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2 months ago

Q13. A stone is dropped from a height of 5 km. The distance it falls through varies directly with the

Mathematics

2 answers:

Leona [12.6K]2 months ago

8 0

I’m not really certain, but I think C could be the answer; my apologies if that's inaccurate.

zzz [12.3K]2 months ago

3 0

Answer:

During the 5th second, the stone travels 36 meters. The correct answer is A.

Step-by-step explanation:

Proportions

Two quantities are considered proportional if one can be derived from the other by multiplying by a constant. If we denote these variables as y and x, it can be expressed as:

y=k.x

There are other forms of proportions where the relationship is non-linear. For example, if y varies with the square of x, we can represent this as:

$y=k.x^2$

According to the problem's parameters, the distance a stone drops from a height of 5 km is directly proportional to the square of the time taken during the descent. If d denotes the distance and t indicates time, we have:

$d=k.t^2$

To determine the constant k, we apply the provided information: the stone falls d=66 meters in t=4 seconds. By substituting:

$64=k.4^2=16k$

Solving this yields:

$k=64/16=4$

Using the value of k in the equation completes the model.

$d=4.t^2$

Next, we calculate the distance after t=5 seconds:

$d=4\cdot 5^2=4\cdot 25=100$

After 5 seconds, the stone has traveled 100 meters. However, we need the distance for just the 5th second, specifically between 4 and 5 seconds.

We already know the distance at t=4 seconds is 64 meters and at t=5 seconds it's 100 meters:

distance in the 5th second = 100 m - 64 m = 36 m

The stone covers 36 m in the 5th second. Select option A.

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The slope between any two points can be calculated using the following formula:

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Insert the values into the formula:

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Therefore,

the result for Part A) is

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Case B) Point $D(11,6)\ E(5,9)$

Calculate the slope of DE

Plug the values into the formula:

$m=\frac{9-6}{5-11}$

$m=\frac{3}{-6}$

$m=-0.5$

Thus,

The equation $y=-0.5x-3$ is parallel to the line that goes through the points $D(11,6)\ E(5,9)$

Therefore,

the result for Part B) is

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Determine the slope of FG

Insert the values into the formula:

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$m=\frac{-20}{10}$

$m=-2$

Thus,

Any linear equation with slope $m=-2$ will be parallel to the line through the points $F(-7,12)\ G(3,-8)$

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Calculate the slope of HI

Substitute the values in the formula:

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Thus,

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Therefore,

the result for Part D) is

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Determine the slope of JK

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