The leftmost of the the two digits is 10x that of the right one.
Well the line is straight so it will always have the same slope no matter what points you use but to solve it mathematically you do change in y/change in x
(3.5-(-1))/(4-(-5))
4.5/9 = 0.5
So the slope is 0.5
Now pick 2 random points on the line
(-3,0) and (5,4)
Now do the same thing for these 2 points
(4-0)/5-(-3)
4/8 = 0.5
So no matter what points the slope is always 0.5
1. The problem statement tells you to find "the area of the hexagonal face".
2. If we assume the intent is to find the shaded area of the face only, it differs from the area of a regular hexagon in that there is a hole in the middle.
3. You must find the area of the regular hexagon, and subtract the area of the circular hole in the middle.
4. The formula for the area of a circle in terms of its radius is
... A = πr²
5. The formula for the area of a regular hexagon in terms of the radius of the circumcircle is
... A = (3√3)/2·r²
6. The radius of the circumcircle of the regular hexagon is given. No additional information is needed.
7. You can use the trig functions of the angles of an equilateral triangle to find the apothem, but there is no need for that when you use the formula of 5.
8. All this is unnecessary. The apothem is (8 mm)·(√3)/2 = 4√3 mm ≈ 6.9282 mm, the shorter leg is (8 mm)·(1/2) = 4 mm. The perimeter is 6·8 mm = 48 mm.
9. The area of the hexagon is
... A = 3√3/2·(8 mm)² = 96√3 mm² ≈ 166.277 mm²
10. The area of the circle is
... A = π·(4 mm)² = 16π mm² ≈ 50.265 mm²
11. The area of the hexagonal face is approximately ...
... 166.277 mm² - 50.265 mm² = 116.01 mm²
Yes,
Every 2 minutes = 3 inches of water, so that means every minute = 1.5 inches of water.
So in 10 minutes:
10*(1.5) = 15 inches of water.
So in 10 minutes the tub will fill an additional 15 inches of water which is exactly how much you need to fill up the remaining tub (3+15 = 18)
