Question

1.Спростіть вираз xy(2x-3y)-3y(x^2-xy) 2.Знайти нулі функції y=x^2-1/x-13. У рівнобедреному трикутнику основа дорівнює 12 см а бічна сторона - 10 см. Знайти площу трикутника.Пожалуйста помогите, не могу разобраться

Answer 1

№3

площадь находится по формуле1/2* на высоту*на основание

1)проводим высоту к основанию

2) рассмотрим один из получившихся треугольников

по теореме пифагора высота(в квадрате)=сторона(в квадрате)-часть основания (в квадрате)

высота(в квадрате)=10(в квадрате)-6(в квадрате)

3)а дальше подставляй в формулу1)(только не забудь от квадрата избавиться)

Answer 2

Simplifying the Expression

To simplify the expression xy(2x-3y)-3y(x^2-xy), we can follow the order of operations (PEMDAS) and distribute the terms:

1. Distribute the terms in the first part of the expression: xy(2x-3y) becomes 2x^2y - 3xy^2. 2. Distribute the terms in the second part of the expression: -3y(x^2-xy) becomes -3yx^2 + 3xy^2.

Now we can combine like terms:

2x^2y - 3xy^2 - 3yx^2 + 3xy^2

The terms -3xy^2 and 3xy^2 cancel each other out, leaving us with:

2x^2y - 3yx^2

So, the simplified expression is 2x^2y - 3yx^2.

Finding the Zeros of the Function

To find the zeros of the function y = x^2 - 1/x - 13, we need to set the function equal to zero and solve for x:

x^2 - 1/x - 13 = 0

To simplify the equation, we can multiply through by x to eliminate the fraction:

x^3 - 1 - 13x = 0

Now, we can rearrange the equation to get all the terms on one side:

x^3 - 13x - 1 = 0

Unfortunately, finding the exact solutions to this cubic equation is not straightforward. We can use numerical methods or calculators to approximate the solutions.

Using a calculator or numerical methods, we find that the approximate solutions are:

x ≈ -2.0801 x ≈ 0.0401 x ≈ 2.0400

Therefore, the zeros of the function are approximately x = -2.0801, x = 0.0401, and x = 2.0400.

Finding the Area of an Isosceles Triangle

To find the area of an isosceles triangle, we need to know the length of the base and the length of one of the equal sides.

In this case, the base of the triangle is given as 12 cm, and one of the equal sides is given as 10 cm.

To find the area of the triangle, we can use the formula:

Area = (1/2) * base * height

In an isosceles triangle, the height is the perpendicular distance from the base to the vertex opposite the base.

To find the height, we can use the Pythagorean theorem:

height^2 = (side length)^2 - (1/2 * base)^2

Substituting the given values:

height^2 = 10^2 - (1/2 * 12)^2

height^2 = 100 - 36

height^2 = 64

height = 8 cm

Now we can calculate the area:

Area = (1/2) * 12 cm * 8 cm

Area = 48 cm^2

Therefore, the area of the isosceles triangle is 48 square centimeters.