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3 years ago

Maria and John love their skateboards. One day they were on

Mathematics

2 answers:

Alchen [17]3 years ago

6 0

Given Information:

Distance between Maria and John = 30 miles

Maria's speed = 10 mph

John's speed = 5 mph

Butterfly's speed = 30 mph

Required Information:

How far did the butterfly travel = ?

Answer:

How far did the butterfly travel = 60 miles

Step-by-step explanation:

The speed, distance and time are related as,

Distance = speed*time

The distance that Maria has to cover = 10t miles

The distance that John has to cover = 5t miles

The total distance between them is 30 miles

Mathematically,

10t + 5t = 30

15t = 30

t = 30/15

t = 2 hours

So that means it took Maria and John 2 hours to meet.

We know that a butterfly starting on Maria's skateboard flew back and forth

between the two skateboards until they met.

So that means butterfly flew for 2 hours at a speed of 30 mph.

Then the distance covered by the butterfly is

Distance = speed*time

Distance = 30*2

Distance = 60 miles

Therefore, the butterfly traveled a distance of 60 miles.

Evgen [1.6K]3 years ago

6 0

Answer:

The butterfly traveled a distance of 69 miles.

Step-by-step explanation:

Given that:

- The distance between Maria and John = 30 miles

- Maria's speed = 10 mph

- John's speed = 5 mph

- Butterfly's speed = 30 mph

We want to find how far the butterfly traveled.

First note that Speed is the ratio of distance traveled to the time taken.

It is given as

s = D/t

where s is speed, D is distance, and t is time.

From this, we can say that

D = st

That is, distance is the product of speed and time.

Maria ran at 10mph. Let the distance she ran be D1. Then

D1 = 10×t = 10t miles

John ran at 5mph. Let the distance he ran be D2. Then

D2 = 5×t = 5t miles

The total distance between them is 30 miles. That is the sum of D1 and D2 is 30

D1 + D2 = 10t + 5t = 30

15t = 30

t = 30/15

t = 2 hours

Meaning it took Maria and John 2 hours to meet.

Now, a butterfly starting on Maria's skateboard flew back and forth between the two skateboards until they met. It flew at a speed of 30mph, and at time 2 hours, we can easily obtain the distance it covered.

D = st

D = 30×2

= 60

Distance = 60 miles

Therefore, the butterfly traveled a distance of 60 miles.

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The slope of the demand function is -1/2
The equation of the demand function is: $R(x) = (300 - 10x) \times (20 + 5x)$
The price that maximizes her revenue is: Ghc 85

From the question, we have:

$Plates = 300$

$Price = 20$

The number of plates (x) decreases by 10, while the price (y) increases by 5. The table of value is:

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The slope (m) is calculated using:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

So, we have:

$m = \frac{25-20}{290-300}$

$m = \frac{5}{-10}$

$m = -\frac{1}{2}$

The equation of the demand is as follows:

The initial number of plates (300) decreases by 10 is represented as: (300 - 10x).

Similarly, the initial price (20) increases by 5 is represented as: (20 + 5x).

So, the demand equation is:

$R(x) = (300 - 10x) \times (20 + 5x)$

Open the brackets to calculate the maximum revenue

$R(x) =6000 + 1500x - 200x - 50x^2$

$R(x) =6000 + 1300x - 50x^2$

Equate to 0

$6000 + 1300x - 50x^2 =0$

Differentiate with respect to x

$1300 - 100x =0$

Collect like terms

$100x =1300$

Divide by 100

$x =13$

So, the price at maximum revenue is:

$Price= 20 + 5x$

$Price= 20 + 5 * 13$

$Price= 85$

In conclusion:

The slope of the demand function is -1/2
The equation of the demand function is: $R(x) = (300 - 10x) \times (20 + 5x)$
The price that maximizes her revenue is: Ghc 85

Read more about demand equations at:

brainly.com/question/21586143

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