You put $600 in an account. The account earns $31 simple interest in 10 months. What is the annual interest
2 answers:
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Answer:
a) Function:Yes
b) Domain:
c) Range:
Step-by-step explanation:
The given graph passes vertical line test hence it is a function
The given function has x-intercepts at
We can therefore write this function in factored form as
There is a y-intercept at (0,-2)
The required function is
b) The domain refers to all values of x for which this function is defined.
The domain from the graph is because there are holes at the end of the graph.
c) The range is the value of y for which x is defined or the graph exists.
From the graph the range is
We have
In order to obtain easily the table, we need to clear y
then we evaluate for values of x
if x=0
y=-4(0)+1=1
y=1
if x=1
y=-4(1)+1=-3
y=3
if x=2
y=-4(2)+1=-7
y=-7
if x=3
y=-4(3)+1=-11
y=-11
So the table for the given equation is
x y
0 1
1 -3
2 -7
3 -11
We have to calculate the fourth roots of this complex number:
We start by writing this number in exponential form:
Then, the exponential form is:
The formula for the roots of a complex number can be written (in polar form) as:
Then, for a fourth root, we will have n = 4 and k = 0, 1, 2 and 3.
To simplify the calculations, we start by calculating the fourth root of r:
<em>NOTE: It can not be simplified anymore, so we will leave it like this.</em>
Then, we calculate the arguments of the trigonometric functions:
We can now calculate for each value of k:
Answer:
The four roots in exponential form are
z0 = 18^(1/4)*e^(i*π/8)
z1 = 18^(1/4)*e^(i*5π/8)
z2 = 18^(1/4)*e^(i*9π/8)
z3 = 18^(1/4)*e^(i*13π/8)