Archimedes went to sleep beside a big rock.

He wanted to get up at 8 AM, but the alarm clock was yet to be invented! He decided to sleep at the spot where the rock's shadow should end when it's 8 AM so as to be awakened by the direct sunlight.

Archimedes knew that at 8 AM, the sunlight reaches the ground at an angle of 43°. The rock beside which he slept was 7 meters tall.

7.5065 m.

Step-by-step explanation:

Let, he has to sleep at d distance from the rock.

Then, tan43 = 7 / d

=> d = 7 / tan43

=> d = 7.5065 (Approx.)

[If there's any mistake, please inform me]

correct answer is infinitely many solutions

step-by-step explanation:

2(2x + 3) = -4 + 2(2x + 5)

solving the above equation:

4x + 6 = -4 +4x +10

combining like terms

4x -4x = -4+10-6

0=0

since both sides are 0=0, we end up into true statement it means it has infinite many solutions.

so correct answer is infinitely many solutions

just needed some points but try socratic