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
lozanna [386]
2 years ago
13

A jumping spider's movement is modeled by a parabola. The spider makes a single jump from the origin and reaches a maximum heigh

t of 10 mm halfway across a horizontal distance of 80 mm.
Part A: Write the equation of the parabola in standard form that models the spider's jump. Show your work. (4 points)

Part B: Identify the focus, directrix, and axis of symmetry of the parabola. (6 points)
Mathematics
1 answer:
aleksklad [387]2 years ago
4 0

The spider's movement is an illustration of a parabola.

  • The equation of a parabola is: \mathbf{y = -\frac{1}{160}(x - 40) + 10}
  • The focus of a parabola is: (40,-30)
  • The axis of symmetry is: \mathbf{x = 40}
  • The directrix is:\mathbf{y = 50}

<u>(a) The equation</u>

The spider passes through the origin.

So, we have:

\mathbf{(x,y) = (0,0)}

The spider jumps to a maximum height of 10mm, midway 80mm.

So, the vertex is:

\mathbf{(h,k) =  (40,10)}

The equation of a parabola is:

\mathbf{y = a(x - h)^2 + k}

So, we have:

\mathbf{0 = a(0 - 40)^2 + 10}

Subtract 10 from both sides

\mathbf{a(0 - 40)^2 =- 10}

\mathbf{1600a =- 10}

Solve for a

\mathbf{a =- \frac{1}{160}}

Substitute \mathbf{a =- \frac{1}{160}} and \mathbf{(h,k) =  (40,10)} in \mathbf{(h,k) =  (40,10)}

\mathbf{y = -\frac{1}{160}(x - 40) + 10}

<u>(b) The focus, directrix and the axis of symmetry</u>

The focus of a parabola is:

\mathbf{Focus= (h, k + p)}

Where:

\mathbf{p = \frac{1}{4a}}

So, we have:

\mathbf{p = \frac{1}{4 \times -1/160}}

\mathbf{p = -\frac{160}{4}}

\mathbf{p = -40}

So, we have:

\mathbf{Focus = (40,10-40)}

\mathbf{Focus = (40,-30)}

The axis of symmetry is:

\mathbf{x = h}

So, we have:

\mathbf{x = 40}

The directrix is:

\mathbf{y = k - p}

\mathbf{y = 10 + 40}

\mathbf{y = 50}

Read more about parabolas at:

brainly.com/question/25237745

You might be interested in
What is the value of x in degrees?
Brums [2.3K]
180-55-39=86
x=86
Hope it helps
3 0
3 years ago
trans.phobic, homo.phobic, white and thinks you can be rac.ist to white people, also says the r sl.ur what else can you do wrong
almond37 [142]

seems like you need to go to therapy for this one.

8 0
2 years ago
Read 2 more answers
Bruce's graduation picnic will cost $12 if it has 4 attendees. At most how many attendees can there be if Bruce budgets a total
ASHA 777 [7]

Answer:

6 peaple

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Use the number line to add the fraction. + + 1 1 7 3 -1 10 9 10 1 -1 10 4 5 3 5 Niat 1 2 + 1 5 N GIN 3 10 0 -1 3 10 1 10 + 1 2 +
user100 [1]
This is hard to understand , do u have a photo
8 0
2 years ago
I need help i don't know how to do this i am stuck!!
PolarNik [594]
121/100 is the answer. it cant be simplified anymore
8 0
1 year ago
Other questions:
  • One of the two hypotheses is to be chosen based on an observation of the random variable X. If H0 is true, then X is exponential
    9·1 answer
  • Tiffany works at a nail salon. In the first week she has 38 clients. In the second week she has 12 clients on Monday , 11 client
    13·1 answer
  • Your cell phone plan gives you 500 minutes monthly. If you have used 310 minutes already and there is a week left in this month,
    15·2 answers
  • What is the circumference of this circle? Use 3.14 for
    15·1 answer
  • I need you to Help please ASAP
    11·1 answer
  • Explain how you can use a multiplication equation to find 36÷6​
    8·1 answer
  • How much will the taxi driver earn if he takes one passenger 4.8 miles and another passenger 7.3 miles? Explain your process.
    13·1 answer
  • How do you complete this One-Step equation?<br>5 1/2 + p = 6
    12·2 answers
  • What is the y-intercept of the function f(x)=-2/9+1/3?<br>A. -2/9<br>B. -1/3<br>C. 1/3<br>D. 2/9​
    9·1 answer
  • PLEASE HELP ME PLEASE HELP ME PLEASE HELP ME PLEASE HELP ME PLEASE HELP ME
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!