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: $\mathbf{y = 50}$

(a) The equation

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

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

(b) The focus, directrix and the axis of symmetry

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

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3 years ago

Multiply. Write the answer in simplest form. 5/6 x 2/9

alukav5142 [94]

Answer:

5/27

Step-by-step explanation:

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3 years ago

Find the area of oC. Round your answer to the nearest hundredth,

IrinaK [193]

Answer:

Area ≈ 314.16 square inches

Step-by-step explanation:

Radius of circle (r) = ½(20) = 10 in.

Formula for area of circle, A = πr²

Plug in the value into the formula

Area = π × 10²

Area = π × 100

Area = 314.159265

Area = 314.16 in.² (nearest hundredth)

8 0

3 years ago

Dana ran 1/4 mile Trish ran 445 yards. Who ran the greater distance? Explain

alukav5142 [94]

445 yards is equal to 0.253841 Miles

445 yards > 1/4 miles

Trish ran farther by 5 yards

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3 years ago

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