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Scrat [10]
2 years ago
12

Find an asymptote of this conic section. 9x^2-36x-4y^2+24y-36=0

Mathematics
1 answer:
ki77a [65]2 years ago
8 0
We will begin by grouping the x terms together and the y terms together so we can complete the square and see what we're looking at. (9x^2-36x)-(4y^2+24y)-36=0.  Now we need to move that 36 over by adding to isolate the x and y terms.  (9x^2-36x)-(4y^2+24y)=36.  Now we need to complete the square on the x terms and the y terms.  Can't do that, though, til the leading coefficients on the squared terms are 1's.  Right now they are 9 and 4.  Factor them out: 9(x^2-4x)-4(y^2-6y)=36.  Now let's complete the square on the x's. Our linear term is 4.  Half of 4 is 2, and 2 squared is 4, so add it into the parenthesis.  BUT don't forget about the 9 hanging around out front there that refuses to be forgotten.  It is a multiplier.  So we are really adding in is 9*4 which is 36.  Half the linear term on the y's is 3.  3 squared is 9, but again, what we are really adding in is -4*9 which is -36.  Putting that altogether looks like this thus far: 9(x^2-4x+4)-4(y^2-6y+9)=36+36-36.  The right side simplifies of course to just 36.  Since we have a minus sign between those x and y terms, this is a hyperbola.  The hyperbola has to be set to equal 1.  So we divide by 36.  At the same time we will form the perfect square binomials we created for this very purpose on the left: \frac{(x-2)^2}{4}- \frac{(y-3)^2}{9}=1.  Since the 9 is the bigger of the 2 values there, and it is under the y terms, our hyperbola has a horizontal transverse axis.  a^2=4 so a=2; b^2=9 so b=3.  Our asymptotes have the formula for the slope of m=+/- \frac{b}{a} which for us is a slope of negative and positive 3/2.  Using the slope and the fact that we now know the center of the hyperbola to be (2, 3), we can solve for b and rewrite the equations of the asymptotes.  3= \frac{3}{2}(2)+b give us a b of 0 so that equation is y = 3/2x.  For the negative slope, we have 3=- \frac{3}{2}(2)+b which gives us a b value of 6.  That equation then is y = -3/2x + 6.  And there you go!
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A company's stock begins the week with a price of $43.85 per share. THe price changes by +$2.70 each day for the first two days,
mixas84 [53]

Given:

Initial price of the stock=$43.85

Change for the first two days=+$2.70

Change for next two days=-$1.10

Last day=-$4.45

The objective is to find the price at the last day.

Let's take the price at final day as <em>x</em>.

\begin{gathered} x=43.85+2.70+2.70-1.10-1.10-4.45 \\ x=42.6 \end{gathered}

Hence, the price of the stock at the last day is $42.6

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1 year ago
Caroline is trying to earn money to pay for her field trip by doing odd jobs around the house. She needs to raise more than $35
Alenkasestr [34]

The inequality that represents how much money Caroline needs to earn will be m>35.

In this case, Caroline needs an amount that's greater than $35, therefore, the amount must be greater than $35

From the options given, the correct inequality will be m>35. This means m is greater than $35.

Read related link on:

brainly.com/question/24751617

8 0
2 years ago
Javier is considering two lawn care services. Premier Landscaping charges $15.00 for travel to the job site and $55.00 per hour
Wittaler [7]

Answer:

Time in which both companies charge same cost = 1.5 hour

Step-by-step explanation:

Given:

                                                        Fixed    Variable

Premier Landscaping charges          $15        $55

Ace Landscaping charges                               $65

Find:

Time in which both companies charge same cost:

Computation:

Assume in X time both companies charge same cost:

So,

Premier Landscaping total cost = Ace Landscaping total cost

⇒ $15 + $55(Time taken) = $65 (Time taken)

⇒ $15 = $65 (Time taken) - $55(Time taken)

⇒ $15 = $10 (Time taken)

⇒ Time taken = 1.5 hour

Time in which both companies charge same cost = 1.5 hour

6 0
3 years ago
I need the top 2 pls
Andreas93 [3]

Answer:

Step-by-step explanation:

7:8 is 7/8

9:5

5 0
2 years ago
(-10x-8)-70 (4x-11) + 46 -43(6x6) -54+ (8x5)
STatiana [176]
I feel like you just put random numbers in to waste someone time... but I did the problem any way.

7 0
2 years ago
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