write up four different equations for the line passing through these points

Less than 1 is the eccentricity of an infinitely long ellipse.

The ratio of the focus's distance from the ellipse's centre and the ellipse's distance from one of its ends is called the eccentricity of an ellipse.

It is easy to understand how circular an ellipse is in relation to a circle when we assume its eccentricity. It also estimates the ovalness of the ellipse, and eccentricity close to 1 directs to the high degree of ovalness.

The eccentricity of an ellipse is always < 1, i.e. e < 1. The formula of the eccentricity of an ellipse is as follows:

Eccentricity = Distance from Focus/Distance from Directrix

Which can be written as

=> e = c/a.    

Where

e = Eccentricity of the ellipse

c = Distance of the focus from the centre of the ellipse

a = Distance of the endpoint of an ellipse from its centre

As we know, the eccentricity of an ellipse is always less than 1, So we can conclude that the eccentricity of an infinitely long ellipse is less than 1.

Therefore, less than 1 is the eccentricity of an infinitely long ellipse.

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Answer:

With the given information we can find the unit rate at least

We know that the artist used 60 pounds of clay to make 80 bowls. If we divide those magnitudes, we would find the total number of pounds per bowl.

\(p=\frac{60}{80}=0.75 \ lb/bowl\)

Therefore, the artist used 0.75 pounds per bowl.

We can also express the proportional relationship as

\(clay=0.75(bowl)\)

Which indicates that the total number of pounds of clay represents 75% of the total number of bowls, that's the relation.

Answer: 0.1714 miles / hour

Step-by-step explanation:

Given the following :

Distance to the store = 3 miles

Time taken to get to store = 12 hours

Time taken to return = 23 hours

The average rate of speed for the trip =?

Average Speed = total distance traveled / total time taken

Total distance traveled = 2 × 3 miles = 6 miles

Total time taken = 12 + 23 = 35 hours

Average speed = 6 miles / 35 hours

Average speed = 0.1714 miles / hour

Answer:

0.1714 mph

5.14 mph

Step-by-step explanation:

Answer: a

.

y

=

sec

x

Step-by-step explanation:

Derivative of z, dz/dt = (∂z/∂x)(dx/dt) + (∂z/∂y)(dy/dt) = (3/2)(-2) + (0)(-3) = -3

We need to use the chain rule:

dz/dt = (∂z/∂x)(dx/dt) + (∂z/∂y)(dy/dt)

We can find ∂z/∂x and ∂z/∂y by differentiating the given equation with respect to x and y, respectively:

2z(dz/dx) = 3x² + 2y(dy/dx)

2z(dz/dy) = 2y

Solving for dz/dx and dz/dy, we get:

dz/dx = (3x² + 2y(dy/dx))/(2z)

dz/dy = y/z

Plugging in the given values, we get:

dz/dx = (3(4)²)/(2(2sqrt(4³))) + 0 = 3/2

dz/dy = 0/sqrt(4³) = 0

So, dz/dt = (∂z/∂x)(dx/dt) + (∂z/∂y)(dy/dt) = (3/2)(-2) + (0)(-3) = -3

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Derivative of z, dz/dt = (∂z/∂x)(dx/dt) + (∂z/∂y)(dy/dt) = (3/2)(-2) + (0)(-3) = -3

We need to use the chain rule:

dz/dt = (∂z/∂x)(dx/dt) + (∂z/∂y)(dy/dt)

We can find ∂z/∂x and ∂z/∂y by differentiating the given equation with respect to x and y, respectively:

2z(dz/dx) = 3x² + 2y(dy/dx)

2z(dz/dy) = 2y

Solving for dz/dx and dz/dy, we get:

dz/dx = (3x² + 2y(dy/dx))/(2z)

dz/dy = y/z

Plugging in the given values, we get:

dz/dx = (3(4)²)/(2(2sqrt(4³))) + 0 = 3/2

dz/dy = 0/sqrt(4³) = 0

So, dz/dt = (∂z/∂x)(dx/dt) + (∂z/∂y)(dy/dt) = (3/2)(-2) + (0)(-3) = -3

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The distance between the two landmarks on the ground below is approximately 3,007 feet.

