when does a parametric equations describe a physical situation where a standard relationship between two variables does not suffice

The points of intersection of the system formed by the circle (x - 2)² + (y - 3)² = 16 and the ellipse (x - 2)² / 16 + (y - 3)² / 64 = 1 are (x₁, y₁) = (- 2, 3) and (x₂, y₂) = (6, 3).

Herein we get a system formed by two conics, the former represents a circle and the latter represents an ellipse. There are different methods to solve the system, the use of graphing tools offers a quick though reasonable approach to find that. First, write the equations corresponding to the conics:

Circle

(x - 2)² + (y - 3)² = 16

Ellipse

(x - 2)² / 16 + (y - 3)² / 64 = 1

Second, plot the two graphs of the functions. (Please see the image attached below)

Third, write the points of intersection:

(x₁, y₁) = (- 2, 3), (x₂, y₂) = (6, 3)

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Answer:

Below

Step-by-step explanation:

I do not know which conversion factor you are to use, but here is one:

1 km = .62137 mi

then   40 miles becomes :

40 miles / ( .62137 mi / km) = 64.4 km

Answer:

7^6

Step-by-step explanation:

7 to the power of 6

Answer: [tex]7^{6}[/tex]

Step-by-step explanation:

Exponential form denotes how many times a value is multiplied by itself.

This is 7 times itself 6 times, so it is written as 7 with a 6 in the top right corner.

There will be "sample size."=102 Below is an additional explanation.

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.

The probability of an event can be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

In order to better grasp probability, let's look at a straightforward application.

Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.

There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.

hence, There will be "sample size."=102 Below is an additional explanation.

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Answer:

138

Step-by-step explanation:

23 x 6 (sides) = 138

The solution is Option D.

The equation of line that passes through the point P ( 4 , -3 ) and the point Q ( 0 , -2 ) is y = ( -1/4 )x - 2

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the first point be P = P ( 4 , -3 )

Let the second point be Q = Q ( 0 , -2 )

Now , the slope of the line passing through the points is calculated from the formula slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( -2 - ( -3 ) ) / ( 0 - 4 )

Slope m = ( -2 + 3 ) / -4

Slope m = -1/4

Now , the equation of line is given by

y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - ( -3 ) = ( -1/4 ) ( x - 4 )

On simplifying the equation , we get

y + 3 = ( -1/4 )x + 1

Subtracting 3 on both sides of the equation , we get

y = ( -1/4 )x - 2

Therefore , the value of A is y = ( -1/4 )x - 2

Hence , the equation of line is y = ( -1/4 )x - 2

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Addition is used to find the sum of the number of miles lauren ran

Two or more expressions with an Equal sign is called as Equation.

Given,

Lanren ran 2.76. Miles in a track event.

Then she ran 0.4 Mile home after the event

We need to find the sum of the number of miles lauren ran.

By addition we find the sum of the number of miles lauren ran.

Two point seven six plus zero point four

2.76+0.4

Three point one six

3.16

Hence, addition is used to find the sum of the number of miles lauren ran

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Answer:

post cards cost .06 each and envelopes cost .08 each.

Step-by-step explanation:

Let p = the cost of the post cards

Let e = the cost of the envelopes

15p + 10e = 1.70

e = p + .02  Substitute  p + .02 for e in the first equation

15p + 10(p + .02) = 1.70   Distribute the 10

15p + 10p + .2 = 1.70     Combine like terms

25p + .2 = 1.70  Subtract .2 from both sides

25p = 1.50  Divide both sides by 25

p = .06

Post cards cost .06 each.

Envelopes cost .08 each

Answer:

d

Step-by-step explanation:

Answer:

r = .5 units  

Step-by-step explanation:

8.7 R is an improper  FRACTION of the 2 pi R of the entire circle ....set up a ratio:

8.7 / (2 pi)  =  3.9 / x       where x is the entire circumference measurement

x = 3.9 / (8.7 / (2 pi) )   = 2.82 units    

To find the radius    circumf = 2 pi r

                                     2.82 = 2 pi r      shows r = .5 units

The solutions of the equation x² +3x - 4=0 are x=1 and x= -4 .

