Step-by-step explanation:
Answer:
SA = 31.714 km²
Step-by-step explanation:
SA = πr² + πrl
SA = 3.14(1)² + 3.14(1)(9.1)
SA = 3.14 + 28.574
SA = 31.714 km²
2x^2 + 8x - 12 = 0..divide by 2
x^2 + 4x - 6 = 0
x^2 + 4x = 6...add 4 to both sides of the equation
x^2 + 4x + 4 = 6 + 4
(x + 2)^2 = 10....<== ur constant is 10
x + 2 = (+-)sqrt 10
x = -2 (+ - ) sqrt 10
x = -2 + sqrt 10
x = -2 - sqrt 10
Answer:
Step-by-step explanation:
Polynomial f(x) has the following conditions: zeros of -2 (multiplicity 3), 3 (multiplicity 1), and with f(0) = 120.
The first part zeros of -2 means (x+2) and multiplicity 3 means (x+2)^3.
The second part zeros of 3 means (x-3) and multiplicity 1 means (x-3).
The third part f(0) = 120 means substituting x=0 into (x+2)^3*(x-3)*k =120
(0+2)^3*(0-3)*k = 120
-24k = 120
k = -5
Combining all three conditions, f(x)
= -5(x+2)^3*(x-3)
= -5(x^3 + 3*2*x^2 + 3*2*2*x + 2^3)(x-3)
= -5(x^4 + 6x^3 + 12x^2 + 8x - 3x^3 - 18x^2 - 36x - 24)
= -5(x^4 + 3x^3 - 6x^2 - 28x -24)
= -5x^4 - 15x^3 + 30x^2 + 140x + 120
Answer:
look below
Step-by-step explanation:
y = 2 (x + 3)^2 - 2
Geometric figure: parabola
Alternate forms:
y = 2 (x + 2) (x + 4)
y = 2 (x^2 + 6 x + 8)
-2 x^2 - 12 x + y - 16 = 0
Expanded form:
y = 2 x^2 + 12 x + 16
Roots:
x = -4
x = -2
<u>Properties as a real function:
</u>
Domain
- R (all real numbers)
Range
- {y element R : y>=-2}
Partial derivatives:
d/dx(2 (x + 3)^2 - 2) = 4 (x + 3)
d/dy(2 (x + 3)^2 - 2) = 0
Implicit derivatives:
(dx(y))/(dy) = 1/(12 + 4 x)
(dy(x))/(dx) = 4 (3 + x)
Global minimum:
min{2 (x + 3)^2 - 2} = -2 at x = -3