Height difference refers to the vertical distance or change in elevation between two points or objects. It is the difference in height between a higher point and a lower point, and can be expressed in units such as feet, meters, or any other unit of length.

Let's call the distance between the two landmarks "x". We can use trigonometry and the given angles to set up two equations:

First, we can use the angle between the vertical and the line of sight to one of the landmarks (62°) to find the height difference between the observation deck and that landmark:

tan(62°) = height difference / 1150 ft

height difference = 1150 ft x tan(62°) = 2245.6 ft (rounded to one decimal place)

Similarly, we can use the angle between the vertical and the line of sight to the other landmark (46°) to find the height difference between the observation deck and that landmark:

tan(46°) = height difference / 1150 ft

height difference = 1150 ft x tan(46°) = 1263.3 ft (rounded to one decimal place)

Next, we can use the angle between the lines of sight to the two landmarks (37°) to set up a trigonometric equation involving x:

tan(37°) = (2245.6 ft - 1263.3 ft) / x

x = (2245.6 ft - 1263.3 ft) / tan(37°) = 3006.8 ft (rounded to the nearest foot)

Therefore, the distance between the two landmarks on the ground below is approximately 3,007 feet.

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Answer:

x+3

I hope this helps you

If a local park is open for biking every 12 day open for paddling every 8 day and if today the park is open for both options, then the next date when the park will be open will be on the 24th day. So Hana should pick 24th day from today next.

Every 12 day the local park is open its path for biking and every 8 day they open their lake or paddling. That is in every multiple of 12 days the biking option is available and every multiple of 8 days the paddling option is available.

If today both the biking and paddling option are open, then the next day where both options will be open can be determined by calculating the least common multiple of 12 and 8.

12 = 2×2×3

8 = 2×2×2

LCM (12, 8) = 2×2×2×3

LCM(12, 8) = 24

LCM of 12 and 8 is 24. So 24 days from today, the park will be open for both options.

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Answer:

(0,0)

Step-by-step explanation:

The y intercept is the value of y when x = 0

Based off of the table, when x = 0 , y also = 0

So the y intercept is at (0,0)

Answer:

Buttercup weighs 8 pounds

Step-by-step explanation:

Sorry I can't pick a diagram, since we can't see a photo.

if b is Buttercup and f is Fifi, substitute in Fifi's weight, and solve for b

b x 7 = f

7b = 56

divide both sides by 7

b = 8

Answer:

a sense of cohesion

Step-by-step explanation:

Team cohesion is a concept of how a team stays committed and values the interest of its members. A group can remain in a stable state when cohesion is strong, but the lack of cohesion made it prone to fall apart. The research of group cohesion is an important subject for study o how people stay interested in making large institutions work efficiently. It is referred to as a group of individuals with the same values and skills. And such a group and members of their group are dependable on each other.

In other to command respect and the acceptance of other people's view during a group discussion, it is imperative than contributing members can prove their inputs or view with evidence.

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Since both sides are equal, we have shown that ∑(i=1 to 6) (dx_i + e) = d(∑\((i=1 to 6) x_i\)) + 6e. This represents the summation of the terms \((5x_3 + i)\) for i = 1 to 6.

To show that ∑(i=1 to 6) \((dx_i + e)\)= d(∑(i=1  \(x_i\)) + 6e, we can expand both sides and compare.

Left-hand side:

∑\((i=1 to 6) (dx_i + e) = (dx_1 + e) + (dx_2 + e) + (dx_3 + e) + (dx_4 + e) +\)(dx_5 + \(e) + (dx_6 + e)\)

                        = \(dx_1 + dx_2 + dx_3 + dx_4 + dx_5 + dx_6 + e + e + e + e\)+ e + e

                        = \((dx_1 + dx_2 + dx_3 + dx_4 + dx_5 + dx_6) + 6e\)

Right-hand side:

d(∑\((i=1 to 6) x_i)\)+ 6e = d\((x_1 + x_2 + x_3 + x_4 + x_5 + x_6)\)+ 6e

Now, let's compare the two sides:

Left-hand side: \((dx_1 + dx_2 + dx_3 + dx_4 + dx_5 + dx_6)\) + 6e

Right-hand side: d\((x_1 + x_2 + x_3 + x_4 + x_5 + x_6)\) + 6e

Since both sides are equal, we have shown that ∑\((i=1 to 6) (dx_i + e)\) = d(∑(i=1 to 6)\(x_i)\) + 6e.

