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]

step-by-step explanation:

f(x)=2x^2 -1 

translation is a function transformation that transform the function in a way of translating. by translating the function its graph is moved  up an down. moving the function f(x) 2 units to the left will be the new function g(x) with the equation: g(x)=f(x+2)=2(x+2)^2 -1

70

step-by-step explanation: