Answer:
Step-by-step explanation:
Comment
The basic equation of a circle is
(x - a)^2 + (y - b)^2 = r^2
a and b are the coordinates of the center of the circle
r is the radius.
Development of the equation
r = 1 - 1/2 = 1/2. r is the distance between the red dot and the blue dot.
So far what you have is (x - a)^2 + (y - b)^2 = (1/2)^2
The center is the red dot.
x = 1
y = - 1
Answer: (x - 1)^2 + (y + 1/2)^2 = 1/4
Step-by-step explanation:
I'm not sure what you mean by 'written method' but the sum is 2,654.
The equivalent expression of x^3 (x^2 + 5x + 7) is x^5 + 4x^4 + x^4 + 8x^3 - x^3
<h3>How to determine the equivalent expression?</h3>
The expression is given as:
x^3 (x^2 + 5x + 7)
Expand the expression
x^3 * x^2 + x^3 * 5x + x^3 * 7
Evaluate the product
x^5 + 5x^4 + 7x^3
Expand the expression
x^5 + 4x^4 + x^4 + 8x^3 - x^3
Hence, the equivalent expression of x^3 (x^2 + 5x + 7) is x^5 + 4x^4 + x^4 + 8x^3 - x^3
Read more about equivalent expression at:
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If complex coefficients are allowed, the answer is 3.
If the polynomial must have real coefficients, then each complex root comes as a pair of complex conjugate roots.
Root -5 is real, so that is 1 root, and degree 1.
Root 1 + 4i is complex, so it must come with its complex conjugate, 1 - 4i. This adds 2 roots to the polynomial, and now we're up to degree 3.
Root -4i is also complex. It also must come with its complex conjugate, 4i. That adds two more roots, and the degree is 5.
Answer: The least possible degree is 5 with real coefficients.