To represent the equation\((5x_3 + 4) + (5x_3 + 5) + (5x_3 + 6) + (5x_3 +\)7) + \((5x_3 + 8) + (5x_3 + 9)\) using a Sigma operator notation, we can write it as:

∑\((i=1 to 6) (5x_3 + i)\)

This represents the summation of the terms \((5x_3 + i)\)for i = 1 to 6.

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Answer:

x = \(\frac{1}{4}\)

Step-by-step explanation:

Given

\(\frac{x}{7}\) + x - \(\frac{2}{14}\) = \(\frac{1}{7}\)

Multiply through by 14 to clear the fractions

2x + 14x - 2 = 2 ( add 2 to both sides )

16x = 4 ( divide both sides by 16 )

x = \(\frac{4}{16}\) = \(\frac{1}{4}\)

The correct value is 720 ft of fencing.

Answer:

Max Area = 64800 sq.ft

Step-by-step explanation:

A square will always give us the maximum area.

Thus, one side would be;

720/4 = 180 feet

So, we want a square 180 ft by 180 ft

however, from the question, we are to use the creek as one side. So, we'll take the 180 ft that we don't need because of the creek and then add it to the opposite side to get 180 + 180 = 360 ft.

Thus,we now have a rectangle with dimensions: 180 ft by 360 ft

Area is given by;

area = length × width

Maximum Area = 180 × 360

Max Area = 64800 sq.ft

The given function f(x) = x³ + 2x² - 3 has three solutions.

To determine the number and types of solutions for the function:

f(x) = x³ + 2x² - 3,

we need to find the roots of the function. The roots are the values of x where the function equals zero.

The roots of the equation are given as:

x³ + 2x² - 3 = 0

x(x-3)(x+1)=0

From the above expression, x has 3 values for which the function terminates itself to zero. It means the given function has three solutions.

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Adam Vinatieri made 14 field goals and 7 extra points.

Given that,

a field goal is 3 points and the field goal after a touchdown is only 1 point.

Adam Vinatieri made 21 field goals and extra point kicks for 49 points.

Let x be the number of field goals and y be the extra point kicks.

So we get,

x + y = 21 -------------(1)

3x + y = 49 -----------(2)

Subtracting equation (1) from equation (2),

2x = 28

 x = 14

putting the value of x in equation (1),

14 + y = 21

       y = 7

Therefore Adam Vinatieri made 14 field goals and 7 extra points.

Field goal means a score of three points in football made by drop kicking or placekicking the ball over the crossbar from ordinary play. A field goal is a successful kick of the ball by a kicker through the goalpost. It is an offensive play that can score three points for a team.

Adam Vinatieri is an American former football placekicker who played in the National Football League.

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Answer:

Step-by-step explanation:

A function does not have any repeating domains (x-coordinates).

Hope it helps!

Answer:

6/7

Step-by-step explanation:

3/4÷7/8

you do the reciprocal of the second fraction

So it will be: 3/4 x 8/7

= 6/7

Answer:

it's 6/7

Step-by-step explanation:

As 3/4÷7/8

=3/4×8/7

=24/28

=6/7

(a)  (r, θ) = (√58, arctan(7/3)).

(b) (r, θ) = (8√2, π/4).

(c) (r, θ) = (√85, -arctan(7/6)).

(d) (r, θ) = (√85, arctan(-2/9)).

(e) (r, θ) = (√89, -arctan(8/5)).

(f) (r, θ) = (4, -π/2).

To find the polar coordinates (r, θ) from the given Cartesian coordinates (x, y), we use the following conversions:

r = √(x^2 + y^2)

θ = arctan(y/x)

(a) For (x, y) = (3, 7):

r = √(3^2 + 7^2) = √58

θ = arctan(7/3)

Therefore, (r, θ) = (√58, arctan(7/3)).

