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January 21, 2025
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January 21 of 2025
1.2. ORDER 7. Prove the following inequalities: (a) \( 0<\frac{1}{2}<1 \), (b) \( 1<\frac{3}{2}<2 \),
Find the ratio of the velocities of two vehicles, one powered by a liquid-chemical rocket and the other by a solid-chemical one, when they are used for acceleration of a \( 8,838[\mathrm{~kg}] \) payload in a zero-gravity field. Both vehicles have a total initial mass of 455,556 [ kg\( ] \).…
Find the ratio of the velocities of two vehicles, one powered by a liquid-chemical rocket and the other by a solid-chemical one, when they are used for acceleration of a \( 8,869[\mathrm{~kg}] \) payload in a zero-gravity field. Both vehicles have a total initial mass of \(…
give me the solution to the entire question paper
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a) What is the magnitude of the maximum acceleration of the car during the 30 seconds ? b) Find the total distance travelled by the car during the 30 seconds
A box of mass 1.4 kg is held at rest on a rough plane. The plane is inclined at 30 degrees to the horizontal. The box is released from rest and moves 3.6 m during the first three seconds of its motion. a) Find the acceleration of the particle. ( 3 marks) b) Find the magnitude of the force…
\( A_{13}=\int^{\frac{1}{4}} \frac{x^{4}+1}{x^{6}+1} d x \)
A particle is projected with an initial speed \( \mathrm{u} \mathrm{m} / \mathrm{s} \) at an angle of \( 40^{\circ} \) above the horizontal. It lands at a point 10m vertically below its starting position. It takes 2 seconds to reach the highest point of its trajectory. a) Find u. (4 marks) b)…
Question A particle moves in a straight line and, at time t , has velocity \( \mathrm{v} \mathrm{ms}^{-1} \) with \[ v=4 t-12 e^{-t}(t \geq 0) \] a) i. Find an expression for the acceleration of the particle at time t . (2 marks) ii. State the range of values of the acceleration of the…
A ball is released from rest at a height of \( \mathrm{x} \mathbf{m} \) from the ground. It hits the ground \( \mathbf{2 . 2} \) seconds after it is released. Model the ball as a particle. a) Show that the speed of the ball when it hits the ground is \( 21.56 \mathrm{~m} / \mathrm{s} \). ( 2…
Kinematics in two dimensions Question 3 Question A quadrilateral has vertices with position vectors: \[ \begin{array}{l} \overrightarrow{\mathrm{OA}}=-2 \mathbf{i}-\mathbf{j}+4 \mathbf{k} \\ \overrightarrow{\mathrm{OB}}=4 \mathbf{i}+2 \mathbf{j}+\mathbf{k}…
b \( \left(\frac{5}{10} \times 10\right)+15+\left(\frac{3}{5} \times 25\right)=35 \) passengers.
List the elements in {a,b,c} x {1,2,c}
Describe the set by listings its elements {m E Z | m*n = 60 for some n E Z}
Describe the set by listing its elements {m E Z | m^2 + m = 6}
ex. (1) Let \( X\{2, a, b, c\} \) and \( T=\{X, \phi,\{a\},\{a, b\}\} \) lot \( A= \) tanc\} Pind eook of the filluwn sots. \[ \begin{array}{l} A=A^{\prime} \quad B \quad A \cup A^{\prime} \\ C=\bar{A} \end{array} \] (2) let \( A=[0,0] \quad \cup[1,2] \quad \in\left(R_{T} U\right) \) find the…
Describe the set by listing its elements {x E R | x^2 = 3}
question 1 of is e Matmillar \( \square \) What is the Nhationting between these povis"