Question

5t +1,1<0,2(t-3)+2,1-4t(t-2)>4(1-6)(t+1);​

Answer 1

Ответ:

Пошаговое объяснение:

Преобразуем первое неравенство

5t+1.1<0.2t-0.6+2

5t-0.2t<1.4-1.1

4.8t<0.3

t<0.0625

Теперь второе

1-4t²+8t>-20(t+1)

-4t²+8t+20t+20>0

-4t²+28t+20>0

Умножаем на (-1), знак неравенства меняется

4t²-28t-20<0

t²-7t-5<0

D=49+20=69

$t_1=\frac{7-\sqrt{69} }{2} \\t_2=\frac{7+\sqrt{69} }{2}$

t²-7t-5=0 - это уравнение параболы. Ветви верх. Значит, отрицательные значения находятся между t₁ и t₂

$t\in(\frac{7-\sqrt{69} }{2} ;\frac{7+\sqrt{69} }{2} )$

$\frac{7-\sqrt{69} }{2} \approx -0.65331$

$\frac{7+\sqrt{69} }{2} \approx 7.6533$

Объединяя оба решения, окончательно получаем

$t\in(\frac{7-\sqrt{69} }{2} ;0,0625)$

Answer 2

It seems like you've provided an inequality expression involving variable "t". The expression is a bit unclear due to the formatting. However, I'll do my best to help you interpret and solve it. Please correct me if I misunderstood any part of the expression:

The given inequalities are:

1. $5t + 1.1 < 0.2(t - 3) + 2.1 - 4t(t - 2)$
2. $2.1 - 4t(t - 2) > 4(1 - 6)(t + 1)$

Let's solve these inequalities step by step:

Inequality 1: $5t + 1.1 < 0.2(t - 3) + 2.1 - 4t(t - 2)$

Simplify the right side: $5t + 1.1 < 0.2t - 0.6 + 2.1 - 4t^2 + 8t$

Combine like terms: $5t + 1.1 < 0.2t + 1.5 - 4t^2 + 8t$

Simplify further: $5t + 1.1 < 1.5 + 8t - 4t^2$

Rearrange to get a quadratic inequality on one side: $0 < 1.5 + 8t - 5t - 4t^2 - 1.1$

Simplify: $0 < 0.4t - 4t^2 + 0.4$

Divide by common factor 0.4: $0 < t - 10t^2 + 1$

This is a quadratic inequality. To solve it, we need to find the values of "t" for which the inequality is true. The solution will involve solving for the roots of the quadratic expression:

$t - 10t^2 + 1 = 0$

Solving this equation will give us the critical points where the inequality might change. The solutions might be real numbers between those critical points where the expression is negative.

Inequality 2: $2.1 - 4t(t - 2) > 4(1 - 6)(t + 1)$

Simplify both sides: $2.1 - 4t^2 + 8t > 4(-5)(t + 1)$

Simplify further: $2.1 - 4t^2 + 8t > -20(t + 1)$

Expand: $2.1 - 4t^2 + 8t > -20t - 20$

Combine like terms: $-4t^2 + 28t + 2.1 > -20t - 20$

Move all terms to one side: $-4t^2 + 48t + 22.1 > 0$

This is a quadratic inequality. Similar to the first inequality, you would solve for its roots and then determine the intervals where the expression is greater than zero.

Please provide me with specific values of "t" that you want to substitute into these inequalities, or let me know if you want further assistance with solving these inequalities graphically or analytically.