Answer:
Therefore the required polynomial is
M(x)=0.83(x³+4x²+16x+64)
Step-by-step explanation:
Given that M is a polynomial of degree 3.
So, it has three zeros.
Let the polynomial be
M(x) =a(x-p)(x-q)(x-r)
The two zeros of the polynomial are -4 and 4i.
Since 4i is a complex number. Then the conjugate of 4i is also a zero of the polynomial i.e -4i.
Then,
M(x)= a{x-(-4)}(x-4i){x-(-4i)}
=a(x+4)(x-4i)(x+4i)
=a(x+4){x²-(4i)²} [ applying the formula (a+b)(a-b)=a²-b²]
=a(x+4)(x²-16i²)
=a(x+4)(x²+16) [∵i² = -1]
=a(x³+4x²+16x+64)
Again given that M(0)= 53.12 . Putting x=0 in the polynomial
53.12 =a(0+4.0+16.0+64)

=0.83
Therefore the required polynomial is
M(x)=0.83(x³+4x²+16x+64)
The value of y=29
the value of x=61
I believe the correct answer is 151
Answer:
f(m) = 75-8m
Step-by-step explanation:
She began with $75. After the first movie, she had $67 remaining; this means she spent
75-67 = $8
After the second movie, she had $59 remaining; she spent
67-59 = $8
After the third movie, she had $51 remaining; she spent
59-51 = $8
Each movie costs $8. Letting m represent the number of movies, this gives us 8m.
Since she is spending money, we subtract this from the original amount, $75; this gives us
f(m) = 75-8m