Derive the equation of the parabola with a focus at (0, 1) and a directrix of y = -1. ​

Answers

Answer 1

Answer:

The equation of the parabola is y = x²/4

Step-by-step explanation:

The given focus of the parabola = (0, 1)

The directrix of the parabola is y = -1

A form of the equation of a parabola is presented as follows;

(x - h)² = 4·p·(y - k)

We note that the equation of the directrix is y = k - p

The focus = (h, k + p)

Therefore, by comparison, we have;

k + p = 1...(1)

k - p = -1...(2)

h = 0...(3)

Adding equation (1) to equation (2) gives;

On the left hand side of the addition, we have;

k + p + (k - p) = k + k + p - p = 2·k

On the right hand side of the addition, we have;

1 + -1 = 0

Equating both sides, gives;

2·k = 0

∴ k = 0/2 = 0

From equation (1)

k + p = 0 + 1 = 1

∴ p = 1

Plugging in the values of the variables, 'h', 'k', and 'p' into the equation of the parabola, (x - h)² = 4·p·(y - k), gives;

(x - 0)² = 4 × 1 × (y - 0)

∴ x² = 4·y

The general form of the equation of the parabola, y = a·x² + b·x + c, is therefore;

y = x²/4.


Related Questions

Shannon was born on 12/21/1982. How many eight digit codes could she make using the digits in her birthday?

Answers

Answer:   1120

============================================================

Explanation:

Ignoring the slashes, there are 8 digits here. If we could tell those '1's and '2's apart, then we'd have 8! = 40,320 different codes. The exclamation mark indicates a factorial.

However, the '1's and '2's are indistinguishable. We have to divide by a!*b! = 3!*3! = 6*6 = 36 to account for this.

The a! = 3! = 6 is from the fact we have 3 copies of '1'.

The b! = 3! = 6 is from the fact we have 3 copies of '2'

Dividing by 36 gets us (40,320)/36 = 1120

i don’t get this plz help

Answers

9514 1404 393

Answer:

  f(x) = x(x-1) does not have an inverse function

Step-by-step explanation:

As you know, a function must be single-valued. That is, it can only have one y-value for each x-value.

If the inverse relation is to be a function, the original function must have only one x-value for each y-value. In general, even-degree polynomials, such as quadratic equations, cannot satisfy this requirement. This is often described as "the horizontal line test." That is, if a horizontal line intersects the graph in more than one place, the inverse relation is not a function.

The attachment shows a horizontal line intersecting f(x) = x(x-1) in more than one place. The inverse of this relation is not a function.

Correct answer :-

[tex] \rm{f(x) = x(x - 1)}[/tex]

[tex] \\ [/tex]

What’s the ratio of 20 to 3

Answers

Answer:

666.666666666667%

Step-by-step explanation:

Convert fraction (ratio) - 20 / 3 Answer: -666.666666666667%

20:3
20/3
Think of it as a fraction

An account earns simple interest. Find the annual interest rate.

I=$35
P= $1000
t = 6 months

The annual interest rate is

Answers

Answer:

This is the answer $2100

Step-by-step explanation:

$35×$1000×6/100=2100

Find the area of the kite with diagonals a= 12 and b=9

A) 30
B) 72
C) 54
D) 108

Answers

maybe 108 is the answer.

Mark Brainliest please

Answer :

A=pq/2=12*9/2=54

A person must score in the upper of the population on an IQ test to qualify for membership in Mensa, the international high-IQ society. If IQ scores are normally distributed with a mean of and a standard deviation of , what score must a person have to qualify for Mensa (to whole number)

Answers

Answer:

The person must score at least [tex]X = \mu + Z\sigma[/tex], in which Z has a p-value of [tex]1 - \frac{p}{100}[/tex], considering p the upper percentage the person must score, [tex]\mu[/tex] is the mean IQ score for the population and [tex]\sigma[/tex] is the standard deviation.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

In this question:

Mean [tex]\mu[/tex], standard deviation [tex]\sigma[/tex]

What score must a person have to qualify for Mensa?

Score of at least X, given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]X - \mu = Z\sigma[/tex]

[tex]X = \mu + Z\sigma[/tex]

In which Z has a p-value of [tex]1 - \frac{p}{100}[/tex], considering p the upper percentage the person must score.

The radius of a circle is 10 cm. Find its circumference in terms of \piπ.

Answers

[tex]{ \bf{ \underbrace{Given :}}}[/tex]

Radius of the circle "[tex]r[/tex]" = 10 cm.

[tex]{ \bf{ \underbrace{To\:find:}}}[/tex]

The circumference of the circle.