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

Given equation:

x² +3x - 4=0

Standard form of a quadratic equation:

ax² +bx+c=0

On comparing, a=1, b= 3, c= -4

Quadratic formula:

x = [ -b ± √(b² - 4ac ) ] /(2a)

Substitute the values

x = [ -3 ± √(3² - 4*1*(-4) ) ] /(2*1)

x= [ -3 ± √(9 + 16 ) ] /(2)

On simplifying,

x=1 and x= -4

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Answer:

look at the y axis. :)

The correct statements regarding Marc's account balance are given as follows:

Mark's account balance is the amount of money that he has on his account.

Hence the balance is obtained as follows:

The statements are given by the image shown at the end of the answer.

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So, for f(x)=xa(9-x)b on the interval 0≤x≤9, the maximum value of f(x) is 0, and a and b are positive numbers.

A function is an expression, rule, or law in mathematics that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are common in mathematics and are required for the formulation of physical relationships in the sciences. Functions are broadly classified into four categories. Element-based: one-to-one function, many-to-one function, onto function, one-to-one and onto function, into function

Here,

f(x)=xa(9-x)b

If we put x=0,

f(x)=0

If we put x=9,

f(x)=0

So, the maximum value of f(x) is 0 for f(x)=xa(9-x)b on the interval 0 ≤ x ≤ 9 and a and b are positive numbers.

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Answer:   1/2 |x| = -3?

Step-by-step explanation:

a) A random family is chosen and then a random child within that family is chosen the mean is 1.45 and the variance is 0.38.

b) A random child is chosen in the town, the mean is 1.579 and the variance is 0.454.

For part A:

A random family is chosen and then a random child within that family.

P(X=1)= P(X=1 | family with one child). P(family with one child)

             + P(X=1 | family with two children).P(family with two children)

             +P(X=1 | family with three children).P(family with three children)

           = 1.30/100 + 1/2 . 50/100 + 1/3 . 20/100 = 37/60

P(X=2)=P(X=2 | family with one child). P(family with one child)

             + P(X=2 | family with two children).P(family with two children)

             +P(X=2 | family with three children).P(family with three children)

           = 0.30/100 + 1/2 . 50/100 + 1/3 . 20/100 = 19/60

P(X=3)=P(X=3 | family with one child). P(family with one child)

             + P(X=3 | family with two children).P(family with two children)

             +P(X=3 | family with three children).P(family with three children)

           = 0.30/100 + 0 . 50/100 + 1/3 . 20/100 = 4/40

hence, using these probabilities we can find,

E(X) = 1(37/60) + 2(19/60) + 3(4/60) = 1.45,

therefore, Var(x) = 149/60 − [tex]1.45^{2}[/tex] = 457/1200 ≈ 0.38

hence, the mean of the child's birth is 1.45 and the variance of the child's birth ranks 0.38.

For part B,

When a random child is chosen in the town with equal probabilities.

There are 1 x 30 + 2 x 50 + 3 x 20 = 190 children in the town where 100 of them are first born, 70 of them are second born, and 20 of them are third born. Let X be a random variable that marks the birth rank of a child.

Hence,

E(X) = 1(100/190) + 2(70/190) + 3(20/190) ≈ 1.579

and

Var(X) = 2.947 − [tex]1.579^{2}[/tex] ≈ 0.454

For a random child chosen, the mean of the child's birth is 1.579 and the variance of the child's birth ranks 0.454.

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the original price was "x", which oddly enough is the 100%.

now, we know the TV is 75% off, that means the sale price is 100% - 75% = 25%, and we know that's 24 bucks.

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 24& 25 \end{array} \implies \cfrac{x}{24}~~=~~\cfrac{100}{25} \implies \cfrac{ x }{ 24 } ~~=~~ 4\implies x=96[/tex]

