Acircle in the xy-plane has a diameter with endpoints whose coordinates are negative 1 comma negative 3 and 7 comma 3. if the point with coordinates 0 comma b lies on the circle and b is greater than 0, what is the value of b ?

First we look for the coordinates of the center of the circle. For this, we use the following formula:

 ((x1 + x2) / 2, (y1 + y2) / 2)

 Where,

 (x1, y1) = (- 1, -3)

 (x2, y2) = (7, 3)

 Substituting values we have:

 ((-1 + 7) / 2, (-3 + 3) / 2)

 ((6) / 2, (0) / 2)

 (3, 0)

 We are now looking for the diameter of the circle. For this we use the formula of distance between points:

 d = root ((x2-x1) ^ 2 + (y2-y1) ^ 2)

 Substituting values:

 d = root ((7 - (- 1)) ^ 2 + (3 - (- 3)) ^ 2)

 d = 10

 Then, the radius of the circle is:

 r = d / 2 = 10/2

 r = 5

 The circle equation will be

 (x-h) ^ 2 + (y-k) ^ 2 = r ^ 2

 Where,

 (h, k) = (3, 0)

 r = 5

 Substituting

 (x-3) ^ 2 + (y-0) ^ 2 = 5 ^ 2

 Substituting

 (x, y) = (0, b)

 (0-3) ^ 2 + (b-0) ^ 2 = 5 ^ 2

 b = root (25-9)

 b = root (16)

 b = 4

 Answer

 the value of b is

 b = 4

you can first factor out the n to get n(1+5). we know that 1+5 is 6, so we just have 6n.

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