PLEASE HELP!! 4 Digit Lock * Enter 4 digit number code with no spaces
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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)
Answer:
Step-by-step explanation:
To write the equation of a line we need 2 points. We know:
- If the y-intercept of the line is -3 then the point is (0,-3).
- If the x-intercept of the line is -4.5 then the point is (-4.5,0).
Using these two point, we will find the slope and then substitute it into the point slope form with a point.
Slope:
This decimal is -2/3. We will now substitute -2/3 and (0,-3) into the point slope form.
Answer:
Step-by-step explanation:
Given inequality:
In order to represent the solution on the number line, we will first solve the given inequality.
We have
Subtracting both sides by 4.
Dividing both sides by -3.
[On dividing both sides by a negative number the sign of the inequality reverses.]
So, solution of this inequality will range from -3 to -∞
The number line is represented below.
