X^3-3x^2+81x-243
2 answers:
The given <span>polynomial is ⇒⇒⇒ </span><span>f(x) = x³ - 3x² + 81x - 243
</span>
by factoring the absolute term (243) to find one of the factors of the the polynomial
∴ 243 = (1 * 243) or (3 * 81) or (9 * 27)
check which of the numbers {1 , 3 , 9 , 27 , 81 , 243} make f(x)<span>= 0
</span>
i have checked 3 and it makes <span>polynomial = 0
</span>
i.e: f(3) = 0 ⇒⇒ (x - 3) is one of the factors of f(x)
By using the reminder theorem ⇒⇒ see the attache figure
∴
And ⇒⇒ (x² + 81) is a sum of two squares which can be factored using the complex numbers as following
x² + 81 = ( x + 9i ) ( x - 9i )
∴ f(x) = <span>x³ - 3x² + 81x - 243 = (x - 3)(x + 9i)(x - 9i)
</span>
</span>
by factoring the absolute term (243) to find one of the factors of the the polynomial
∴ 243 = (1 * 243) or (3 * 81) or (9 * 27)
check which of the numbers {1 , 3 , 9 , 27 , 81 , 243} make f(x)<span>= 0
</span>
i have checked 3 and it makes <span>polynomial = 0
</span>
i.e: f(3) = 0 ⇒⇒ (x - 3) is one of the factors of f(x)
By using the reminder theorem ⇒⇒ see the attache figure
∴
And ⇒⇒ (x² + 81) is a sum of two squares which can be factored using the complex numbers as following
x² + 81 = ( x + 9i ) ( x - 9i )
∴ f(x) = <span>x³ - 3x² + 81x - 243 = (x - 3)(x + 9i)(x - 9i)
</span>
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I think it is C. 60.
You can eliminate A because it is not a right angle, and D because the angle is bigger than the given angle. So it is between 50 and 60, and I hope this is right and the picture makes sense
You can eliminate A because it is not a right angle, and D because the angle is bigger than the given angle. So it is between 50 and 60, and I hope this is right and the picture makes sense
The distance between both lines is 2.24 units
Step-by-step explanation:
There is no straight method to find the distance between two lines. The distance can be found out by finding a point on one line and then finding the distance of that point from the other line. The y-coordinate of point is obtained by putting any value of x in equation . The x and y combined give us the point.
Given
We have to find the distance of this point from y=2x+5
The formula for finding distance of a point (x,y) from a line is:
A=2
B=-1
C=5
Putting the values in the formula
Rounding off will give: 2.24 units
The distance between both lines is 2.24 units
Keywords: Equations of lines
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