Question

Если (x0;y0)- решение системы{0.2^(5x-y)=125{11^(2x-y)=1/121то сумма X0+Y0= Реклама googletag.cmd.push(function() { googletag.display('gpt-ad-brainly_rectangle_in_question'); }); Попроси больше объяснений СледитьОтметить нарушение Nata7858 15.07.2013 Войти чтобы добавить комментарий googletag.cmd.push(function() { googletag.display('gpt-ad-brainly_rectangle_below-question-first'); }); googletag.cmd.push(function() { googletag.display('gpt-ad-brainly_rectangle_below-question-second'); }); Ответы и объяснения Опытпочетный грамотей5^(Y-5X)=5^311^2x-y=11^-2 y-5x=32x-y=-2 -3x=1x=-1/3y=3+5x=3-5/3=4/3x+y=4/3-1/3=1   0.0 0 оценок 0 оценок Оцени! Оцени! Спасибо2 Комментарии Отметить нарушение Войти чтобы добавить комментарий Реклама googletag.cmd.push(function() { googletag.display('gpt-ad-brainly_rectangle_stream'); }); МозгПомощник Сомневаешься в ответе? Сомневаешься в ответе? Смотреть другие ответы Узнавай больше на Знаниях! Узнавай больше на Знаниях! У тебя проблема с домашними заданиями? Попроси о помощи!80% ответов приходят в течение 10 минут Мы не только ответим, но и объясним Качество гарантируется нашими экспертами Хочу завести аккаунт! Что ты хочешь узнать? Задай вопрос Задай вопросСамые новые вопросыАлгебра 6 баллов 53 минуты назад Найдите экстремум функции: y=1-x^2 Ответь Алгебра 5 баллов 6 часов назад Log₃ [tex]\frac{1}{2}[/tex] =

Answer 1

Translated Question:

Answer in detail. If (x0;y0) is a solution of the system:

{0.2^(5x-y)=125 {11^(2x-y)=1/121

then the sum of x0 and y0 is?

Translated Answer:

To find the sum of x0 and y0, we need to solve the given system of equations:

Equation 1: 0.2^(5x-y) = 125 Equation 2: 11^(2x-y) = 1/121

Let's solve these equations step by step:

Step 1: Solving Equation 1

We can rewrite Equation 1 as:

(1/5)^(5x-y) = 125

Taking the logarithm of both sides with base 1/5:

log(1/5) [(1/5)^(5x-y)] = log(1/5) [125]

Simplifying the left side using logarithmic properties:

(5x-y) log(1/5) (1/5) = log(1/5) (125)

Simplifying the logarithm:

(5x-y) * (-1) = log(125) / log(1/5)

Simplifying further:

y - 5x = log(125) / log(1/5) ----(Equation 3)

Step 2: Solving Equation 2

We can rewrite Equation 2 as:

11^(2x-y) = 1/121

Taking the logarithm of both sides with base 11:

log(11) [11^(2x-y)] = log(11) [1/121]

Simplifying the left side using logarithmic properties:

(2x-y) log(11) (11) = log(11) (1/121)

Simplifying the logarithm:

(2x-y) * 1 = log(1/121) / log(11)

Simplifying further:

2x - y = log(1/121) / log(11) ----(Equation 4)

Step 3: Solving the System of Equations

Now, we have two equations:

Equation 3: y - 5x = log(125) / log(1/5) Equation 4: 2x - y = log(1/121) / log(11)

We can solve this system of equations using various methods such as substitution or elimination. Let's solve it using substitution:

From Equation 3, we can express y in terms of x:

y = log(125) / log(1/5) + 5x

Substituting this expression for y in Equation 4:

2x - (log(125) / log(1/5) + 5x) = log(1/121) / log(11)

Simplifying:

2x - log(125) / log(1/5) - 5x = log(1/121) / log(11)

Combining like terms:

-3x - log(125) / log(1/5) = log(1/121) / log(11)

Multiplying both sides by log(1/5) to eliminate the denominator:

-3x * log(1/5) - (log(125) / log(1/5)) * log(1/5) = (log(1/121) / log(11)) * log(1/5)

Simplifying:

-3x * log(1/5) - log(125) = (log(1/121) * log(1/5)) / log(11)

Multiplying further:

-3x * log(1/5) - log(125) = log(1/121 * 1/5) / log(11)

Simplifying the logarithms:

-3x * log(1/5) - log(125) = log(1/605) / log(11)

Multiplying both sides by log(11) to eliminate the denominator:

-3x * log(11) * log(1/5) - log(125) * log(11) = log(1/605)

Simplifying further:

-3x * log(11 * 1/5) - log(125) * log(11) = log(1/605)

Using logarithmic properties:

-3x * log(11/5) - log(125) * log(11) = log(1/605)

Dividing both sides by (-3 * log(11/5)):

x = (log(1/605) - log(125) * log(11)) / (-3 * log(11/5))

Calculating this expression gives us the value of x.

Once we have the value of x, we can substitute it back into Equation 3 to find the value of y:

y = log(125) / log(1/5) + 5x

Finally, we can find the sum of x0 and y0 by adding the values of x and y obtained from the equations.

Please note that the calculations can be quite complex, and it is recommended to use a calculator or software program to perform the calculations accurately.