Ushtrime Te Zgjidhura Matematika E Avancuar 10 Pegi39

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Solved Exercises Advanced Mathematics 10 Pegi39: A Useful Resource for Students and Teachers

If you are looking for a way to practice and improve your skills in advanced mathematics, you might be interested in the book Matematika 10 - 11: Pjesa I by Pegi Publishing House. This book covers topics such as algebra, geometry, trigonometry, functions, sequences, and statistics. It also includes exercises with different levels of difficulty and challenge.

However, if you are stuck on some of the exercises or want to check your answers, you might have a hard time finding the solutions online. That's why we have created this website, where you can find solved exercises advanced mathematics 10 Pegi39 for free. We have carefully worked out the solutions for each exercise, showing the steps and explanations. You can also download the PDF files of the solutions for offline access.

Our website is not only useful for students who want to study and review advanced mathematics, but also for teachers who want to prepare lessons and tests. You can use our solutions as a reference or a guide for teaching and grading. You can also find links to other websites that offer more resources and materials for learning and teaching advanced mathematics.

We hope that our website will help you achieve your goals and enjoy advanced mathematics. If you have any questions, suggestions, or feedback, please feel free to contact us. We would love to hear from you.

In this section, we will show you some examples of the solved exercises advanced mathematics 10 Pegi39 that you can find on our website. We will also explain how we solved them and what concepts and methods we used.

Example 1: Algebra

The following exercise is from the chapter 1.1A of the book Matematika 10 - 11: Pjesa I. It asks to simplify the expression $$\\frac{3x^2-12x+15}{x^2-4x+4}$$.

To simplify this expression, we need to factorize the numerator and the denominator. We can use the method of finding two numbers that add up to the coefficient of x and multiply to the constant term. For example, for the numerator, we need to find two numbers that add up to -12 and multiply to 15. These numbers are -3 and -5. So we can write $$3x^2-12x+15=3(x-3)(x-5)$$.

Similarly, for the denominator, we need to find two numbers that add up to -4 and multiply to 4. These numbers are -2 and -2. So we can write $$x^2-4x+4=(x-2)(x-2)$$.

Now we have $$\\frac{3x^2-12x+15}{x^2-4x+4}=\\frac{3(x-3)(x-5)}{(x-2)(x-2)}$$.

To simplify further, we need to cancel out any common factors in the numerator and the denominator. In this case, there are no common factors, so we cannot simplify any more. The final answer is $$\\frac{3(x-3)(x-5)}{(x-2)(x-2)}$$.

Example 2: Geometry

The following exercise is from the chapter 2.1A of the book Matematika 10 - 11: Pjesa I. It asks to find the value of x in the diagram below.

To find the value of x, we need to use the trigonometric ratios of a right triangle. We can choose any of the three ratios: sine, cosine, or tangent. In this case, we will use the tangent ratio, which is defined as $$\\tan \\theta = \\frac{\\text{opposite}}{\\text{adjacent}}$$ where $\\theta$ is an acute angle in a right triangle, opposite is the side opposite to $\\theta$, and adjacent is the side adjacent to $\\theta$.

In our diagram, we can label the sides as follows: opposite = AB, adjacent = BC, and hypotenuse = AC. Then we can write $$\\tan x = \\frac{\\text{AB}}{\\text{BC}}$$.

We know that AC = 8 cm and angle C = 90 degrees. We can use the Pythagorean theorem to find BC. The Pythagorean theorem states that $$\\text{hypotenuse}^2=\\text{opposite}^2+\\text{adjacent}^2$$ in a right triangle. Substituting the values, we get $$8^2=\\text{AB}^2+\\text{BC}^2$$.

Solving for BC, we get $$\\text{BC}=\\sqrt{64-\\text{AB}^2}$$.

Now we can substitute this value into the tangent equation and get $$\\tan x = \\frac{\\text{AB}}{\\sqrt{64-\\text{AB}^2}}$$.

To solve for x, we need to take the inverse tangent of both sides and get $$x=\\tan^{-1}\\left(\\frac{\\text{AB}}{\\sqrt{64-\\text{AB}^2}}\\right)$$.

This is an exact answer, but we can also use a calculator to find an approximate answer. If we assume that AB = 6 cm (which is not given in the question 061ffe29dd