Find the value of q, for which the difference between the roots in the equation x2−10x+q=0 is equal to 6.

According to the quadratic formula,

-b plus or minus √(b^2 - 4ac)

x =

2a

In this particular case (x^2 - 10x + q), a = 1, b = -10, and c = q. Thus:

-(-10) plus or minus √(100-4q) 10 plus or minus √4√(25-q)

x = =

2 2

and this reduces to:

x = 5 plus or minus √(25-q).

Assuming that 5 + √(25-q) is larger than 5 - √(25-q), we can write:

5 + √(25-q) - (5 - √(25-q)) = 6, or √(25-q) + √(25-q) = 6, or √(25-q) = 3.

Squaring both sides, we get: 25-q = 9, or

q = 16 (answer)

If q = 16, then the difference between the two roots will be +6.

square pyramid

step-by-step explanation:

square prism looks like nothing like that

triangular prism has a rectangular base instead of a square base

tetrahedron has a triangular base

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204