Question

1)20^3log5 (2) x (0,25)^log5 (8)-???? 2)16cos(п/5)cos(2п/5) HELP!!!!

Answer 1

На первое. Файл приложен

Answer 2

Let's break down each of your questions:

1. 20^3 * log5(2) * (0.25)^log5(8)

To calculate this expression, we can follow these steps:

Step 1: Calculate the values of log5(2) and log5(8).

log5(2) is the power to which 5 must be raised to get 2. log5(8) is the power to which 5 must be raised to get 8.

log5(2) is approximately 0.4307. log5(8) is approximately 1.292.

Step 2: Substitute these values into the expression and calculate:

20^3 * 0.4307 * (0.25)^1.292

Step 3: Calculate the values inside the parentheses:

20^3 = 20 * 20 * 20 = 8000 (0.25)^1.292 ≈ 0.1322

Step 4: Multiply the values together:

8000 * 0.4307 * 0.1322 ≈ 45.03

So, the result of the expression is approximately 45.03.

2. 16 * cos(π/5) * cos(2π/5)

To calculate this expression, you can use the trigonometric identity:

cos(2θ) = 2 * cos(θ)^2 - 1

In your case:

cos(2π/5) = 2 * cos(π/5)^2 - 1

Let's calculate each part:

cos(π/5) ≈ 0.809

Now, use the identity:

cos(2π/5) = 2 * (0.809)^2 - 1

cos(2π/5) ≈ 2 * 0.809^2 - 1 cos(2π/5) ≈ 2 * 0.654 - 1 cos(2π/5) ≈ 1.308 - 1 cos(2π/5) ≈ 0.308

Now, calculate the final result:

16 * cos(π/5) * cos(2π/5) ≈ 16 * 0.809 * 0.308 ≈ 3.934

So, the result of the expression is approximately 3.934.