Question

СРОЧНО! Даю 50 баллов! 1.Решите задачу с помощью уравненияприусадебный участок имеет форму прямоугольника с длинной на 2 м больше ширины Найдите длинну изгороди участка если площадь 80м2.Решите задачу с помощью урваненияКатер прошел 15 км по течению реки и 10 км против течения реки,затратив на весь путь 1 час.Найдите скорость реки,если известно,что скорость катера в стоячей воде равна 25 км/ч

Answer 1

1)
ширина - а
длина - а+2
S=a^2+2a=80
a^2+2a-80=0
a=8 a≠-10
ширина 8м, длина - 10м

2)
х- скорость течения
по течению - 15км - 25+х
против течения - 10 км - 25-х

15/(25+х)+10/(25-х)=1 (час)

(375-15х+250+10х-625+х^2)/(25-х)(25+х)=0

х≠25 х≠-25

х^2-5х=0
х(х-5)=0
х=5 х≠0

5 км/час - скорость катера

Answer 2

Task 1: Solved using an equation

To find the length of the fence surrounding a rectangular plot, we need to use the given information that the plot has the shape of a rectangle with a length 2 meters longer than its width, and the area of the plot is 80 square meters.

Let's assume the width of the plot is x meters. Then the length of the plot would be x + 2 meters.

The formula for the area of a rectangle is length × width. We can set up an equation using this formula and solve for the width of the plot.

The equation is: (x + 2) × x = 80

Simplifying the equation, we get: x^2 + 2x = 80

Rearranging the equation, we have: x^2 + 2x - 80 = 0

To solve this quadratic equation, we can factor it or use the quadratic formula. Let's use the quadratic formula:

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

For our equation, the coefficients are: a = 1, b = 2, and c = -80.

Plugging these values into the quadratic formula, we get:

x = (-2 ± √(2^2 - 4 × 1 × -80)) / (2 × 1)

Simplifying further, we have:

x = (-2 ± √(4 + 320)) / 2

x = (-2 ± √324) / 2

x = (-2 ± 18) / 2

Now we have two possible values for the width of the plot: x = (-2 + 18) / 2 and x = (-2 - 18) / 2.

Calculating these values, we get:

x = 16 / 2 = 8 or x = -20 / 2 = -10

Since the width cannot be negative, we discard the negative value.

Therefore, the width of the plot is 8 meters.

To find the length of the plot, we can substitute this value back into the equation: length = x + 2.

So, the length of the plot is 8 + 2 = 10 meters.

Therefore, the length of the fence surrounding the plot is 2 × (length + width) = 2 × (10 + 8) = 36 meters.

Answer: The length of the fence surrounding the plot is 36 meters.

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