Algebraic moves
The term that describes this type of function:
1/(1 + e-x)
Logistic
What the Fundamental Theorem of Algebra says about this function:
x4 - 6x3 + 10x2 - 6x + 9
It has 4 complex (real and non real) zeros.
The following expression written as a single logarithm:
4 log (xy) - 3 log (yz)
log (x4y/z3)
The value of csc(pi/3) with a rationalized denominator.
(2 √3)/3
The simplification of
tan x cos x
sin x
The factors of x2 + 3x - 40
(x - 5) and (x + 8)
The list of potential rational zeros for
3x3 + 4x2 - 5x - 2
1, -1, 2, -2, 1/3, -1/3, 2/3, -2/3
log7 x written only using the natural log
ln x / ln 7
The sign (+ or -) of sin, cos, and tan for the angle 4pi/3
sin: -, cos: -, tan: +
The exact value of cos(7pi/12)
(√2 - √6)/4
This fraction in simplest form once the denominator has been rationalized:
2√ 3/√ 2
(2 root 3 over root 2)
√ 6
The work showing 3x3 + 4x2 - 5x - 2 divided synthetically by 1
1| 3 4 -5 -2
3 7 2
3 7 2 0
The value of x if
ln(x - 3) + ln(x + 4) = 3 ln 2
4
The value of x that solves sec x = -2 when pi < x < 3pi/2
4pi/3
cos-1(sin(5pi/4))
3pi/4
The product of
(5 - 2i) and (5 + 2i)
29
What the Factor Theorem says about
f(x) = 3x3 + 4x2 - 5x - 2 and the number 1, and why
x - 1 is a factor because f(1) = 0
The initial number of students infected with flu if, after t days the function is modeled by
800/(1 + 49e^(-0.2t))
16
The value of sec(x) if sin = 1/2 and cos < 0
-(2 √3)/3
The number of triangles determined by these measurements:
C = 30° , a = 18, c = 9
and why.
1 triangle
Because c = a sin C
The factored form of
15x4 - 78x3 + 72x2
3x2(5x - 6)(x - 4)
The linear and irreducible factors of 2x4 - 162
2(x + 3)(x - 3)(x2 + 9)
The day the number of students infected with flu reaches 200 if, after t days the function is modeled by
800/(1 + 49e^(-0.2t))
about 14
The values of all 6 trig functions for the angle 7pi/6
sin = -1/2, cos = -√3/2, tan = √3/3
sec = -(2 √3)/3, csc = -2, cot = √3
The value of cos(2x) if sin(x) = 12/13 and x has a terminal side in Quadrant II
-119/169