer:

y = e^(-1/2x -1)

Step-by-step explanation:

You want the equation for y(x), which is graphed as a straight line on a semi-log scale.

Graph

Let z = ln(x). The graph shows a straight line with a z-intercept of -1 and a slope of "rise"/"run" = -1/2. That means the slope-intercept equation for this line can be written as ...

z = -1/2x -1

Equation

Using z = ln(y), we can find the equation for y by taking antilogs:

ln(y) = -1/2x -1

y = e^(-1/2x -1)

Additional comment

The attached graph shows y = f(x) and the line ln(y).

suppose that y1 and y2 are independent and that both are uniformly distributed on the interval (0,1), and Let U1 and U2 be independent uniform random variables, both on (0,1). Let Y1 = U1U2 and let Y2=U2. (a) Find the joint density of Y1 and Y2.
(b) What is the marginal density for Y1?

Answers

a) The joint density of Y1 and Y2 is f(y1, y2) = 1, for 0 ≤ y1, y2 ≤ 1.

b) The marginal density for Y1 is f(y1) = 1, for 0 ≤ y1 ≤ 1.

Explanation:

(a) The joint density of Y1 and Y2 is found by multiplying the two individual densities together. Since Y1 and Y2 are independent, this is simply the product of the two densities.

The density for U1 is the same for all values of U1 on the interval (0,1), which is 1. The density for U2 is also the same for all values of U2 on the interval (0,1), which is also 1.

Therefore, the joint density of Y1 and Y2 is:

f(Y1,Y2) = f(U1U2,U2)

= f(U1) x f(U2)

= 1 x 1

= 1

(b) The marginal density for Y1 is the density of Y1 without regard to Y2. Since Y2 is uniform on (0,1), we can integrate the joint density over the interval (0,1) to obtain the marginal density of Y1:

f(Y1) = ∫f(Y1,Y2)dY2

= ∫1dY2

Y2 = 1

Therefore, the marginal density of Y1 is 1

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Please help I've done it but I want to check my answer!

There are several marbles of different colours in a bag in front of you. Your job is to select three marbles and record the colour of each marble you chose. In the bag, there are 22 blue marbles, 17 red marbles, 8 yellow marbles and 3 purple marbles. What are the chances of selecting one red marble, one yellow marble and a blue marble?

Assume that once each marble is chosen, it is not returned to the bag.

Answers

Answer:

the probability of selecting one red marble, one yellow marble, and a blue marble is 1/52. This can also be expressed as a percentage by dividing the probability by 1 and multiplying by 100%, which gives a probability of approximately 1.9%.

Step-by-step explanation:

A four-wheel-drive vehicle is transporting an injured hiker to the
hospital from a point that is 30 km from the nearest point on a straight
road. The hospital is 50 km down that road from that nearest point. If
the vehicle can drive at 30 kph over the terrain and at 120 kph on the
road, how far down the road should the vehicle aim to reach the road
to minimize the time it takes to reach the hospital?

Answers

The final distance is 31 km.

Time, t = Distance, d/Velocity, v

Let's assume the ambulance drives a distance of x along the road, which leaves us 50-x on the road, after which it has reached the road.

It forms a triangle, after which we can use Pythagoras Theorem.

Using it, we get distance down the hill, d1, and we can calculate distance on the road remaining till the hospital, d2.

t = d1/v1 + d2/v2

= [tex]\frac{\sqrt{x^{2} + 30^{2} } }{30} + \frac{50 - x}{120}[/tex]

We need to minimise t. Therefore, we have to differentiate.

On differentiating and equating it to 0, we get the value of x as [tex]\sqrt{60} = 7.75[/tex]

How far down the road should the vehicle aim to reach the road to reach the hospital at the minimum time?

[tex]= \sqrt{900 + 7.75^{2} } = 31 km[/tex]

Thus, the final distance is 31 km.

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Consider exponential functions f and g.

f(x) = 4(5)x

Complete the statements comparing the two functions.

Because the y-intercept of function f is

, it is

the y-intercept of function g.

Both functions

on all intervals of x, but their end behavior is different as x approaches

infinity.

Answers

The correct statements regarding the comparisons of the exponential functions are given as follows:

Because the y-intercept of function f is of 4, it is lower than the y-intercept of function g.Both functions are increasing on all intervals of x, however, their end behavior is different as x approaches negative infinity.

How to define the exponential functions?

The definition of function f(x) is given as follows:

f(x) = 4(5)^x

Meaning that it has an y-intercept and an asymptote given as follows:

y-intercept of 4.asymptote of 0, as when x goes to negative infinity, y goes to zero.

From the graph of function g(x), we have that:

The y-intercept is of 5, which is the value that the graph crosses the y-axis.The horizontal asymptote is of y = 2, hence they have different end behavior when x goes to negative infinity.

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1. 4

2. less than

3. increase

4. negative

Got it right on Edmentum

Function f is represented by an equation in standard form with a = 4 and b = 5. This function is increasing and has a y-intercept of 4. The function approaches 0 as x approaches -∞ and approaches ∞ as x approaches ∞.

Function g crosses the y-axis at (0,5). The function approaches 2 as x approaches -∞ and approaches ∞ as x approaches ∞.

Because the y-intercept of function f is 4, it is less than the y-intercept of function g. Both functions increase on all intervals of x, but their end behavior is different as x approaches negative infinity.

In detail please I’m getting graded and can’t find the answer

Answers

Answer:

x = 75

y = 15

Step-by-step explanation:

What you need to know to solve this question:

1. Angles in a triangle sum up to 180

2. Angles on a straight line add up to 180

3. A right-angle is 90

4. The triangle illustrated is a right-angle triangle

Solving for x:

According to principle 2:

x + 105 = 180

x = 180 - 105

x = 75

Solving for y:

According to principles 1 and 3:

x + y + 90 = 180

(75) + y + 90 = 180

y = 180 - 90 - 75

y = 15

Which of these relations on the set of all people are equivalence relations? Determine the properties of an equivalence relation that the others lack.
a) {(a, b) | a and b are the same age}
b) {(a, b) | a and b have the same parents}
c) {(a, b) | a and b share a common parent}
d) {(a, b) | a and b have met} e) {(a, b) | a and b speak a common language}

Answers

Relations in the options (a), (b) and (e) are the Equivalence relations as, the relations are reflexive, symmetric and transitive all.

Given, five relations as,

a) {(a, b) | a and b are the same age}

b) {(a, b) | a and b have the same parents}

c) {(a, b) | a and b share a common parent}

d) {(a, b) | a and b have met}

e) {(a, b) | a and b speak a common language}

we have to find which of them are equivalence relations

a) as, (a , a) ∈ R ∀ a hence, Reflexive.