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1 year ago

Use the data in the table to describe how the population in a town is changing. Then identify a function that

Mathematics

1 answer:

marshall27 [118]1 year ago

4 0

The data given illustrates that there's a constant ratio of 2 and y = 600(2)^x; 38400

<h3>How to compute the ratio?</h3>

The ratio based on the information given will be:

= 1200/600

= 2

Therefore, the constant ratio is 2.

In 6 years, the population will be:

= 600 × 2^6

= 600 × 64

= 38400

Learn more about ratio on:

brainly.com/question/2328454

#SPJ1

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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

aleksklad [387]

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

4 0

2 years ago

How many students were surveyed? Puzzle has 20 students

Vladimir [108]

I believe the answer would be 58 students

5 0

2 years ago

Read 2 more answers

The scale on a map is 2 cm = 25 miles. Dave measured the distance to the next town at 5cm. How many miles away is the next town?

Daniel [21]

Answer:

62.5 miles

Step-by-step explanation:

1 cm = 12.5 miles

then

12.5 x 5 cm = 62.5 miles

5 0

2 years ago

Approximately how many times greater is 9.75 * 10^6 than 1.25 * 10^2?

alexgriva [62]

9.75 / 1.25 = 7.8

10^6 - 10^2 = 10^4

= 7.8 x 10^4 greater

5 0

3 years ago

Ion get this bro someone help I got school in a hour

worty [1.4K]

Answer:

of Example 6

5 and 14

Step-by-step explanation:

IN EXAMPLE 6

Opposite angles are equal so you equate the first one like this

3x + 20 = 10x - 15

15 + 20 = 7x

35/7 = x

x = 5

In next question b

It is a straight line thus it's 180°

so 4n + 22 +8n -10 = 180

12n + 12 = 180

12n = 180 - 12

n =168÷ 12

n = 14

6 0

2 years ago