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17 days 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 [4.1K]17 days ago

8 0

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

zzz [4K]17 days 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.

A. C. E. F.

Which correspond to 2, 3, 5, and 6.

Step-by-step explanation:

Within geometry, exterior angles are defined as those angles formed between any side of a polygon and the extension of an adjacent side, as demonstrated in the diagram.

Observing the figure, angles 2 and 3 arise from a side of the triangle and a line extended from the following side. Likewise, angles 5 and 6 are created similarly. Thus, these four angles are classified as exterior angles.

8 0

15 days ago

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On a coordinate plane, 3 triangles are shown. Triangle B C D has points (1, 4), (1, 2), (5, 3). Triangle B prime C prime D prime

Svet_ta [4321]

The transformation sequence that maps ΔBCD to ΔB"C"D" is:

Reflection across the y-axis combined with a translation of 6 units in the x direction and -5 units in the y direction.

Step-by-step explanation:

Let's break down the reflection across the y-axis, horizontal translation, and vertical translation:

1. For point (x, y), reflecting it across the y-axis gives the point (-x, y).

2. Translating point (x, y) h units to the right results in (x + h, y), and h units to the left results in (x - h, y).

3. If point (x, y) is moved k units up, it becomes (x, y + k), and if moved k units down, it is (x, y - k).

∵ The vertices of triangle BCD are (1, 4), (1, 2), (5, 3).

∵ The vertices of triangle B'C'D' are (-1, 4), (-1, 2), (-5, 3).

∵ The x-coordinates of ΔB'C'D' have the same absolute value as those of ΔBCD but with opposite signs, indicating that ΔB'C'D' results from reflecting ΔBCD across the y-axis.

∵ The vertices of triangle B'C'D' are (-1, 4), (-1, 2), (-5, 3).

∵ The vertices of triangle B''C''D'' are (5, -1), (5, -3), (1, -2).

∵ The reflected x-coordinate -1 becomes +5, and -5 becomes +1,

thus the x-coordinates of triangle B'C'D' are increased by 6.

∵ The images of 4, 2, and 3 yield -1, -3, and -2 respectively,

hence subtracting 5 from the y-coordinates of triangle B'C'D' leads us to ΔB"C"D" through a translation of 6 units right and 5 units down ⇒ (x + 6, y - 5).

The transformation sequence that maps ΔBCD to ΔB"C"D" is:

Reflection across the y-axis combined with a translation of 6 units in the x direction and -5 units in the y direction.

Learn more:

You can explore more about reflection at

3 0

15 hours ago

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Joe wants to paint the outside of a wooden box. He needs to find the surface area of the box

Zina [3914]

4 multiplied by 2 equals 8

4 multiplied by 1.5 equals 6

2 multiplied by 1.5 equals 3

8 multiplied by 2 equals 16

2 multiplied by 6 equals 12

2 multiplied by 3 equals 6

16 plus 12 plus 6 totals 34 ft

3 0

11 days ago

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Amir drove from Jerusalem down to the lowest place on Earth, the Dead Sea, descending at a rate of 12 meters per minute. He was

tester [3916]

Answer:

Plot the following two coordinates: (0, 360), (30, 0)

Step-by-step explanation:

Amir drove at a rate of 12 meters for 30 minutes, beginning at an altitude of 360 feet. To represent this on a graph, place a dot at (0, 360) and mark another at (30, 0).

8 0

7 days ago

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Christopher is a graphic designer who creates business websites. It takes him 2.4 hours to complete one website page. He finds o

babunello [3635]

1.2x + 15 = 2.4x

Let's solve the equation:
Starting with 1.2x + 15 = 2.4x,
Subtract 2.4x from both sides: 1.2x - 2.4x + 15 = 0,
Simplify: -1.2x + 15 = 0,
Subtract 15: -1.2x = -15,
Divide both sides by -1.2: x = 12.5.
Thus, Christopher must produce 12.5 pages for his time using the new software to equal his current time.

Any number of pages greater than 12.5 will result in time savings with the new program.

4 0

13 days ago

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