(b) For (x, y) = (8, 8):

r = √(8^2 + 8^2) = √128 = 8√2

θ = arctan(8/8) = arctan(1) = π/4

Therefore, (r, θ) = (8√2, π/4).

(c) For (x, y) = (-6, 7):

r = √((-6)^2 + 7^2) = √(36 + 49) = √85

θ = arctan(7/-6) = -arctan(7/6)

Therefore, (r, θ) = (√85, -arctan(7/6)).

(d) For (x, y) = (9, -2):

r = √(9^2 + (-2)^2) = √85

θ = arctan((-2)/9)

Therefore, (r, θ) = (√85, arctan(-2/9)).

(e) For (x, y) = (-5, 8):

r = √((-5)^2 + 8^2) = √89

θ = arctan(8/-5) = -arctan(8/5)

Therefore, (r, θ) = (√89, -arctan(8/5)).

(f) For (x, y) = (0, -4):

r = √(0^2 + (-4)^2) = √16 = 4

θ = arctan((-4)/0) = -π/2

Therefore, (r, θ) = (4, -π/2).

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Answer:

2 1/2 weeks

Step-by-step explanation:

120 plus 24 2 times is 168 add it another time it is 192.

Answer:

48 degrees

Step-by-step explanation:

Because the angles are on the same line (the vertical one) we know that both of them would add up to 180 degrees. So first we subtract 180-32 to get 148. Now we know that 3h+4=148. To solve for h, our first step would be to subtract 4. Now the equation is 3h=144. Lastly, we divide both sides by 3 to get h=48.

The information for the man's path in pieces are added below

The missing figure is added as an attachment, where the equation of the function that passes through the three points is calculated as

f(x) = -x^2/3 - x + 10/3

Using the above as a guide, we have the following:

Track direction "cutting hole":

The track direction of the man's path is downward as the coefficient of x^2 is negative (-1/3).

Route starting point:

From the graph, we have the starting point to be (-5, 0)

Path end point:

From the graph, we have the path end point to be (2, 0)

The highest point

Recall that

f(x) = -x^2/3 - x + 10/3

Differentiate and set to 0

-2x/3 - 1 = 0

So, we have

-2x/3 = 1

This gives

x = -3/2

So, we have

Highest = -(-3/2)^2/3 + 3/2 + 10/3

Highest = 49/12

So, the highest point is 49/12 units high

Maximum value:

This is the same as the highest point

i.e. Max = 49/12

Axis of Symmetry

We have

x = -3/2

This means that axis of symmetry is x = -3/2

The field:

The area under the curve represents the area of the region covered by the man's path on the mountain.

Term:

These are the terms of the function

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Answer:

4>d+q

Step-by-step explanation:

Answer: 0.10d+0.25q≥4

Step-by-step explanation:

"no less than 4" means 4 or more/ at least 4.

Answer:

Yes it does

Step-by-step explanation:

did it on edge

Answer:

92

Step-by-step explanation:

Elementary and middle school groups typically run for 6 to 8 weeks, depending on administrator and teacher support for allowing students to miss class for the group sessions.

Elementary education,  can as well be described as the  primary education, which is the first stage of education that is followed in the traditional  formal education,  children at  about age 5 to 7 are those that are usually found in the elementary seetings of school.

Its should be noted that Elementary and middle school groups typically run for 6 to 8 weeks, depending on administrator .

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In the theater, that have 1,464 seats.

1426 seats are in "regular" sections

38 seats are  "premium" front-row section

The seat arrangement is solved by division. In this case the 62 equal spaced is the divisor while the number of seats is the in each row is the quotient

The division is as follows

1464 / 62

= 23 19/31

The number of seats in the regular section is 23 * 62 = 1426

The remainder will be arranged in premium front row

using equivalent fractions

19 / 31 = 38 / 62

the remainder is 38 and this is the seat for the premium front row section

OR 1464 - 1426 = 38 seats

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