2m - 6 = 8m then 3m =

Answer:

The height of the triangular pyramid base is represented by s√3/2 units.

Step-by-step explanation:

This question focuses on calculating the height of the equilateral triangle at the base of the oblique pyramid.

According to the question, the equilateral triangle side has a length of a units.

Let’s review some properties of equilateral triangles:

a. All sides are identical in length, in this case, side s represents all sides.

b. All angles measure the same, at 60 degrees each.

c. Drawing a perpendicular line from the top vertex to the base divides the triangle into two right triangles, which have angles of 60 and 30 degrees, respectively.

To find the height of this triangular base, we can utilize either of the two right-angled triangles.

Recall the angles of 30, 60 and the side length s.

For height h calculation, trigonometric functions will assist us.

The relevant trigonometric relationship involves the sine of the angle (where side length s is the hypotenuse and height h is the opposite side relative to the 60-degree angle).

Thus, we can express this as:

Sine of an angle = opposite side length/hypotenuse length

sin 60 = h/s

Consequently, h = s sin 60.

In surd form, this yields:

sin 60 = √3/2.

Therefore, we find:

h = s * √3/2 = s√3/2 units.

This question reveals an intriguing pattern.

The rule or pattern to follow here is:

For the left side of the number compared to its predecessor: (First digit x Third digit + 1)

For the right side: (Second digit x Fourth digit -1)

For instance, consider 6447. Next, let's examine its previous number, 9876.

Now, and

that's how we arrived at 6447

Next, for the third number, 2527, let's look at its previous number, 6447

Now,

and

that's how we reached 2527

Following the same reasoning, the missing number should be 534.

This conclusion came from applying the rule of the pattern as:

and

Thus, we derived 534.

To find the maximum number of identical packs we see we have 72 pencils and 24 calculators.

This involves discovering the largest number that divides both 72 and 24 evenly,
which is known as the GCM or greatest common multiplier.

To determine the GCM, factor 72 into primes and group them:
72=2 times 2 times 2 times 3 times 3
24=2 times 2 times 2 times 3
Thus, the common grouping is 2 times 2 times 2 times 3, equating to 24.
Therefore, the maximum number of packs is 24.

For pencils:
72 divided by 24=3
Resulting in 3 pencils per pack.

For calculators:
24 divided by 24=1
So, 1 calculator per pack.

The outcome is 3 pencils and 1 calculator in each pack.

Response:c

Detailed explanation:

Response:

the solution can be found in the image