Answer:
x^3-4x^2+25x-100
Step-by-step explanation:
We have 2 roots -5i and 4. Using the conjugate root theorem for the root -5i, we know that 5i should be another root
Combining the roots into a polynomial gives us:
(x+5i)(x-5i)(x-4)
Expand:
(x^2 + 25)(x-4)
x^3-4x^2+25x-100
<span>We have lateral faces that are rectangles and 2 congruent polygons that are bases. This must be 3-dimensional solid figure - quadrilateral prism. If those 2 bases are squares then it is a rectangular prism, but the bases also can be 2 rhombuses. Answer: Quadrilateral prism.</span><span />
Answer:
To satisfy the hypotheses of the Mean Value Theorem a function must be continuous in the closed interval and differentiable in the open interval.
Step-by-step explanation:
As f(x)=2x3−3x+1 is a polynomial, it is continuous and has continuous derivatives of all orders for all real x, so it certainly satisfies the hypotheses of the theorem.
To find the value of c, calculate the derivative of f(x) and state the equality of the Mean Value Theorem:
dfdx=4x−3
f(b)−f(a)b−a=f'(c)
f(x)x=0=1
f(x)x=2=3
Hence:
3−12=4c−3
and c=1.
Answer:
6.32
Step-by-step explanation:
To find the side length on a right angled triangle we follow The Pythagorean Theorem:
c being the hypothesis (longest side: the hypotenuse is always opposite the right angle)
so..
Answer:
7 Caterpillars
Step-by-step explanation:
14/2