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
stich3 [128]
3 years ago
8

PLEASE HELP

Mathematics
1 answer:
Bas_tet [7]3 years ago
7 0
Question 1
We are given horizontal hyperbola in its conic form:
\frac{(x-1)^2}{49}-\frac{(y+3)^2}{9}=1
The general formula for hyperbola in conic form is:
\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1
This is a horizontal hyperbola if we want to get vertical hyperbola we simply switch places of y and x:
\frac{(y-h)^2}{a^2}-\frac{(x-k)^2}{b^2}=1
If we look at our parabola we can see that a=7, b=3, h=1 and k=-3.
We know that center of a parabola is at the point (h,k) and that vertices are at (h+a,k) and (h-a,k). 
We that mind we find:
Center:(1,-3)\\ Vertices:(8,-3),(-6,-3)
The answer is C. Please click this link to see that graph(https://www.desmos.com/calculator/g2pbnxs9ad)
Question 2
Standard form is the same as the conic form that we mention in part 1.
We are given:
Vertices:(0,\pm 2)\\ Foci:(0,\pm 11)
What we can notice right away is that this is a vertical hyperbola. 
We know that vertices are at:
(h,k\pm a)
And that foci are at:
(h,k\pm c)
We know that h=0. We can also conclude that k=0. We know that vertices are a point far away from the center. So our vertices are:
k+a=2\\ k-a=-2
We solve this system and we get that a=2 and k=0. That means that our center is at (0,0).
Our foci are given with these two equations:
k+c=11\\ k-c=-11\\
Since we know that k=0, c=11. We that in mind we can find b:
c^2=a^2+b^2\\ b^2=c^2-a^2\\ b^2=117\\ b=\sqrt{117}
Now we have all the information to write the equation for the parabola:
\frac{(y-h)^2}{a^2}-\frac{(x-k)^2}{b^2}=1\\ \frac{y^2}{4}-\frac{x^2}{117}=1
The answer is A. Link to the graph: https://www.desmos.com/calculator/gw6fnf8pg0 .
Question 3
We are given:
Vertices:(0,\pm 8)\\ Asymptotes:y=\pm \frac{x}{2}
We notice that this is a vertical hyperbola (look at the coordinates of vertices, they are changing along the y-axis).
We know that our vertices are given by the following formula:
k+a=8\\ k-a=8
From this, we can conclude that k=8, and a=8. We know that our center is at (0,0).
Asymptote for the vertical hyperbola is given by this formula:
y=\pm \frac{a}{b}(x-h)+k
For the horizontal hyperbola, you just swap a and b. 
We knot that our h and k are zeros, and if we look at our asymptotes we notice that:
\frac{a}{b}=\frac{1}{2}
We know that a=8 so we can find b from the above equation:
\frac{8}{b}=\frac{1}{2}\\ b=16. 
This is all we need to write down the equation of this hyperbola:
\frac{(y-h)^2}{a^2}-\frac{(x-k)^2}{b^2}=1\\ \frac{y^2}{64}-\frac{x^2}{256}=1
The answers is B. Link to the graph(https://www.desmos.com/calculator/tbecgjct6g).
<span>Question 4
</span>We are given these two equations:
x=t-3\\ y=\frac{2}{t+5}
To eliminate t, we will express t, from the first equation, in terms of x and then plug it back into the second equation:
x=t-3\\ y=\frac{2}{t+5}\\ t=x+3\\ y=\frac{2}{x+3+5}\\ y=\frac{2}{5+8}
The answer is D.
Question 5
We are given polar coordinates:
(7,\frac{2\pi}{3})
To conver polar cordinates in rectangular one with use the following formula:
x=r\cos(\theta)\\ y=r\sin(\theta)\\
In our case r=7 and \theta =\frac{2\pi}{3}.
Let us calculate the rectangular coordinates:
x=7\cos(\frac{2\pi}{3})\\ y=7\sin(\frac{2\pi}{3})\\ x=\frac{-7}{2}\\ y=\frac{7\sqrt{3}}{2}}
Coordinates are:
(\frac{-7}{2},\frac{7\sqrt{3}}{2}})
The answer is A.
Question 6
We are given a point P with the following coordinates:
P(1,\frac{\pi}{3})
What you should keep in mind is that for any point there are two pairs of polar coordinates, because you can reach the same point rotating your point vector clock-wise or counter-clockwise. If you are given a pair of polar coordinates this is the formula you can use to get the second pair:
(r,\theta),(-r,\theta+\pi)
Reason for this is because you rotate your pointing vector by 180 degrees. This means you are doing a reflection on the y=x line and therefore you end up with the same point if you use -r instead of r.With that in mind the second pair for our points is:
(-1,\frac{\pi}{3}+\pi)\\ (-1,\frac{4\pi}{3})
If we rotate our pointing vector by 360 degrees(2pi radians) we will always end up at the same point. In fact, if you any number of full circles you end with the same point.So, the final answer is:
(-1,\frac{4\pi}{3}+2n\pi),(1,\frac{\pi}{3}+2n\pi)
None of the answers you provided are correct. You can change r to -r and end up at the same point without changing the angle.

You might be interested in
Write the expression as a product of the to factors: 6m+ 8n+ 4 ​
Whitepunk [10]

Answer:

No answer do u today

Step-by-step explanation:

Lol

H hi ha job un hi is ihnihniuniunihn como te quiero

8 0
3 years ago
-(-4)(-6)-3/5(10+15)/1/3
Ksenya-84 [330]

Answer:

-29

solving steps:

\sf \hookrightarrow -\left(-4\right)\left(-6\right)-3/5\left(10+15\right)/1/3

\sf \hookrightarrow  -\left(-4\right)\left(-6\right)-3/5\cdot \:25/1/3

\sf \hookrightarrow  -24-3/5\cdot \:25/1/3

\sf \hookrightarrow  -24-5

\sf \hookrightarrow  -29

3 0
2 years ago
Read 2 more answers
Type the correct answer in each box. Round your answers to the nearest tenth.
Alexxandr [17]
To find the length of the ladder, you need to do Pythagorean theorem.
50^2 + 30^2 = x^2
2500 + 900 = x^2
x^2 =3400
x= square root of 3400
58.31 OR 10 root34

To find the angle: 
tan theta = opposite/adjacent
50/30 = 5/3
theta = tan inverse of 5/3
= 59.04
6 0
3 years ago
What is -x2+2-1+6x2-4x2?
Alexandra [31]

Answer:

x^2+1

Step-by-step explanation:

6 0
3 years ago
PLEASE HELP ME!! this is due tonight and i really need help with this so i can do other assignments
Mamont248 [21]

Answer:

64cm² I think :) if u get it wrong dont blame it on me.

5 0
3 years ago
Read 2 more answers
Other questions:
  • Identify the slope of the line shown in the graph below:
    7·2 answers
  • Graph the linear equation y=×/3-4
    11·1 answer
  • An x-ray machine for animals cost $125,000. if the loan is for 10 years, and the interest paid is $65,625, what's the interest r
    6·1 answer
  • »
    5·2 answers
  • Plz help pic is shown I don't know how to do this 7th grade
    11·2 answers
  • Please help me!!! math!!!
    14·1 answer
  • HELP ASAP Will give brainliest!!
    15·1 answer
  • (-5.1)&amp;(-3,-8) find the slope
    13·1 answer
  • Hello i need help please
    7·2 answers
  • 138.867545518 to 4 decimal places.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!