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2 years ago

Somebody help me out!!!!!!

Mathematics

2 answers:

Nikolay [14]2 years ago

4 0

It’s b 25 can’t be simplified anymore

spin [16.1K]2 years ago

3 0

Answer:

Step-by-step explanation:

Root 26

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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

8 divided by 2 times 10 plus 14

BARSIC [14]

Answer:

Step-by-step explanation:

8 0

3 years ago

15/23 - 5/23 lets see who can solve

seraphim [82]

Answer:

10/23

Step-by-step explanation:

15/23 - 5/23 = 10/23(Ans)

7 0

2 years ago

Read 2 more answers

What is the value of x in the equation LaTeX: \frac{3}{2}\left(4x-2\right)-3x=5-\left(x+2\right) 3 2 ( 4 x − 2 ) − 3 x = 5 − ( x

Helen [10]

Answer:

3/2

Step-by-step explanation:

Given the equation 3/2(4x-2)-3x = 5-(x+2)

Open the parenthesis

3/2(4x) - 3/2(2) -3x = 5-x-2

6x-3-3x = 3-x

3x-3 = 3-x

Collect like terms

3x+x = 3+3

4x = 6

Divide both sides by

4x/4 = 6/4

x = 3/2

Hence the value of x is 3/2

6 0

2 years ago

Evaluate the expession. x=12, y=8, z=3 4x-yz

Nataly_w [17]

Given:
 x=12, y=8, z=3

4x-yz = 4(12) - (8)(3)
4x-yz = 48 - 24
4x-yz = 24

8 0

3 years ago

Read 2 more answers