The longest ladder available at many hardware stores is 40 feet. What is the highest floor you could safely reach with this ladder? Explain and model your answer by drawing.

The highest floor that the ladder could safely reach is approximately 38.73 feet

Step-by-step explanation:

OSHA requirement for the use of non-self-supporting ladders includes the requirement that the horizontal distance between the point at the top where the ladder is supported and the foot of the ladder should be about a quarter of the ladder's working length

The given length of the longest ladder available at hardware stores, l = 40 feet

Therefore;

The horizontal distance between top support and the foot of the ladder, d = 1/4 × 40 feet = 10 feet

According to Pythagoras theorem, the height, 'h', of the ladder is goven as follows;

l² = d² + h²

∴ h² = l² - d²

Therefore, we have;

h² = 40² - 10² = 1500

h = √1500 = 10·√15

Therefore, the height of the highest floor that can be safely reached with the ladder, h = 10·√15 feet ≈ 38.73 feet.

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."