[tex]{ \bf{ \underbrace{Solution :}}}[/tex]

[tex]\sf\orange{The\:circumference \:of\:the\:circle\:is\:20\:π\:cm.}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

We know that,

[tex]\sf\purple{Circumference\:of\:a\:circle \:=\:2πr }[/tex]

[tex] = 2 \: \pi \times 10 \: cm \\ \\ = 20 \: \pi \: cm[/tex]

Therefore, the circumference of the circle is 20 π cm.

[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}[/tex]

What is the best description of the data in the histogram
A The data is set symmetrical
B The data interval is four
C The data set has a peak
D The data set has a cluster

Answers

A-the data set is symmetrical

Deborah finds that that the theoretical probability of flipping "heads" on a fair coin was 50%. After she flipped the fair coin 100 times, she calculated that she flipped heads 45 times. what is the percent difference in theoretical and experimental probability​

Answers

Answer: 5% if it’s bubble sheet then 0.05

Step-by-step explanation:

Probability of flipping heads=50%

Probability of flipping practically = 45/100

=45

So 50%-45% = 5%

help help help help help

Answers

Answer:

11.

Step-by-step explanation:

The scores 60-69 has two people. The scores 70-79 have 9 people. Both are lower or below 80.

Answer:

11

Step-by-step explanation:

Add the number of people in the 60-69 range ( 2) and the number of people in the 70-79 range (9) to get the number of people below 80

2+9 = 11

Please help meeeeeee!!​

Answers

Since m is parallel to n, the angle opposite to 4x-23 will be 2x+17. These are vertical angles, meaning they’re the same.
4x-23=2x+17
2x=40
x=20
Problem:-

Find x so that m || n. Show your work.

Solution:-

Since m || n, 4x – 23 = 2x + 17 by the Converse of alternate exterior angles theorem.

Solve for x.

[tex]\sf{4x-23=2x+17}[/tex]

[tex]\sf{4x-2x-23=2x-2x+17}[/tex]

[tex]\sf{2x-23=17}[/tex]

[tex]\sf{2x-23+23=17+23}[/tex]

[tex]\sf{2x=40}[/tex]

[tex]\sf{\frac{2x}{2}={\frac{40}{2}}}[/tex]

[tex]\sf{x={\color{magenta}{20}}}[/tex]

========================

#Hope it helps!

(ノ^_^)ノ

I ONLY HAVE 5 minutes HELP!!!


Alvarez has $650 deposited into his bank account. The account earns simple interest of 6,5% per year. No other money is added or withdrawn from the account
for a period of four years. What is the total amount of money in the account after four years?
$143
O $685.75
C $793
D 8805.24

Answers

Answer:

685.75

Step-by-step explanation:

650*0.055+650

You roll a 6-sided die.
What is P(odd)?
Write your answer as a percentage.
%
Submit

Answers

Answer:

it is 50%

Step-by-step explanation:

>:( im doing ixl and im in paine but here is the answer ok

Solve x^2+14x=15 by completing the square.

Answers

The answer to your question is x=1

Answer:

-15, 1

Step-by-step explanation:

See image below:)

Soosie's Cookie Company had fixed costs of $1250 and variable costs of $4.25 per dozen gourmet cookies that were baked and packaged for sale. Write an equation that can be used to determine the total cost when x dozens of cookies are baked and sold. Then determine the total cost of baking and selling 85 dozen gourmet cookies.

Answers

Answer:

$1250.00 + (x)$4.25 =

Step-by-step explanation

So fixed costs are $1,250.00.....every dozen you bake add $4.25 to the costs, cook one dozen you have $1,250.00 plus $4.25 or a total of $1,254.25.

Cook 10 dozen and you add $45.25 = the $1,250.00 for a new total of $1,295.25.

First and 2nd question is easier.
1) What is 3% of 0.80 and what is 7% of 0.40
2) what is 90$ of 3 and what is 40% of 24

Answers

Answer:

3% of 0.80 = 0.024

7% of 0.40 = 0.028

90% of 3 = 2.7

40% of 24 = 9.6

Step-by-step explanation:

help me this question ​

Answers

Answer:

Option B

Step-by-step explanation:

The length and breadth of a rectangular field are 312m and 186m respectively; correct to the nearest metres. Between what limits must the field's perimetre lie? (Write your final answer as an inequality)​

Answers

Answer:

[tex] P \geq 1000 \; meters [/tex]

Step-by-step explanation:

Given the following data;

Length = 312 meters

Breadth = 186 meters

To find the perimeter of the rectangle;

Mathematically, the perimeter of a rectangle is given by the formula;

Perimeter = 2(L + W)

Perimeter = 2(312 + 186)

Perimeter = 2(498)

Perimeter = 996 meters

To the nearest meters, we have;

Perimeter = 996 ≈ 1000 meters

Let P represent the perimeter of a rectangular field.

