In a theater, there are 15 chairs in the first row, each row has 3 more chairs than the previous row, and there are 15 rows. how
1 answer:
The 1st row has 15 chairs.
The 2nd row has 15 + 3 = 18 chairs.
The 3rd row has 18 + 3 = 15 + 2•3 = 21 chairs.
The 4th row has 21 + 3 = 15 + 3•3 = 24 chairs.
The pattern continues, so that the n-th row has 15 + (n - 1)•3 = 3n + 12 chairs.
If there are 15 rows, then the total number of chairs is
where we use the formulas
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The acceleration of the pendulum mass D is; r"_d = [x''(t) + lθ'' cos θ - lθ'² sin θ]i - l[θ'' sin θ - θ'² cos θ]j
<h3>What is Kinematics of particles?</h3>Kinematics is the study of the geometry of motion of particles, rigid bodies, etc., disregarding the forces associated with these motions. However, Kinematics of a particle is the motion of a point in space.
From the sample problem, we can solve it using the (x, y, z) coordinate system to get;
r_c = x(t) i
r_d = [x(t) + l sin θ]i + l cos θ j
Finding the first derivative of r_d gives velocity as;
r'_d = [x'(t) + lθ' cos θ]i - lθ' sin θ j
Taking the second derivative of r_d gives the acceleration as;
r"_d = [x''(t) + lθ'' cos θ - lθ'² sin θ]i - l[θ'' sin θ - θ'² cos θ]j
A sample problem of kinematics of particles is;
A block C slides along the horizontal rod, while a pendulum attached to the block can swing in the vertical plane. Find the acceleration of
the pendulum mass D.
Read more about Kinematics of Particles at; brainly.com/question/26269548
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