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andrezito [222]

3 years ago

12

PLEASE HELP ME (20 POINTS)

1 answer:

trasher [3.6K]3 years ago

5 0

Answer:

Not always.

Step-by-step explanation:

brainly.com/question/18051242?referrer=fromSearch

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

Stella [2.4K]

A parabola is a mirror-symmetrical U-shape.

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

From the question, we have:

$\mathbf{Vertex: (h,k) = (80,10)}$

$\mathbf{Origin: (x,y) = (0,0)}$

The equation of a parabola is:

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

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

$\mathbf{0 = a(0 - 80)^2 + 10}$

$\mathbf{0 = a(- 80)^2 + 10}$

$\mathbf{0 = 6400a + 10}$

Collect like terms

$\mathbf{6400a =- 10}$

Solve for a

$\mathbf{a =- \frac{1}{640}}$

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

$\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}$

The focus of a parabola is:

$\mathbf{Focus = (h, \frac{k+1}{4a})}$

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

$\mathbf{Focus = (80, \frac{10+1}{4 \times -\frac{1}{640}})}$

$\mathbf{Focus = (80, -\frac{11}{\frac{1}{160}})}$

$\mathbf{Focus = (80, -11\times 160)}$

$\mathbf{Focus = (80, -1760)}$

The equation of the directrix is:

$\mathbf{y = -a}$

So, we have:

$\mathbf{y = \frac{1}{640}}$ ----- the directrix

The axis of symmetry is:

$\mathbf{x = -\frac{b}{2a}}$

We have:

$\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}$

Expand

$\mathbf{y = -\frac{1}{640}(x^2 -160x + 6400) +10}$

Expand

$\mathbf{y = -\frac{1}{640}x^2 +\frac{1}{4}x - 10 +10}$

$\mathbf{y = -\frac{1}{640}x^2 +\frac{1}{4}x }$

A quadratic function is represented as:

$\mathbf{y = ax^2 + bx + c}$

So, we have:

$\mathbf{a = -\frac{1}{640}}$

$\mathbf{b = \frac{1}{4}}$

Recall that:

$\mathbf{x = -\frac{b}{2a}}$

So, we have:

$\mathbf{x = -\frac{1/4}{2 \times -1/640}}$

$\mathbf{x = \frac{1/4}{1/320}}$

This gives

$\mathbf{x = \frac{320}{4}}$

$\mathbf{x = 80}$

Hence, the axis of the symmetry of parabola is: $\mathbf{x = 80}$

Read more about parabola at:

brainly.com/question/21685473

6 0

2 years ago

At which point do the two equations

Lena [83]

The lines intersect at two places.

They intersect at approximately (-2,8) and (2,3)

Looking at the choices they would be at (1.8,3.2) and (-2.8,7.8)

The answer is D. Both A and B.

4 0

2 years ago

(8.75-2.16)÷7.1+(4.5+1.3)÷4.3

kirill [66]

Answer:

2.27700622339

Step-by-step explanation:

Calculated your welcome

7 0

2 years ago

Read 2 more answers

How do you graph -1/5x-1 and 4/5x-6

kakasveta [241]

Answer:

The points for the given to linear equations is (5 , - 2) and (5 , - 1)

The points is plotted on the graph shown .

Step-by-step explanation:

Given as :

The two linear equation are

y = $\dfrac{-1}{5}$ x - 1 ...........1

y = $\dfrac{4}{5}$ x - 6 ...........2

Now, Solving both the linear equations

Put the value of y from eq 2 into eq 1

I.e $\dfrac{4}{5}$ x - 6 = $\dfrac{-1}{5}$ x - 1

Or, $\dfrac{4}{5}$ x + $\dfrac{1}{5}$ x = 6 - 1

Or, $\dfrac{4 + 1}{5}$ x = 5

or, $\dfrac{5}{5}$ x = 5

∴ x = 5

Now, Put the value of x in eq 1

So, y = $\dfrac{-1}{5}$ x - 1

Or, y = $\dfrac{-1}{5}$ × 5 - 1

or, y = $\dfrac{-5}{5}$ - 1

Or, y = - 1 - 1

I.e y = -2

So, For x = 5 , y = - 2

Point is ( $x_1$ , $y_1$ ) = (5 , - 2)

Again , put the value of x in eq 2

So, y = $\dfrac{4}{5}$ x - 6

Or, y = $\dfrac{4}{5}$ × 5 - 6

Or, y = $\frac{4\times 5}{5}$ - 6

Or, y = 4 - 6

I.e y = - 2

So, For x = 5 , y = - 2

Point is ( $x_2$ , $y_2$ ) = (5 , - 2)

Hence, The points for the given to linear equations is (5 , - 2) and (5 , - 2)

The points is plotted on the graph shown . Answer

5 0

3 years ago

Determine the measure of each numbered angle. Show work, provide a brief explanation.

monitta

Huhvgujvdthb friend gf t if y h iutzyreRx it’s g. Ttussuesru. G h

5 0

2 years ago