1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Lilit [14]
3 years ago
12

Please help!! (click on pic)

Mathematics
1 answer:
Natali5045456 [20]3 years ago
7 0

Answer:

1/2x³y^6

Step-by-step explanation:

You might be interested in
Ples help me find slant assemtotes
FrozenT [24]
A polynomial asymptote is a function p(x) such that

\displaystyle\lim_{x\to\pm\infty}(f(x)-p(x))=0

(y+1)^2=4xy\implies y(x)=2x-1\pm2\sqrt{x^2-x}

Since this equation defines a hyperbola, we expect the asymptotes to be lines of the form p(x)=ax+b.

Ignore the negative root (we don't need it). If y=2x-1+2\sqrt{x^2-x}, then we want to find constants a,b such that

\displaystyle\lim_{x\to\infty}(2x-1+2\sqrt{x^2-x}-ax-b)=0

We have

\sqrt{x^2-x}=\sqrt{x^2}\sqrt{1-\dfrac1x}
\sqrt{x^2-x}=|x|\sqrt{1-\dfrac1x}
\sqrt{x^2-x}=x\sqrt{1-\dfrac1x}

since x\to\infty forces us to have x>0. And as x\to\infty, the \dfrac1x term is "negligible", so really \sqrt{x^2-x}\approx x. We can then treat the limand like

2x-1+2x-ax-b=(4-a)x-(b+1)

which tells us that we would choose a=4. You might be tempted to think b=-1, but that won't be right, and that has to do with how we wrote off the "negligible" term. To find the actual value of b, we have to solve for it in the following limit.

\displaystyle\lim_{x\to\infty}(2x-1+2\sqrt{x^2-x}-4x-b)=0

\displaystyle\lim_{x\to\infty}(\sqrt{x^2-x}-x)=\frac{b+1}2

We write

(\sqrt{x^2-x}-x)\cdot\dfrac{\sqrt{x^2-x}+x}{\sqrt{x^2-x}+x}=\dfrac{(x^2-x)-x^2}{\sqrt{x^2-x}+x}=-\dfrac x{x\sqrt{1-\frac1x}+x}=-\dfrac1{\sqrt{1-\frac1x}+1}

Now as x\to\infty, we see this expression approaching -\dfrac12, so that

-\dfrac12=\dfrac{b+1}2\implies b=-2

So one asymptote of the hyperbola is the line y=4x-2.

The other asymptote is obtained similarly by examining the limit as x\to-\infty.

\displaystyle\lim_{x\to-\infty}(2x-1+2\sqrt{x^2-x}-ax-b)=0

\displaystyle\lim_{x\to-\infty}(2x-2x\sqrt{1-\frac1x}-ax-(b+1))=0

Reduce the "negligible" term to get

\displaystyle\lim_{x\to-\infty}(-ax-(b+1))=0

Now we take a=0, and again we're careful to not pick b=-1.

\displaystyle\lim_{x\to-\infty}(2x-1+2\sqrt{x^2-x}-b)=0

\displaystyle\lim_{x\to-\infty}(x+\sqrt{x^2-x})=\frac{b+1}2

(x+\sqrt{x^2-x})\cdot\dfrac{x-\sqrt{x^2-x}}{x-\sqrt{x^2-x}}=\dfrac{x^2-(x^2-x)}{x-\sqrt{x^2-x}}=\dfrac
 x{x-(-x)\sqrt{1-\frac1x}}=\dfrac1{1+\sqrt{1-\frac1x}}

This time the limit is \dfrac12, so

\dfrac12=\dfrac{b+1}2\implies b=0

which means the other asymptote is the line y=0.
4 0
3 years ago
Circle R has equation
Rudiy27

Answer:

The center is (-10,10)  and the radius is 4sqrt(3)

Step-by-step explanation:

(x + 10)^2 + (y - 10)^2 = 48

We can write the equation of a circle as

(x -h)^2 + (y - k)^2 = r^2  where (h,k) is the center and r is the radius

(x-  -10)^2 + (y - 10)^2 = (sqrt(16*3) )^2

(x-  -10)^2 + (y - 10)^2 = (4sqrt(3)) ^2

The center is (-10,10)  and the radius is 4sqrt(3)

5 0
2 years ago
180= 90+30+x? what is the value of x? make sure you give good reasoning
levacccp [35]
180=110 + x
-110. -110
70 = x
3 0
2 years ago
Read 2 more answers
Write 1270 in expanded form using exponents
erastova [34]

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
A 120 watt light bulb uses about 0.1 kilowatt of electricity per hour.if electricity costs $0.20 per kilowatt hour how much does
Ksivusya [100]
A 120 watt light bulb uses about 0.1 kilowatt of electricity per hour.if electricity costs $0.20 per kilowatt hour. Let's solve how much does it cost to have a bulb on for an hour. => 120 watt = 0.1 kilowatt per hour which costs 0.20 per kilowatt per => 0.1 kilowatt per hour * 0.20 = 0.02 dollars in an hour.
8 0
2 years ago
Read 2 more answers
Other questions:
  • Julissa has 8 yards of fabric. Each blanket that she makes needs 23 yard of fabric. How many blankets can she make?
    13·1 answer
  • if you're standing on the trail 220 feet from the bottom of the tree, you have to look up at a 60 degree angle to see the top .
    11·2 answers
  • Solve for x <br><br> Please help
    6·1 answer
  • Evaluate mentally. Share your strategies.
    8·1 answer
  • What is the absolute value of Point B labelled on the number line? A number line with point A at coordinate negative 2.2, point
    13·1 answer
  • Using the point-slope equation, find the equation containing (-2, -4) and slope m = -1
    5·1 answer
  • X^2-10x+27 in the form (x-a)^2+B​
    5·1 answer
  • PLEASE HELP ME! I am stuck on 12 and 13. Thanks in advanced! :)
    7·1 answer
  • Which interval is the solution set to 0.35x – 4.8 &lt; 5.2 – 0.9x? (–∞, –8) (–∞, 8) (–8, ∞) (8, ∞)
    14·2 answers
  • The last one under m&lt;1+m&lt;3 is m&lt;5+M&lt;6
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!