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4 years ago

Write the equation of the ellipse in standard form

Mathematics

2 answers:

emmasim [6.3K]4 years ago

6 0

Answer:

h = 1, k = 2, a = 6 and b = 2.

Step-by-step explanation:

Start by grouping the terms in x and y together:

4x^2 - 8x + 36y^2 - 144y = -4

Factor out the coefficient:

4(x^2 - 2x) + 36(y^2 - 4y) = -4

Complete the squares:

4 [(x - 1)^2 - 1] + 36 [y - 2)2 - 4] = -4

4(x - 1)^2 - 4 + 36(y - 2)^2 - 144 = -4

4(x - 1)^2 + 36(y - 2)^2 = 144

Divide through by 144:

(x - 1)^2 / 36 + (y - 2)^2/ 4 = 1

(x - 1)^2 / 6^2 + (y - 2)^2 / 2^2 = 1 (answer).

NNADVOKAT [17]4 years ago

5 0

Answer:

h=1 K =2 a =6 b=2

Step-by-step explanation:

look this solution :

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12. Martina rents a room in her home to guests. She charges a $25 flat fee per night for one person. Additional guests are welco

gtnhenbr [62]

Answer:

Step-by-step explanation:

the answer is A

BECAUSE the fixed charged or the charged that is always there is 25 dollars plus and additional cost for 10 dollars per person plus additional cost depending on how many hours u stay past 10 am

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3 years ago

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T models the temperature (in degrees Celsius) in New York City when it's t hours after midnight on a given day. Match each state

Klio2033 [76]

Answer:

Please check explanation

Step-by-step explanation:

Here, we want to do a matching.

We shall be matching the given statements with the features we have on the graph

Hence we shall be looking closely at the graph to answer the questions.

The y-intercept is the point at which the graph touches the y-axis

And it was at -3 degrees celsius at the beginning of the day.

The temperature was above zero between 8am and 8pm. The matching statement is that it is increasing or decreasing interval

We can see that the graph rose from 8am before it finally comes to zero at 8pm

Positive or negative interval matches with it was getting warmer between 2am and 2pm.

While temperature was lowest at 2am, we can see a peak at 2pm.

8 0

3 years ago

PLEASE HELP MEEEEEEEEE!!!!!!!!! MUST ANSWER BOTH!!

aleksklad [387]

The first one is C y=-2x+20 the second ones is 17.6

4 0

3 years ago

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In a competition, a school awarded medals in different categiories.40 medals in sport 25 medals in danceand 212 medals in music,

aleksley [76]

Answer:

210

Step-by-step explanation:

Given:

Medals in sports = 40

Medals in dance = 25

Medals in music = 212

Total students that received medals = 55

Total students that received medals in all three categories = 6

Required:

How many students get medals in exactly two of these categories?

Take the following:

A = set of persons who got medals in sports.

B = set of persons who got medals in dance

C = set of persons who got medals in music.

Therefore,

n(A) = 40

n(B) = 25

n(C) = 212

n(A∪B∪C)= 55

n(A∩B∩C)= 6

To find how many students get medals in exactly two of these categories, we have:

n(A∩B) + n(B∩C) + n(A∩C) −3*n(A∩B∩C)

=n(A∩B) + n(B∩C) + n(A∩C) −3*6 ……............... (1)

n(A∪B∪C)=n(A)+n(B)+n(C)−n(A∩B)−n(B∩C)−n(A∩C)+n(A∩B∩C)

Thus, n(A∩B)+n(B∩C)+n(A∩C)=n(A)+n(B)+n(C)+n(A∩B∩C)−n(A∪B∪C)

Using equation 1:

=n(A)+n(B)+n(C)+n(A∩B∩C)−n(A∪B∪C)−18

Substitute values in the equation:

= 40 + 25 + 212 + 6 − 55 − 18

= 283 - 73

= 210

Number of students that get medals in exactly two of these categories are 210

6 0

4 years ago

Suppose the number of insect fragments in a chocolate bar follows a Poisson process with the expected number of fragments in a 2

leonid [27]

Answer:

a)The expected number of insect fragments in 1/4 of a 200-gram chocolate bar is 2.55

b)0.6004

c)19.607

Step-by-step explanation:

Let X denotes the number of fragments in 200 gm chocolate bar with expected number of fragments 10.2

X ~ Poisson(A) where $\lambda = \frac{10.2}{200} = 0.051$

a)We are supposed to find the expected number of insect fragments in 1/4 of a 200-gram chocolate bar

$\frac{1}{4} \times 200 = 50$

50 grams of bar contains expected fragments = \lambda x = 0.051 \times 50=2.55

So, the expected number of insect fragments in 1/4 of a 200-gram chocolate bar is 2.55

b) Now we are supposed to find the probability that you have to eat more than 10 grams of chocolate bar before ending your first fragment

Let X denotes the number of grams to be eaten before another fragment is detected.

$P(X>10)= e^{-\lambda \times x}= e^{-0.051 \times 10}= e^{-0.51}=0.6004$

c)The expected number of grams to be eaten before encountering the first fragments :

$E(X)=\frac{1}{\lambda}=\frac{1}{0.051}=19.607 gram$ s

7 0

3 years ago