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P = 2x+2(450-x)=900
A = x(450 - x)
A = x(450 - x)
-x² + 450x = A
-x² +450x = A
A is going to be maximum, when x is a vertex.
-(x² - 450x) = A
-(x² - 2*225x+225²) - 225² =A
-(x-225)² -225² = A
Vertex when x=225
Largest are 225(450-225) = 225² = 50625 ft²
The square has a largest area.
A = x(450 - x)
A = x(450 - x)
-x² + 450x = A
-x² +450x = A
A is going to be maximum, when x is a vertex.
-(x² - 450x) = A
-(x² - 2*225x+225²) - 225² =A
-(x-225)² -225² = A
Vertex when x=225
Largest are 225(450-225) = 225² = 50625 ft²
The square has a largest area.
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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