The function that have a zero at x = 4  are

The first function is

f(x) = -2x^2 - 18x - 40

Substitute the value of x = 4

f(4) = -2(4)^2 - 18(4) - 40

= -2(16) - 72 - 40

= -32 - 72 - 40

= -144

The result is not zero

The second function is

f(x) = 2x^2 - 11x + 12

f(4) = 2(4)^2 - 11(4) +12

= 32 - 44 + 12

= 0

The result is zero

The third function is

f(x) = 3x^3 + x^2 - 48x - 16

f(4) = 3(4)^3 + 4^2 - 48(4) - 16

= 192 + 16 - 192 - 16

= 0

The result is zero

The fourth function is

f(x) = x^2 - 3x - 28

f(4) = 4^2 - 3(4) - 28

= 16 - 12 - 28

= -24

The fifth function is

f(x) = x^3 - 4x^2 - x + 4

f(4) = 4^3 - 4(4)^2 - 4 + 4

= 64 - 64 - 4 + 4

= 0

Therefore, the function f(x) = 2x^2 - 11x + 12, f(x) = 3x^3 + x^2 - 48x - 16 and  f(x) = x^3 - 4x^2 - x + 4 have zero at x equals 4

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y = mx + b
y = -4

m = 0
b = -4

Since the slope (m) is 0, the line is horizontal. The y-intercept (b) is -4, meaning that the graph is a horizontal line at y = -4.

See the attached file for the graph.

1. The minimum number (Lower Limit) of pets one can find in the area is 1,680 pets, given the margin of error.

2. The maximum number (Upper Limit) of pets in the area will be 2,640 pets, given the margin of error.

The margin of error shows the statistical difference between actual and projected results in a random survey sample.

In other words, the margin of error reveals the level of unpredictability in research outcomes.

The statistical difference can be explained with an upper limit (maximum) and lower limit (minimum) between which the statistical value lies, thereby offering some level of confidence.

Average (mean) number of pets in each household = 1.8 pets

The margin of error = ±0.4 pets

The total number of households in the area = 1,200

Upper limit (maximum) of pets in the area = 2,640 pets (1,200 x 1.8 +0.4)

Lower limit (minimum) of pets in the area = 1,680 pets (1,200 x 1.8 - 0.4)

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What are the minimum and maximum numbers of pets you expect to find in her area?

1. The percentages chosen are given as follows:

2. The maximum amount that can be spent in each category is given as follows:

The percentages for each of the four applications can be divided in any form, as long as the sum of the five percentages is of 100%.

This is the case for the attributed percentages, as:

35 + 20 + 20 + 20 + 5 = 100.

The maximum amounts are found applying the proportions, multiplying the decimal equivalents of the maximum percentages by the bi-weekly net pay of $1,502.45.

Then the amounts in this problem are calculated as follows:

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The final temperature is calculated to be 41.8 degrees Celcius if the gas is compressed to 0.80 m^3 and the pressure rises to 0.82*10^5 Pa

The final temperature can be calculated by using the combined gas law as follows;

[tex]\frac{P_{1}V_{1} }{T_{1} } = \frac{P_{2}V_{2} }{T_{2} }[/tex]

Here [tex]P_{1}[/tex] and [tex]P_{2}[/tex] represent the initial and final pressure respectively,

[tex]V_{1}[/tex] and [tex]V_{2}[/tex] represent the initial and final volume respectively

[tex]T_{1}[/tex] and [tex]T_{2}[/tex] represent the initial and final temperature respectively

Converting [tex]T_{1}[/tex] to kelvin as follows;

[tex]T_{1}[/tex] = 27 degrees Celcius = 27 + 273 = 300 K

Now the final temperature can be determined by substituting the values in this equation of the combined gas law as follows;

(0.50×10^5)(1.25) / 300 = (0.82×10^5)(0.80) / [tex]T_{2}[/tex]

208.333333333 = (0.82×10^5)(0.80) / [tex]T_{2}[/tex]

208.333333333 ([tex]T_{2}[/tex]) = (0.82×10^5)(0.80)

[tex]T_{2}[/tex] = (0.82×10^5)(0.80) ÷ 208.333333333

[tex]T_{2}[/tex] = 314.8 K

Converting K to degree Celcius as follows;

[tex]T_{2}[/tex] = 314.8 - 273 = 41.8 degree Celcius

Hence 41.8 degrees Celcius is calculated to be the final temperature.

Although a part of your question is incorrect, you might be referring to this question:

A cylinder fitted with a movable piston contains ideal gas at 27 degrees C, pressure 0.50*10^5 Pa, and volume 1.25 m^3. What will be the final temperature if the gas is compressed to 0.80 m^3 and the pressure rises to 0.82*10^5 Pa?

