Answer:
The cabin is located 567 yards away.
Step-by-step solution:
The bearing angle of 21.2° corresponds to the interior angle near the cabin in the triangle.
Apply the tangent function:
Opposite side length: 220 yards
Adjacent side length: x (distance to cabin)
tan(21.2°) = opposite / adjacent
tan(21.2°) = 220 yards / x
Multiply both sides by x:
x × tan(21.2°) = 220 yards
Isolate x:
x = 220 yards / tan(21.2°)
x = 220 / 0.388
x = 567 yards
Hence, the cabin is 567 yards away.
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.
You might have better success by searching for answers individually:)
<span><span>Center coordinates: (x0, y0, z0)</span></span> and radius r.
<span>The equation of the sphere is:</span>
<span>(x - x0)^2 + (y - y0)^2 + (z - z0)^2 = r^2</span>
