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

Answers

Answer 1

A parabola is a mirror-symmetrical U-shape.

The equation of the parabola is [tex]\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}[/tex]The focus is [tex]\mathbf{Focus = (80, -1760)}[/tex]The directrix is [tex]\mathbf{y = \frac{1}{640}}[/tex]The axis of the symmetry of parabola is: [tex]\mathbf{x = 80}[/tex]

From the question, we have:

[tex]\mathbf{Vertex: (h,k) = (80,10)}[/tex]

[tex]\mathbf{Origin: (x,y) = (0,0)}[/tex]

The equation of a parabola is:

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

Substitute the values of origin and vertex in [tex]\mathbf{y = a(x - h)^2 + k}[/tex]

[tex]\mathbf{0 = a(0 - 80)^2 + 10}[/tex]

[tex]\mathbf{0 = a(- 80)^2 + 10}[/tex]

[tex]\mathbf{0 = 6400a + 10}[/tex]

Collect like terms

[tex]\mathbf{6400a =- 10}[/tex]

Solve for a

[tex]\mathbf{a =- \frac{1}{640}}[/tex]

Substitute the values of a and the vertex in [tex]\mathbf{y = a(x - h)^2 + k}[/tex]

[tex]\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}[/tex]

The focus of a parabola is:

[tex]\mathbf{Focus = (h, \frac{k+1}{4a})}[/tex]

Substitute the values of a and the vertex in [tex]\mathbf{Focus = (h, \frac{k+1}{4a})}[/tex]

[tex]\mathbf{Focus = (80, \frac{10+1}{4 \times -\frac{1}{640}})}[/tex]

[tex]\mathbf{Focus = (80, -\frac{11}{\frac{1}{160}})}[/tex]

[tex]\mathbf{Focus = (80, -11\times 160)}[/tex]

[tex]\mathbf{Focus = (80, -1760)}[/tex]

The equation of the directrix is:

[tex]\mathbf{y = -a}[/tex]

So, we have:

[tex]\mathbf{y = \frac{1}{640}}[/tex] ----- the directrix

The axis of symmetry is:

[tex]\mathbf{x = -\frac{b}{2a}}[/tex]

We have:

[tex]\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}[/tex]

Expand

[tex]\mathbf{y = -\frac{1}{640}(x^2 -160x + 6400) +10}[/tex]

Expand

[tex]\mathbf{y = -\frac{1}{640}x^2 +\frac{1}{4}x - 10 +10}[/tex]

[tex]\mathbf{y = -\frac{1}{640}x^2 +\frac{1}{4}x }[/tex]

A quadratic function is represented as:

[tex]\mathbf{y = ax^2 + bx + c}[/tex]

So, we have:

[tex]\mathbf{a = -\frac{1}{640}}[/tex]

[tex]\mathbf{b = \frac{1}{4}}[/tex]

Recall that:

[tex]\mathbf{x = -\frac{b}{2a}}[/tex]

So, we have:

[tex]\mathbf{x = -\frac{1/4}{2 \times -1/640}}[/tex]

[tex]\mathbf{x = \frac{1/4}{1/320}}[/tex]

This gives

[tex]\mathbf{x = \frac{320}{4}}[/tex]

[tex]\mathbf{x = 80}[/tex]

Hence, the axis of the symmetry of parabola is: [tex]\mathbf{x = 80}[/tex]

Read more about parabola at:

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Answer:

500.

Step-by-step explanation:

The last digit must end with 0, 2, 4, 6, 8   for the Pin code to be even.

The middle 2 digits may be any numbers.

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Answer:

ITS A

trust me it's quite simple. you just need to find the overall pattern of the sequence

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Answers

Answer:

5)42º

6)112º

7)112º

8)38º

Step-by-step explanation:

m<6         180-68=112

m<5         180=26+112+x            42=x

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Step-by-step explanation:

bro, MO bisects into 2 equal halves. ..

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Answers

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2/3

Step-by-step explanation:

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Answers

Answers:
a. -80
b. -60
c. 98
d. -54

Answer:

a)-30

b)-60

c)98

d)-54

Step-by-step explanation:

320/-4

-180/3

-14X-7

6X-9

HELP ME PLEASE I legit suck at rounding

Answers

Answer:

Alright, this is a lot, here are the answers.

Round to the nearest thousand:

1. 14,000

2. 30,000

3. 3,000

4. 10,000

5. 56,000

6. 90,000

Round to the nearest ten thousand:

1. 20,000

2. 40,000

3. 150,000

4. 20,000

5. 300,000

6. 80,000

Round to the nearest ten:

1. 90

2. 2,680

3. 270

4. 510

5. 100

6. 2,750

Round to the nearest hundred:

1. 800

2. 3,000

3. 5,000

4. 300

5. 5,500

6. 600

One More!

Round to the nearest hundred thousand:

1. 900,000

2. 100,000

3. 1,000,000

4. 800,000

5. 200,000

6. 400,000

There those are the final answers! Let me know if any are incorrect and I'll fix them!

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Answers

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40.65 - C = 5.10

Solve for C.

40.65 - 5.10 = C

C = 35.55

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