Answer:
5,612.55 cm3
Step-by-step explanation:
i worked it out on paper
Hi there!
The question here asks us to find all the roots, or solutions, of the quartic equation x⁴ - 4x³ + x² + 12x - 12 = 0. We can start off by using the Rational Root Theorem, which calls for the constant over the leading coefficient, which for us would be 12 over 1. Since we need to list all the factors of 12, they all become + or -.
<u>+</u>12 / <u>+</u> 1
=> <u>+</u>1, <u>+</u>2, <u>+</u>3, <u>+</u>4, <u>+</u>6, <u>+</u>12 / <u>+</u>1
Now, just simplify each one. We get the possible roots 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 12, -12. The next part is the most tedious. Plug in each possible factor for x and see if the resulting value is 0. We get that only root 2 makes the whole equation equal to zero. However, we are not done yet. The question asks for the ALL the roots of the equation, not just real, but also imaginary. Let's use synthetic division to find the other roots.
We can set the divisor to 2, as (x - 2) = 0 is equal to x = 2.
2| 1 -4 1 12 -12
2 -4 -6 12
1 -2 -3 6 0
We can now factor the whole original equation to (x - 2)(x³ - 2x² -3x + 6) = 0. Now, we have to factor the expression x³ - 2x² -3x + 6, and grouping seems like the most appropriate way.
x³ - 2x² -3x + 6 = 0
(x³ - 2x²) + (-3x + 6) = 0
x²(x - 2) - 3(x - 2) = 0
(x² - 3)(x - 2) = 0
Next, use the Zero Product Property to get the values of x.
x² - 3 = 0
x² = 3
x = √3
x ≈ <u>+</u> 1.73
x - 2 = 0
x = 2
Therefore, the roots of the equation x⁴ - 4x³ + x² + 12x - 12 = 0 are x = 2,x = 2 (repeated solution), x = 1.73, x = -1.73. Hope this helped and have a great day!
A perfect situation to use a proportion:
(3.9 x 10³³) / 1 = X / (2.45 x 10⁵) .
Solve that proportion for ' X ' in the usual way.
If you can't remember how to solve a proportion, then
THAT's what you have to go look up. It's much more
important to you right now than how much energy the
sun is putting out.
7.4 x 10⁴ mm is the same size as about 243 feet !
If the tracks on a DVD were that far apart, there would not be
room for very many tracks on a DVD. That's not reasonable.
If the tracks are 7.4 x 10⁻⁴ mm apart, then there are about
34,000 tracks in a stripe that's 1-inch wide. I have no idea
how they do this, but it's certainly more reasonable than the
other choice.
Answer:
71%
Step-by-step explanation:
The original price is 200. The dress was sold for 142.
Take the price of the dress divide the original price (142/200) then times 100.