900 < P > 1000

Therefore, [tex] P \geq 1000 \; meters[/tex]

Determine if the two triangles are congruent. If they are, State how you know. NO LINKS!!!! Show your work. Part 2c​

Answers

Answer:

2.  Not enough information

4. Congruent SAS

4. Similar, not enough information to determine congruency.

Step-by-step explanation:

2.  We only know one side and one angle are congruent,  Not enough to determine congruency

4.  We know two sides and the angle between are vertical angles and vertical angles are congruent.  SAS is how the triangles are congruent.

6.  The three angles are congruent which makes the triangles similar.  We need to know a side if they are to be congruent

Ryan orders a pizza with a 20 inch diameter and asks for a cheese stuff crust along its border . The cheese filled border measures blank inches

Answers

C = pi x d
So the border is about 3.1 x 20 = 62 inches

evaluate the expression when f=6 12f+3

Answers

Answer:

75

Step-by-step explanation:

Substitute 6 for f

12f+3=

12*6+3=

72 + 3 = 75

Answer:

12f+3 = 75 when f = 6

Step-by-step explanation:

12f+3

Let f = 6

12*6+3

Multiply

72 +3

Add

75

The scatter plot below shows the ages and heights of a baseball team. Each dot represents one player. What is the total
number of 12-year olds who are more than 60 inches tall?
A 3
B 7
C5
D 2

Answers

Answer:

D

Step-by-step explanation:

if each dot is one person then there are only 2 people that are 12 and that are more than 60in tall

Answer:

its 2 because it says how many are 12 years old and are taller than 60

A is a plane figure bounded by more than four straight lines.

Answers

Answer:

A plane figure with 4 sides is called a quadrilateral.

Step-by-step explanation:

A plane figure bounded by more than four straight lines is generally referred to as a polygon. A polygon is a closed two-dimensional shape formed by connecting multiple line segments. The line segments, also known as sides, should intersect only at their endpoints, forming vertices of the polygon.

Polygons can have various numbers of sides, and their names are typically based on the number of sides they possess. Some common examples include triangles (3 sides), quadrilaterals (4 sides), pentagons (5 sides), hexagons (6 sides), and so on.

However, when the statement specifies that the plane figure is bounded by "more than four" straight lines, it suggests that the figure in question is a polygon with more than four sides. The exact name or classification of the polygon would depend on the specific number of sides it possesses.

To know more about plane figure . here

https://brainly.com/question/29797834

#SPJ2

Estimate by rounding to nearest 100 5428 + 6378 = ?​

Answers

5428 +6378 = 11806
5400 + 6400 = 11800
The other guy is right

Consider the following time series. t 1 2 3 4 5 yt 6 10 8 13 15
(a) Choose the correct time series plot. (i) (ii) (iii) (iv) What type of pattern exists in the data?
(b) Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series. If required, round your answers to two decimal places. y-intercept, b0 = 4.1 Slope, b1 = 2.1 MSE = ????
(c) What is the forecast for t = 6? If required, round your answer to one decimal place. 16.7 I know how to do it all but the MSE.

Answers

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data :

t __1 2 3 4 5

yt_ 6 10 8 13 15

Using technology to produce a linear model :

The linear model obtained shows a positive linear pattern exist for the time series data :

The parameters for the line that minimizes MSE for the then series is :

y = 2.1t + 4.1

Where, slope = 2.1 ; intercept = 4.1

The mean squared error :

Sum of squared estimate of error = 9.1

Mean squared error = √9.1

Mean squared error = 3.02

Forecast for t = 6

y = 2.1t + 4.1

y = 2.1*6 + 4.1

y = 12.6 + 4.1

y = 16.7

20 POINTS!!
Suppose that, based on a sample, the 95% confidence interval for the mean of
a population is (23,39). What was the mean of the sample?
A. 31
B. 37
C. 35
D. 33

Answers

Answer: 31

Step-by-step explanation: just took the test

Jane wants to add chocolate chips to her trail mix. A 3-pound bag of chocolate chips cost $3.22 . What is the unit price ?

Answers

Answer:

It would be 1.073 you can also rojnd ot to 1.07

Answer:

$1.07 per pound

Step-by-step explanation:

$3.22/3lb is about $1.07 per lb.

