Question

(12,5)^0,25*(18,75)^0,75=(x/20)^0,25*(3x/80)^0,75

Answer 1

Ответ:

Ответ внизу на фото

Объяснение:

Answer 2

(12,5)^0,25*(18,75)^0,75=(x/20)^0,25*(3x/80)^0,75

(12,5)^0,25*(18,75)^0,75=(x/20)^0,25*(3x/80)^0,75

Делим обе части на (12,5)^0,25*(18,75)^0,75.

получаем 1=(x/(20*12.5))^0,25*(3x/(80*18,75))*)^0,75/

1= ((0.004x)^0,25)((0.02x)^0,75); 1=х*(0.004^0,25)*(0.002^0,75)

х= 1/((0.004^0,25)*(0.002^0,75))

х=1/((2^0,25)*((0.002)^0,75)*((0.002)^0,25))

х=500/(2^0,25)

Answer 3

To solve the equation, let's break it down step by step:

Starting with the left side of the equation:

(12,5)^0,25 * (18,75)^0,75

To evaluate the expressions, we need to convert the numbers with commas into decimal form:

(12.5)^0.25 * (18.75)^0.75

Now, we can simplify this using exponentiation rules:

√(12.5) * (√(18.75))^3

Taking the square root of 12.5:

√(12.5) ≈ 3.53553

Taking the cube root of 18.75:

(√(18.75))^3 ≈ 2.87228^3 ≈ 23.876

Now, let's simplify the right side of the equation:

(x/20)^0.25 * (3x/80)^0.75

Expanding the expression:

(x^0.25 / 20^0.25) * ((3x)^0.75 / 80^0.75)

Simplifying the constants:

(x^0.25 / √20) * ((3x)^0.75 / ∛80)

Now, we can equate the left and right sides of the equation:

3.53553 * 23.876 ≈ (x^0.25 / √20) * ((3x)^0.75 / ∛80)

Simplifying further:

84.2261 ≈ (x^0.25 / √20) * ((3x)^0.75 / ∛80)

To isolate the variable x, we can multiply both sides by the denominators:

84.2261 * √20 * ∛80 ≈ (x^0.25 * (3x)^0.75)

Simplifying the right side:

84.2261 * √20 * ∛80 ≈ x^(0.25 + 0.75*0.25)

84.2261 * √20 * ∛80 ≈ x^(0.25 + 0.1875)

84.2261 * √20 * ∛80 ≈ x^0.4375

To solve for x, we need to raise both sides to the power of (1/0.4375):

(84.2261 * √20 * ∛80)^(1/0.4375) ≈ x

Calculating the right side:

(84.2261 * √20 * ∛80)^(1/0.4375) ≈ 17.5257

Therefore, the approximate value of x is approximately 17.5257.