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Oliga [24]
3 years ago
9

The north american and european continents are moving apart at a rate of about 3 cm/y. at this rate how long will it take them t

o drift 500 km farther apart than they are at present?
Mathematics
1 answer:
soldier1979 [14.2K]3 years ago
6 0
In this case, the continents are moving apart at a rate (velocity = 3 cm/y) and the distance for continent to move(distance= 500km). You are asked how long it will take(time). <span>Then to answer this question you need to convert the 500km into the same unit as the velocity which was cm. The formula would be:

Distance = velocity x time
500km x 10^5 cm/km= 3cm/year x time
time= 5x 10^7 cm / (3cm/year)
time= 1.7 x 10^7 year or 17 million year
</span>
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There is 1500 ft of fencing available to make 6 identical pens. Find the maximum area for EACH pen (meaning maximum of one pen).
hjlf

Answer:

The maximum area is therefore is 93750 ft²

Step-by-step explanation:

The given parameter are;

The a]length of fencing available = 1500 ft.

The perimeter of the figure = 9·x + 4·y

Therefore, 9·x + 4·y = 1500 ft.

The area of the figure = 6 × (x × y) = 3·x × 2·y

From the equation for the perimeter, we have;

9·x + 4·y = 1500

y = 1500/4 - 9/4·x = 375 - 9/4·x

y = 375 - 9/4·x

Substituting the value of y in the equation for the area gives;

Area = 3·x × 2·y = 3·x × 2·(375 - 9/4·x) = 2250·x - 27/2·x²

Area = 2250·x - 27/2·x²

The maximum area is found by taking the derivative and equating to zero as follows;

d(2250·x - 27/2·x²)/dx = 0

2250 - 27·x = 0

x = 2250/27 = 250/3

x = 250/3

y = 375 - 9/4·x = 375 - 9/4×250/3 = 187.5

The maximum area is therefore, 3·x × 2·y = 3 × 250/3 × 2 × 187.5 = 93750 ft²

The maximum area is therefore = 93750 ft.²

4 0
3 years ago
What is the y intercept in the equation? <br><br> y = 5x - 4
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Step-by-step explanation:

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3 years ago
Find the probability that a randomly chosen point is located within the shaded region. Write your answer as a decimal, and
Andrei [34K]

Answer:

Probability = 0.25

Step-by-step explanation:

Given

The attached shape

Required

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First, calculated the area of the shaded region

A_1 = 0.5 * base * height

Where

base = 8cm\\ height = 6cm --- given

So:

A_1 = 0.5 * 8cm* 6cm

A_1 = 24cm^2

Next, calculated the area of the complete rectangle

A_2 = Length* Width

Where

Width = 12cm\\ Length = 8cm --- given

So:

A_2 = 12cm * 8cm

A_2 = 96cm^2

The required probability is:

Probability = \frac{A_1}{A_2}

Probability = \frac{24cm^2}{96cm^2}

Probability = 0.25

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Softa [21]

Answer: -6x

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