Quiz 1:   Fullscreen Mode Theory of Moments Theory of Moments What is a Moment? The moment of a force is the turning effect produced by a force acting at a distance from a pivot or fulcrum. It depends on: The magnitude of the force (\(F\)) The perpendicular distance (\(d\)) from the line of action of the force to the pivot The formula for calculating the moment is: Moment (\(M\)) = Force (\(F\)) × Perpendicular Distance (\(d\)) Unit: Newton meter (Nm) Law of Moments The law of moments states that for a system in equilibrium: Sum of Clockwise Moments = Sum of Anticlockwise Moments This means there is no net turning effect on the body. Conditions for Equilibrium A body is in equilibrium when: The sum of all forces acting on it is zero (no net force). The sum of all moments about any point is zero (no net moment). Examples and Applications Example 1: Balanci...

Quiz 1   Fullscreen Mode Direct and Inverse Proportions Direct Proportion Two quantities x and y are in direct proportion when they increase or decrease in the same ratio, written as: \[ x \propto y \] \[ \frac{x}{y} = k \] where k is the constant of proportionality Properties of Direct Proportion If x increases, y increases in the same ratio If x decreases, y decreases in the same ratio The ratio x/y remains constant Inverse Proportion Two quantities x and y are in inverse proportion when one increases as the other decreases in the same ratio, written as: \[ x \propto \frac{1}{y} \] \[ xy = k \] where k is the constant of proportionality Applications and Examples Direct Proportion Examples 1. Distance and Time (Uniform Speed): Speed = 75 km/hour Distance in 20 minutes = (75 × 20)/60 = 25 km 2. Cost and Quantity: 5 meters cloth = ₹210 13 meters cloth = (210 × 13)/5 = ₹546 Inverse Proportion Examples 1. Wo...

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Quadratic Functions and Their Graphs A quadratic function is a polynomial function of degree 2, typically written in the form: $$f(x) = ax^2 + bx + c$$ where a, b, and c are constants and a ≠ 0. Important Properties of Quadratic Function Graphs Y-Intercept: The point where the parabola crosses the y-axis (0, c) X-Intercepts: Also known as zeros, roots, or solutions - points where the parabola crosses the x-axis Vertex: The highest or lowest point of the parabola Axis of Symmetry: A vertical line that passes through the vertex, dividing the parabola into two symmetrical halves Forms of Quadratic Functions 1. Standard Form $$f(x) = ax^2 + bx + c$$ To find the axis of symmetry: $$x = -\frac{b}{2a}$$ 2. Vertex Form $$f(x) = a(x - h)^2 + k$$ Where (h, k) is the vertex of the parabola Characteristics of Parabolas If a > 0, the parabola opens upward (U-shaped) If a The larger the absolute value of a, the narrower the parabola...

Review Chapter 2-4 Chapter 2 Given that y is an integer, -3 < y ≤ 2.7, and y ≠ 0, write down all the possible values of y . It is given that z ≥ 41.5. Write down the least possible value of z if z is: an integer a prime number a perfect square Suggest a possible value of z for which z is a factor of 1260 and z is an even number. Solve the inequality 7 - (1/3) x ≥ 5 and represent the solution on a number line. A smartphone costs $750. Form an inequality and solve it to find the maximum number of smartphones that a company can buy with a budget of $25,000. Consecutive Even Numbers: Let the numbers be z , z +2, z +4. If the inequality z +( z +2)+( z +4)>120 is given, find the smallest even number z that satisfies this condition and calculate the product of t...

Understanding Kinetic, Potential, and Mechanical Energy: A Comprehensive Guide Understanding Kinetic, Potential, and Mechanical Energy: A Comprehensive Guide Energy is a fundamental concept in physics, playing a crucial role in understanding how objects move and interact. In this comprehensive guide, we'll explore three important types of energy: kinetic energy, potential energy, and mechanical energy. We'll dive into their definitions, formulas, and real-world applications, complete with illustrative examples and practice problems. 1. Kinetic Energy Kinetic energy is the energy possessed by an object due to its motion. It depends on both the object's mass and its velocity. Formula: KE = ½ mv² Where: KE = Kinetic Energy (measured in Joules, J) m = mass of the object (in kilograms, kg) v = velocity of the object (in meters per second, m/s) ...

Mastering Quadratic Functions: A Comprehensive Guide to Graphs and Properties Mastering Quadratic Functions: A Comprehensive Guide to Graphs and Properties Welcome to our in-depth exploration of quadratic functions and their graphs! Whether you're a student looking to ace your next math test or an enthusiast wanting to deepen your understanding, this guide will walk you through the essential concepts, properties, and applications of quadratic functions. 1. Introduction to Quadratic Functions A quadratic function is a polynomial function of degree 2, typically written in the form: f(x) = ax² + bx + c Where 'a', 'b', and 'c' are constants, and 'a' ≠ 0. The graph of a quadratic function is called a parabola, which has a distinctive U-shape (or inverted U-shape if 'a' is negative). ...

Factoring Quadratic Equations Factoring quadratic equations is a method to express a quadratic expression in the form $$ax^2 + bx + c$$ as a product of its linear factors $$(x - r_1)(x - r_2)$$, where $$r_1$$ and $$r_2$$ are the roots of the equation. Steps for Factoring Quadratic Equations: Identify the coefficients $$a$$, $$b$$, and $$c$$ in the quadratic equation $$ax^2 + bx + c = 0$$. Find two numbers $$p$$ and $$q$$ such that: $$p + q = b$$ $$pq = ac$$ Rewrite the middle term using $$p$$ and $$q$$: $$ax^2 + px + qx + c$$ Group the terms and factor out common factors: $$ax^2 + px + qx + c = (ax^2 + px) + (qx + c) = x(ax + p) + 1(qx + c)$$ Factor out the greatest common factor: $$(x(ax + p) + 1(qx + c)) = (x + \frac{c}{q})(ax + p)$$ Example: Factor the quadratic equation: $$x^2 + 7x + 12 = 0$$ Solution: Identify $$a=1$$, $$b=7$$, and $$c=12$$ Find $$p$$ and $$q$$: $$3 + 4 = 7$$ and $$3 \times 4 = 12$$ Rewrite: $$x^2 + 3x + 4x + 12$$ Group and factor: $$(x^2 + 3...

Quiz 1   Fullscreen Mode

Quiz 1   Fullscreen Mode

Quiz 1   Fullscreen Mode

Quiz 1:   Fullscreen Mode   Acceleration Formula:

Quiz 1   Fullscreen Mode

Quiz 1   Fullscreen Mode

Quiz 1   Fullscreen Mode

Quiz 1   Fullscreen Mode

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