15 POINTS! PLEASE HELP! WILL GIVE BRAINLIEST!
Which expression should you simplify to find the 90% confidence interval for a sample of 36 people with a mean of 64 and standard deviation of 4? O +2 A. 36 2. VOA O B. 64 +2 4 V36 O C. 64 +1.645. 4. V36 4 O D. 36 +1.645 V64 SUBMIT​

Answers

Answer:

c

Step-by-step explanation:

i took the test and got it right

For 90% confidence interval for a sample of 36 people with a mean of 64 and standard deviation of 4 the answer is C. 64 +1.645. 4. V36.

What is confidence interval?

A confidence interval is a range of values that is likely to contain the true population parameter with a certain level of confidence.

In statistics, it is commonly used to estimate the population mean based on a sample mean, standard deviation, and sample size.

The confidence level represents the probability that the true population parameter falls within the calculated interval.

The correct expression to find the 90% confidence interval for a sample of 36 people with a mean of 64 and standard deviation of 4 is:

64 ± 1.645(4/√36)

Simplifying the expression:

64 ± 1.645(4/6)

64 ± 1.645(0.6667)

64 ± 1.0967

The 90% confidence interval is (62.9033, 65.0967).

Therefore, the answer is C. 64 +1.645. 4. V36.

For more details regarding confidence interval, visit:

https://brainly.com/question/29680703

#SPJ5

The function ƒ(x) = −(x + 3)^2 − 4 is not one-to-one. Find a portion of the domain where the function is one-to-one and find an inverse function.

Answers

Answer:

Step-by-step explanation:

The second one I believe.

Ravi bought a pack of 30 biscuits. He ate a fifth of them on Thursday.He ate a third of the remaining biscuits on Friday How Many biscuits did he have left?

Answers

Answer:

if I'm not mistaking (please correct if I'm wrong) but I think he would have 16 left.

Step-by-step explanation:

you have to divide one-fifth of 30 which would get you 6, then divide one-third of 24 ( because 30 - 6 is 24) then total both fractions to get 14. then finally subtract 14 from 30 to get 16.

Other Questions
9)10)22x - 28x + 2A) 5B) 6D 2C) 8A 5C) -10 need help again thank you How can a government print more money than it takes through taxes and borrowing? Why would a government do this What is a surface that reflects a color of 500 nanometer wavelength? The suspense of a story usually reaches its peak during the please help me immediately please guys please my sir was give me homework pls help me I been in this question for hr pls help A wall is 60 feet tall. To avoid tipping over, the ladder must be placed 11 feet from the base of the wall. How tall of a ladder must you have to reach all the way to the top of the 60 foot wall? B. Indica si los siguientes hechos tienen un impacto positivo o negativo en el medioambiente. Escribe P si es positivo, o N si es negativo.1. El gobierno (government) quiere reducir el nmero de animales en peligro deextincin.2. En este pueblo la gente quiege juntarse para resolver los problemas ecolgicos.3. Adems, estamos buscando maneras de luchar contra la destruccin demateriales reciclables: papel, vidrio y latas.4. A algunas personas les parece que no es importante ahorrar energa.5. En mi casa hemos mejorado el sistema de calefaccin. Ahora, funciona mejor, esms eficiente y consume menos electricidad.6. Hay personas que dudan que conservar el medio ambiente sea tan importantecomo dicen los expertos.7. Hay animales y pjaros que estn en peligro de extincin a causa de ladestruccin de las selvas tropicales. what is the molality of a solution that has 4 mol of KCI in 0.800 kg of water? help me pleaseeee What can you tell about a triangle when vibe three side lengths Which is untrue of both state and federal government? Important: (Worth 50 Points)The number of adults at an amusement park, measured in hundreds of people, is represented by the function a(w)=0.4w2+5w+9, where w is the number of weeks since the amusement park opened for the season.The number of children at the same amusement park, measured in hundreds of people, is represented by the function c(w)=0.2w2+9w+12, where w is the number of weeks since the amusement park opened for the season.What function, f(w) , can be used to determine how many more children than adults are at the amusement park any week during the season?f(w)=0.2w2+4w+3f(w)=0.2w2+4w3f(w)=0.2w2+4w+3f(w)=0.2w2+14w+3 How do advertisements influence viewers to buy a product How long does copyright protection last for literary, artistic, or musical work?until the creator dies and there are no longer any living relativesuntil the piece of work is destroyed or rendered obsoletefrom the time the work is publicly presented plus seventy yearsthe duration of the creators life plus seventy years after his or her death Give the name (monomial,binomial, trinomial etc.) anddegree of the polynomial.15x2 Please help with this question. What is the probability of getting 1 red and then blue? 21.5 sq. Cm43 sq. Cm100 sq. Cm68.6 sq. Cm [tex] \sqrt] a3 - b3[/tex]what is answer