Answer:
P(x) = x³-(3i+1)x²+(3i-2)x+6i
Step-by-step explanation:
If -1, 2 and 3i are roots of the polynomial, then the following are factors of the polynomial in x
(x+1), x-2 and x-3i
To get the required polynomial, we will take the product of the factors as shown;
(x+1)(x-2)(x-3i)
(x+1)(x-2) = x²-2x+x-2
(x+1)(x-2) = x²-x-2
(x²-x-2)(x-3i) = (x²)(x)-x²(3i)-x(x)-x(-3i)-2x-2(-3i)
(x²-x-2)(x-3i) = x³-3x²i-x²+3xi-2x+6i
(x²-x-2)(x-3i) = x³-x²(3i+1)+x(3i-2)+6i
(x²-x-2)(x-3i) = x³-(3i+1)x²+(3i-2)x+6i
Hence the polynomial function in standard form with leading coefficient of 1 is x³-(3i+1)x²+(3i-2)x+6i
The graph of f(x) = x^2 has only one x-intercept since its vertex is at the origin, (0,0) and it opens up. When comparing the graph of <span>g(x) = -x^2 -5 with the graph of f(x) = x^2, g(x) is the graph of f(x) first reflected in the x-axis and then translated 5 units down. The graph of g(x) has no x-intercepts since its a parabola that opens downward (result of reflection in x-axis) and its vertex at (0,-5) is situated below the x-axis.</span>
Answer:
Correct option: fourth one -> 254 cubic inches.
Step-by-step explanation:
The volume of a cylinder is given by the equation:
To calculate the internal volume of the pipe, we should use its internal radius.
The external radius of the pipe is half of the diameter, and the internal radius is the external radius minus the thickness of the pipe, so we have:
Then, using the internal radius in the volume equation, we have that:
So the correct option is the fourth one: Volume is approximately 254 cubic inches.
Recall that a ⇒ b ≡ ¬a ∨ b.
• r ⇒ (p ∧ q) ≡ ¬r ∨ (p ∧ q)
In row C, q is false so p ∧ q false, and r is true so ¬r is false.
¬r ∨ (p ∧ q) ≡ false ∨ false ≡ false
• r ⇒ (p ∨ q) ≡ ¬r ∨ (p ∨ q) = p ∨ q ∨ ¬r
In each of rows A, C, and E, at least one of p or q is true, so
p ∨ q ∨ ¬r = true
• (q ∧ r) ⇒ p ≡ ¬(q ∧ r) ∨ p ≡ (¬q ∨ ¬ r) ∨ p = p ∨ ¬q ∨ ¬r
In row E, p is false and both q and r are true, so ¬q and ¬r are both false.
false ∨ false ∨ false = false
• (q ∨ r) ⇒ p ≡ ¬(q ∨ r) ∨ p ≡ (¬q ∧ ¬r) ∨ p
In row E, p is false and both q and r are true, so both ¬q and ¬r are false.
(¬q ∧ ¬r) ∨ p ≡ (false ∧ false) ∨ false ≡ false ∨ false ≡ false
Answer:
The temperature of the liquid 15 minutes later is 
Step-by-step explanation:
This is an example of arithmetic progression
We need to find 15 th term
Here
