Please help...redoing past papers so I need to cross-check with someone to see if they are correct

4 < k < 12

Step-by-step explanation:

The given function is y = 2·x² + k·x + 2·k - 6

Where the curve lies above the x-axis for all values of x, the function does not have a root and the discriminant, Δ, is negative, to give complex roots

∴ The discriminant Δ = k² - 4·2·(2·k - 6) < 0

k² - 4·2·(2·k - 6) = k² - 16·k + 48 < 0

(k - 12)·(k - 4) < 0

∴ k < 12 or k > 4 given that by substitution, we have;

When k = 3  < 4

k² - 16·k + 48 =  3² - 16×3 + 48 = 9 > 0

Also the product of two negative numbers is larger than 0

Therefore, the set of values of k for which the curve lies above the x-axis for all values of x is 4 < k < 12

step-by-step explanation:

there is a formula i can give you:

it is r^2*n*sin(360/n) divided by 2 where r represents the "radius" and n is the number of sides.

plug them in:

(10sqrt(3))^2*6*sin(360/6) divided by 2

100*3*6*sin(60) divided by 2

900*sin(60)

900*sqrt(3)/2

450*sqrt(3)

approx is 779.4 cm^2