What are the steps for using a compass and straightedge to construct a line through point P that is parallel to line m? A horizontal line m and a point P are drawn. The point P is above the horizontal line m. Drag the steps and drop them in order from start to finish.
What are the steps for using a compass and straightedge - 2

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Answer 1
Answer:

Answer:

Here, m is a line and we have to find the draw parallel line of line of m through a point P with the help of straightedge and compass,

The correct order of steps for constructing a line through point P that is parallel to line m are as follows,

Step 1 : Use the straightedge to draw a line n that passes through P and intersect line m, lebel the point of intersection as X,

Step 2 : Place the point of the compass on point X and draw an arc that intersect line m and n, label the intersection point A and B,

Step 3 : Without changing the width of the compass opening, place the point of compass on point P and draw an arc that intersect line n label the intersection point as C,

Step 4 : Place the point of compass on point A and open it to the width of AB,

Step 5 : With the compass opening set the width of AB, place the point of the compass On point C and draw an arc that intersects the arc that was drawn from point P lebel the intersection of arc as point Y,

Step 6 : Use the straightedge to draw PY

Answer 2
Answer:

Answer:

Here's the list of the following sequence in the right order for you (I took the test myself and got this whole sequence right)

1. Use the straightedge to draw a line n that passes through P and intersects line m. Label the point of intersection as point X.

2. Place the point of the compass on point X and draw an arc that intersects lines m and n. Label the intersections as points A and B.

3. Without changing the width of the compass opening, place the point of the compass on point P and draw an arc that intersects line n. Label the intersection as point C.

4. Place the point of the compass on point A and open it to width AB.

5. With the compass opening set to width AB, place the point of the compass on point C and draw an arc that intersects the arc that was drawn from point P. Label the intersection of the arcs as point Y.

6. Use the straightedge to draw line PY.



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Suppose an airline policy states that all baggage must be box shaped with a sum of​ length, width, and height not exceeding 96 in. What are the dimensions and volume of a​ square-based box with the greatest volume under these​ conditions?

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Answer:

Step-by-step explanation:

As the base is a square so the length is a, width is a and the height is h.

According to the question,

a + a + h = 96

h = 96 - 2a     .... (1)

Volume of the box, V = length x width x height

V = a x a x h

V = a² (96 - 2a)    from equation (1)

V = 96a² - 2a³

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Final answer:

A square-based box with the greatest volume under a restriction of the sum of length, width, and height not exceeding 96 inches must have each dimension equal to 32 inches. Therefore, its volume will be 32x32x32 = 32,768 cubic inches.

Explanation:

A square-based box with the greatest volume that can fit the airline's restrictions would have each side (length, width, height) be exactly one third of the total permitted sum, namely 32 inches each, because the volume of a square-based box (a cube in this specific case) is calculated by cubing the edge length. This is due to the nature of a cube, where all sides are equal.

So, the volume of the box would be 32in x 32in x 32in = 32,768 cubic inches. This is the maximum volume because the mathematical principle that for a given sum S of width, length & height, a cube always takes up the most volume.

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