Answer:
Input:
14 x^2 + 57 x - 27
Plots:
Geometric figure:
parabola
Alternate forms:
(7 x - 3) (2 x + 9)
x (14 x + 57) - 27
14 (x + 57/28)^2 - 4761/56
Roots:
x = -9/2
x = 3/7
Polynomial discriminant:
Δ = 4761
Properties as a real function:
Domain
R (all real numbers)
Range
{y element R : y>=-4761/56}
Derivative:
d/dx(14 x^2 + 57 x - 27) = 28 x + 57
Indefinite integral:
integral(-27 + 57 x + 14 x^2) dx = (14 x^3)/3 + (57 x^2)/2 - 27 x + constant
Global minimum:
min{14 x^2 + 57 x - 27} = -4761/56 at x = -57/28
Definite integral:
integral_(-9/2)^(3/7) (-27 + 57 x + 14 x^2) dx = -109503/392≈-279.344
Definite integral area below the axis between the smallest and largest real roots:
integral_(-9/2)^(3/7) (-27 + 57 x + 14 x^2) θ(27 - 57 x - 14 x^2) dx = -109503/392≈-279.344
Step-by-step explanation:
Answer:
Step-by-step explanation:
The standard form of quadratic equation is where a,b and c are real numbers and a ≠ 0.
Answer: The volume of pyramid is 6720 ft³
Step-by-step explanation:
Given: Base edge of a square pyramid = 24 feet
Slant height = 37 feet
Therefore height of pyramid is given by
where h is height, l is slant height and b is base edge of pyramid
So we have
Height of pyramid is 35 feet
Now the volume of a pyramid is given by
where V is volume , b is base edge and h is height of pyramid
Therefore
Hence , the volume of pyramid is 6720 ft³
