Question

1/3z-0,3z=-0,6 Решите уровнение

Answer 1

$\frac{z}{3} - \frac{3z}{10} = - \frac{6}{10} \\ \frac{10z - 9z}{30} = - \frac{6}{10} \\ \frac{z}{30} = \frac{ - 6}{10} \\ z = \frac{ - 6 \times 30}{10} = - \frac{180}{10} = - 18$

Answer 2

1/3z - 0,3x = -0,6 (умножаем всё уравнение на 3 )

z - 0,9z = -1,8

0,1z = -1,8

z = -1,8 : 0,1

z = -18

Answer 3

To solve the equation 1/(3z) - 0.3z = -0.6, we'll follow these steps:

Step 1: Clear the fraction by multiplying both sides of the equation by 3z to get rid of the denominator. Step 2: Simplify the equation. Step 3: Solve for z.

Let's proceed with the solution:

Step 1: Multiply both sides of the equation by 3z: 3z * (1/(3z)) - 3z * 0.3z = -0.6 * 3z

Step 2: Simplify the equation: 1 - 0.9z^2 = -1.8z

Step 3: Now, move all the terms to one side to set the equation to zero: 0.9z^2 - 1.8z - 1 = 0

This is a quadratic equation in terms of z. We can solve it by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:

The quadratic formula is given by: z = (-b ± √(b^2 - 4ac)) / 2a

In our equation, a = 0.9, b = -1.8, and c = -1.

Now, plug these values into the quadratic formula:

z = (1.8 ± √((-1.8)^2 - 4 * 0.9 * -1)) / 2 * 0.9

z = (1.8 ± √(3.24 + 3.6)) / 1.8

z = (1.8 ± √6.84) / 1.8

z = (1.8 ± 2.61) / 1.8

Now, find the two solutions for z:

1. z = (1.8 + 2.61) / 1.8 z = 4.41 / 1.8 z ≈ 2.45

2. z = (1.8 - 2.61) / 1.8 z = -0.81 / 1.8 z ≈ -0.45

So, the two solutions for the equation are approximately z ≈ 2.45 and z ≈ -0.45.