Answer:
y = 4sin [(1/2)t - (4/3)π ] - 2
Step-by-step explanation:
For this question, do not be intimidated by the terminology, just realize the following:
for y = a sin [ (2π/T) t ]
a = amplitude = given as 4
T = period = given as 4π
phase shift is simply horizontal shift, positive values means the graph moves by that amount to left and negative values means the graph moves to the right.
vertical shift ... is well a shift vertically. positive values move the graph up vertically and negative values move the graph down vertically.
so... if we start with the basic formula:
y = a sin [ (2π/T) t ]
given a = 4 and T = 4π (substitute these values into the formula)
y = (4) sin [ (2π/4π) t ] = (4) sin [ (1/2) t ]
y = 4sin [(1/2)t ]
Now for the shifts:
given phase shift, aka horizontal shift is -(4/3)π, equation becomes
y = 4sin [(1/2)t - (4/3)π ]
given vertical shift is -2, the equation simply becomes
y = 4sin [(1/2)t - (4/3)π ] - 2
Answer:
Natalie cannot make it over the fence.
Step-by-step explanation:
After reading the statement, we must demostrate if the following inequation is possible, that is:
After some algebraic handling we find this equivalent expression:
(1)
The polynomial is factorized by the Quadratic Formula:
Since all roots are complex, we conclude that Natalie cannot make it over the fence.
Common stock, preferred stock, municipal bond
Answer:
Clustering
Step-by-step explanation:
Data groups that are grouped closely together
Answer
Step-by-step planation:
The given expression is .
We have to check which of he given options on simplification gives the same given expression.
(A) The expression is:
=
=
which is not equivalent to the given expression, thus this option is incorrect.
(B) The expression is:
=
=
which is not equivalent to the given expression, thus this option is incorrect.
(C) The expression is:
=
=
which is not equivalent to the given expression, thus this option is incorrect.
(D) The expression is:
=
=
which is equivalent to the given expression, thus this option is correct.
(E) The expression is:
=
==
which is equivalent to the given expression, thus this option is correct.
(F) The expression is:
=
which is not equivalent to the given expression, thus this option is incorrect.
