Stretched 1 m beyond its natural length, a certain spring exerts a restoring force of magnitude 50 newtons. how much work, w, does it take to stretch the spring 7 m beyond its natural length?

1,225 J

Step-by-step explanation:

The restoring force exerted by a spring is given by:

Where 'k' is the spring constant and 'x' is the stretched distance.

Since x=1, the spring constant is:

The work required to stretch a spring is given by:

The work needed to stretch this spring 7 m beyond its natural length is:

The work required is 1,225 J.

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)