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
quester [9]
3 years ago
5

Find the vertex, focus, directrix, and focal width of the parabola. (5 points)

Mathematics
1 answer:
Anarel [89]3 years ago
8 0

\bf \textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}

\bf -\cfrac{1}{20}x^2=y\implies \cfrac{x^2}{-20}=y\implies x^2=-20y\implies (x-0)^2=-20(y-0) \\\\\\ (x-\stackrel{h}{0})^2=4(\stackrel{p}{-5})(y-\stackrel{k}{0})

something noteworthy is that the squared variable is the "x", thus the parabola is a vertical one, the "p" value is negative, so is opening downwards, and the h,k is pretty much the origin,

vertex is at (0,0)

the focus point is "p" or 5 units down from there, namely at (0, -5)

the directrix is "p" units on the opposite direction, up, namely at y = 5

the focal width, well, |4p| is pretty much the focal width, in this  case, is simply yeap, you guessed it, 20.

You might be interested in
The CPU of a personal computer has a lifetime that is exponentially distributed with a mean lifetime of six years. a) What is th
amm1812

Answer: Our required probability is 0.39.

Step-by-step explanation:

Since we have given that

X be the exponentially distributed with mean life = 6 years

So, E[x]=6

\dfrac{1}{\lambda}=6\\\\\lambda=\dfrac{1}{6}

So, our cumulative distribution function would be

F(x)=1-e^{-\lambda x}

We need to find the probability that the CPU fails within 3 years.

P(X

Hence, our required probability is 0.39.

7 0
3 years ago
(cos2a *cos 4a+ sin 2a*sin 4a)/sin4a
lyudmila [28]

Answer:

Step-by-step explanation:

(cos 4a*cos 2a+sin 4a*sin 2a)/sin 4a

=[cos (4a-2a)]/sin 4a

=(cos 2a)/sin 4a

=(cos 2a) /(2 sin 2a cos 2a)

=1/(2 sin 2a)

=1/2 csc 2a

4 0
2 years ago
Wane went on a 4-kilometer run he took a break at four third kilometers he took a drink of water at ten third kilometers show Wa
otez555 [7]

Answer:

Given,

The total distance covered = 4 km,

Since, initially he would be in rest,

So, his starting point would be 0.

Now, his first break = \frac{4}{3} km,

Second break = \frac{10}{3} km,

Also, we can write,

4=\frac{4\times 3}{3}=\frac{12}{3}

Drawing number line:

Step 1: Draw a line.

Step 2: Make 12 marks in same distance.

Step 3: Starts from 0, then 1/3, 2/3, 3/3 and so on.

Thus, we can show Wayne's bike on a number line as below.

6 0
3 years ago
Lucy needs to buy some organic apples, and her grocery store is having a sale on them. If she buys 3 or fewer pounds of apples,
Helga [31]
It is A you are correct

7 0
3 years ago
Read 2 more answers
Dina and Masha started out on a 12 mi bike path at the same time. When Dina reached the end of the 12 mi, Masha still had 3 mi l
Anna35 [415]

Answer:

6 mph

Step-by-step explanation:

Use formula

D=r\cdot t,

where

D = distance

r = rate

t = time

In your case,

D = 12 mi

<u>Dina:</u>

D = 12 mi

r = 8 mph

t = ?

So,

12=8t\\ \\t=\dfrac{12}{8}=\dfrac{3}{2}=1.5\ hours

<u>Masha:</u>

D = 12 - 3 = 8 mi

r = ?

t = 1.5 hours

Then

9=1.5r\\ \\r=\dfrac{9}{1.5}=\dfrac{90}{15}=6\ mph

6 0
3 years ago
Read 2 more answers
Other questions:
  • There are 16 types of flowers used to decorate for a party. Twelve of the flowers types last an average of 4 days before they wi
    10·1 answer
  • What is the value of the discriminate of the quadratic equation -1=5x^2-2x
    15·1 answer
  • The following data was collected on a cheetah. It ran ½ mile in 2/3 min, ¼ mile in 1/3 min, and ¾ mile in one minute.
    14·1 answer
  • A bakery has 4 trays with 16 muffins on each tray .the bakery has 3 trays of cupcakes with 24 cupcakes on each tray.If 15cupcake
    6·2 answers
  • The equation represents Function A, and the graph represents Function B:
    8·1 answer
  • Which of the following has the lowest unit price?
    8·1 answer
  • The diameter of a circle is 46 yards. What is the circle's circumference? d=46 yd Use 3.14 for it.
    14·1 answer
  • I need help pls! <br> this test is about angles, and i am having trouble with it.
    5·1 answer
  • Due to changing wind conditions, a pilot is able to fly 150 mph for the first third of the flying time of a trip, 175 mph for th
    5·2 answers
  • Solve for 5 points, will give brainlist
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!