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When the line to be examined's slope is known, and the provided point also serves as the y intercept, the slope intercept formula, y = mx + b, is utilised (0, b). B stands in for the y value of the y-intercept point in the formula.

Determine the equation of the line with a slope of 2/3 and a y intercept of (0, 4).

Solution

Step 1: Replace the provided in the formula.

Provided that the slope, m, is given as 2/3 and the y intercept, (0, 4), b = 4.

y = mx + b

y = 2 3 x + 4

2 /3 x – y = - 4

(Note: You must multiply this by the LCD of 3 to fix this since the conventional form does not support fractional numbers.)

3( 2 /3x – y) = (- 4) (- 4)

3/2x – 3y = - 12

This is the line's determined equation.

Verify is the second step.

Utilizing the formula, plot two points. In this example, y1 = 2 and Y2 = -6. 2x - 3y = - 12 2x – 3y = - 12

Let y = 2 Let y = - 6

2x – 3(2) = - 12 2x – 3(-6) = - 12

2x – 6 = - 12 2x + 18 = - 12

2x = - 6 2x = - 30 \sx = - 3 x = - 15

P1 therefore equals (-3, 2) and P2 equals (-15, -6).

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The length of the ramp Tyree will need to make from window to the sidewalk is 5√17 feet .

In the question ,

it is given that ,

height of the window is = 5 feet ,

distance of sidewalk from the Tyree's house is = 20 feet ,

We know that the angle between the wall and the floor is 90° ,

So , the system is making a right triangle  ,

let the length of the ramp be = "x" ,

So, According to Pythagoras Theorem ,

we get ,

x² = 5² + 20²

x² = 25 + 400

x² = 425

x = √425

x = 5√17 feet .

Therefore , the length of the ramp is 5√17 feet .

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The mean number of people with the genetic mutation in these groups is 80 as this follows a Binomial Distribution.

It is given that 10% of the population has a genetic mutation. We have a sample of 800 here.

Let X be the random variable that defines the number of people with the mutation in the sample.

Since every person can or can't have the mutation, this is a Binomial distribution.

Here,

n = 800

p = 0.1

According to the formula for a Binomial Distribution,

the mean = np

Therefore, the mean for the above distribution will be

800 X 0.1

= 80.

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Answer:

The answer should be A.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Applying the AA similarity theorem, the length of DF is: 15 units.

When two angles in one triangle are congruent to the corresponding two angles in another triangle, both are said to be similar to one another. This means that, the corresponding sides of these two triangles would be proportional or have the same ratio.

In the image attached bellow, triangle DEF and triangle DBC are similar to each other because they have two pairs of corresponding angles that are congruent which are:

<DFE ≅ <DCB [right angles are equal]

<EDF ≅ <BDC [reflexive property of congruence]

Therefore, their corresponding sides will have equal ratios such as:

DC/DF = BC/EF

Substitute:

27/DF = 49.5/27.5

Cross multiply:

DF = (27.5 * 27) / 49.5

DF = 15

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Answer:

x = 54

Step-by-step explanation:

The 2 angles shown are vertical angles, so they are equal.

2x + 2 = 3x - 52

2x - 3x = -52 - 2

-x = -54

x = 54

They are 110° angles

Answer: x = -10

Step-by-step explanation:

1: Add: 2x+2  3x-52 = 5x -50

2: Divide both sides by the same factor: 5x - 50

                                                                      ------------

                                                                      5      5

3: Level: x= -10

The parabola's vertex has the equation y = x² - 8x + 12 is (4, -4).

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line. A plane curve created by a point moving so that its distance from a fixed point equals its distance from a fixed line is known as a parabola. A normal parabola's standard equation is y 2 = 4 an x, where an is the distance from the vertex to the focus.

Given,

Function,

y = x² - 8x + 12

The supplied equation's vertex must be located.

The equation is a parabolic equation when we look at it.

We are aware that a parabolic equation's generic form is

y = x² - 8x + 12

where the parabola's vertex's x and y coordinates are denoted by h and k.

We can determine the following by comparing the aforementioned equation with the parabola's general form:

x = 4, y = 4 and h = -8

The parabola's vertex has the equation y = x² - 8x + 12 is (4, -4).

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