9) A boardwalk is being built along two sides of a beach area.

Is -0.3 a rational number? is 3.14144144414444... a rational number?

Ainat [17]

I will try to make this as simple as possible.

First off, we need to know what a rational number is: A rational number is any number that can be made by dividing 2 integers. For example:

1.5 would be a rational number because 1.5 = 3/2 (3 and 2 are both integers)

With that being said, let's begin.

First off, let's start with -0.3, let's ask ourselves, can we make this number by dividing 2 integers, the answer is yes, we can, by doing $\frac{-3}{10}$ we have the equivalent of -0.3, so now we know it's a rational number.

As for the second one, it can't be a rational number because it can't be made by dividing to integers, so the answer is:

-0.3 is a rational number, but 3.14144144414444 is not.

Hope this helped! c:

3 0

2 years ago

Mercury orbits the Sun in 87 24/25 earth days. Venus orbits the Sun in 224 7/10 earth days and Mars orbits the sun in 686 49/50

Rufina [12.5K]

87 24/25.......24/25 = 0.96......answer is 87.96

224 7/10....7/10 = 0.7....answer is 224.7

686 49/50...49/50 = 0.98...answer is 686.98

7 0

2 years ago

Find all of the equilibrium solutions. Enter your answer as a list of ordered pairs (R,W), where R is the number of rabbits and

zloy xaker [14]

Answer:

$(0,0)$ $(4000,0)$ and $(500,79)$

Step-by-step explanation:

Given

See attachment for complete question

Required

Determine the equilibrium solutions

We have:

$\frac{dR}{dt} = 0.09R(1 - 0.00025R) - 0.001RW$

$\frac{dW}{dt} = -0.02W + 0.00004RW$

To solve this, we first equate $\frac{dR}{dt}$ and $\frac{dW}{dt}$ to 0.

So, we have:

$0.09R(1 - 0.00025R) - 0.001RW = 0$

$-0.02W + 0.00004RW = 0$

Factor out R in $0.09R(1 - 0.00025R) - 0.001RW = 0$

$R(0.09(1 - 0.00025R) - 0.001W) = 0$

Split

$R = 0$ or $0.09(1 - 0.00025R) - 0.001W = 0$

$R = 0$ or $0.09 - 2.25 * 10^{-5}R - 0.001W = 0$

Factor out W in $-0.02W + 0.00004RW = 0$

$W(-0.02 + 0.00004R) = 0$

Split

$W = 0$ or $-0.02 + 0.00004R = 0$

Solve for R

$-0.02 + 0.00004R = 0$

$0.00004R = 0.02$

Make R the subject

$R = \frac{0.02}{0.00004}$

$R = 500$

When $R = 500$ , we have:

$0.09 - 2.25 * 10^{-5}R - 0.001W = 0$

$0.09 -2.25 * 10^{-5} * 500 - 0.001W = 0$

$0.09 -0.01125 - 0.001W = 0$

$0.07875 - 0.001W = 0$

Collect like terms

$- 0.001W = -0.07875$

Solve for W

$W = \frac{-0.07875}{ - 0.001}$

$W = 78.75$

$W \approx 79$

$(R,W) \to (500,79)$

When $W = 0$ , we have:

$0.09 - 2.25 * 10^{-5}R - 0.001W = 0$

$0.09 - 2.25 * 10^{-5}R - 0.001*0 = 0$

$0.09 - 2.25 * 10^{-5}R = 0$

Collect like terms

$- 2.25 * 10^{-5}R = -0.09$

Solve for R

$R = \frac{-0.09}{- 2.25 * 10^{-5}}$

$R = 4000$

So, we have:

$(R,W) \to (4000,0)$

When $R =0$ , we have:

$-0.02W + 0.00004RW = 0$

$-0.02W + 0.00004W*0 = 0$

$-0.02W + 0 = 0$

$-0.02W = 0$

$W=0$

So, we have:

$(R,W) \to (0,0)$

Hence, the points of equilibrium are:

$(0,0)$ $(4000,0)$ and $(500,79)$

4 0

2 years ago

HELP!! Which truck pulled 2,000 pounds at the average<br> speed of 2 yards per minute?

Advocard [28]

The correct answer it would be B

Ford

8 0

2 years ago

First let’s go on a trip! you come into some money and decide to go to canada where the exchange rate is 1.04 canadian dollars t

Ksenya-84 [330]

13092.50 Canadian dollars equals to $10000 US dollars.

6 0

2 years ago