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3 years ago

What is the standard form of 3x^2+3y^2+12x+18y-15=0

Mathematics

1 answer:

vichka [17]3 years ago

6 0

Answer:

(x + 2)^2 + (y + 3)^2 = 18

Step-by-step explanation:

To write this equation in the standard form i.e. (x - h)^2 + (y - k)^2 = R^2, we need to complete the squares on the left side.

For completing the squares, put variables on one side and constants on the other side:

3x^2 + 3y^2 + 12x + 18y - 15 = 0

3x^2 + 3y^2 + 12x + 18y = 15

Rearrange the like terms together:

3x^2 + 12x + 3y^2 + 18y = 15

Since the coefficients of x^2 and y^2 terms are the same, divide both the sides by this coefficient i.e. 3 to get:

x^2 + 4x + y^2 + 6y = 5

Now, square the 1/2 of coefficients for x and y and add them to both sides of the equation:

square of 1/2 of coefficient for x = (4/2)^2 = 4; and

square the 1/2 of coefficient for y = (6/2)^2 = 9

x^2 + 4x + 4 + y^2 + 6y + 9 = 5 + 4 + 9

x^2 + 4x + 4 + y^2 + 6y + 9 = 18

Rewriting this as perfect squares:

(x + 2)^2 + (y + 3)^2 = 18

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Suppose that bugs are present in 1% of all computer programs. A computer de-bugging program detects an actual bug with probabili

lawyer [7]

Answer:

(i) The probability that there is a bug in the program given that the de-bugging program has detected the bug is 0.3333.

(ii) The probability that the bug is actually present given that the de-bugging program claims that bugs are present on both the first and second tests is 0.1111.

(iii) The probability that the bug is actually present given that the de-bugging program claims that bugs are present on all three tests is 0.037.

Step-by-step explanation:

Denote the events as follows:

B = bugs are present in a computer program.

D = a de-bugging program detects the bug.

The information provided is:

$P(B) =0.01\\P(D|B)=0.99\\P(D|B^{c})=0.02$

(i)

The probability that there is a bug in the program given that the de-bugging program has detected the bug is, P (B | D).

The Bayes' theorem states that the conditional probability of an event E given that another event X has already occurred is:

$P(E|X)=\frac{P(X|E)P(E)}{P(X|E)P(E)+P(X|E^{c})P(E^{c})}$

Use the Bayes' theorem to compute the value of P (B | D) as follows:

$P(B|D)=\frac{P(D|B)P(B)}{P(D|B)P(B)+P(D|B^{c})P(B^{c})}=\frac{(0.99\times 0.01)}{(0.99\times 0.01)+(0.02\times (1-0.01))}=0.3333$

Thus, the probability that there is a bug in the program given that the de-bugging program has detected the bug is 0.3333.

(ii)

The probability that a bug is actually present given that the de-bugging program claims that bug is present is:

P (B|D) = 0.3333

Now it is provided that two tests are performed on the program A.

Both the test are independent of each other.

The probability that the bug is actually present given that the de-bugging program claims that bugs are present on both the first and second tests is:

P (Bugs are actually present | Detects on both test) = P (B|D) × P (B|D)

$=0.3333\times 0.3333\\=0.11108889\\\approx 0.1111$

Thus, the probability that the bug is actually present given that the de-bugging program claims that bugs are present on both the first and second tests is 0.1111.

(iii)

Now it is provided that three tests are performed on the program A.

All the three tests are independent of each other.

The probability that the bug is actually present given that the de-bugging program claims that bugs are present on all three tests is:

P (Bugs are actually present | Detects on all 3 test)

= P (B|D) × P (B|D) × P (B|D)

$=0.3333\times 0.3333\times 0.3333\\=0.037025927037\\\approx 0.037$

Thus, the probability that the bug is actually present given that the de-bugging program claims that bugs are present on all three tests is 0.037.

4 0

3 years ago

For his long distance phone service, Keith pays an $8 monthly fee plus 6 cents per minute. Last month, Keith's long distance bil

butalik [34]

Answer:

my answer is 19.90

Step-by-step explanation: so what i did to get this answer is by adding all the numbers so i stack it in order of greater number to least numbers so i did 19.76 + $8 + 6 ( you don't have to put the dollar sign when you add the numbers) and after i added those i got 19.90 as my answer.

hope it helps you

5 0

4 years ago

Read 2 more answers

What number should come next ?

babymother [125]

<h2>Answer: The number that comes next is 52 </h2>

Step-by-step explanation:

2 + (1^2 - 1 ) = 2

2 +( 2^2 - 1 ) = 5

5 + ( 3^2 - 1) = 28

28 + (5^2 - 1) = 52

Thus the next number would be 52

Hope this helps :D

3 0

3 years ago

-2/5n=-30 n=? Please help me with my math! 10 PTNS!!

maks197457 [2]

N =75 i solved for N and got 75

6 0

3 years ago

Read 2 more answers

What two steps are necessary to put this equation into standard form?

ivanzaharov [21]

Answer:

A. Add 4 to both sides and subtract 6x from both sides

Step-by-step explanation:

The correct expression is

x^2-3x+16=6x-4

Add 4 to both sides and subtract 6x from both sides

Add 4 to both sides

x^2-3x+16+4=6x-4+4

x^2-3x+20=6x

Subtract 6x from both sides

x^2-3x-6x+20=6x-6x

x^2-9x+20=0

7 0

4 years ago