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Egypt
If the force \( \overrightarrow{\mathrm{F}_{1}}=(3,-1) \) acts at the point \( \mathrm{A}(1,2), \overrightarrow{\mathrm{F}_{2}} \) acts at the point \( \mathrm{B}(-1,1) \) and the two forces form a couple, then the algebraic measure of the moment of the couple \( = \) \( \qquad \) moment unit. (a) 5 (b) 2 (c) -5 (d) -2 In the opposite figure : A fine lamina of a uniform thickness and density in the form of a right-angled triangle at B and of weight \( 30 \mathrm{~kg} . \mathrm{wt} \). where \( \mathrm{AB}=9 \mathrm{~cm} ., \mathrm{BC}=6 \mathrm{~cm} \). the lamina is suspended in a pin at a small hole near to the vertex \( B \), a couple in its plane acted on it to make it in equilibrium when \( \overline{\mathrm{AB}} \) is horizontal, then the algebraic measure of the moment of the couple \( = \) \( \qquad \) kg.wt.cm. (a) 135 (b) -90 (c) -135 (d) 90
Physics Jan 21, 2025
D \( \overline{\mathrm{AB}} \) is a uniform rod of length 80 cm . and weight 20 newton acts at its midpoint. If the rod rests horizontally on two supports one of them at a distant 20 cm . from \( A \) and the other at a distant 10 cm . from B , find the magnitude of the pressure on each support. What is the magnitude of the weight that must be suspended from the end B so that the rod is about to rotate? What is the magnitude of the pressure on the support near B then? Three vertical like forces of magnitudes \( 10,14,18 \) newton act at the points \( \mathrm{A}, \mathrm{B}, \mathrm{C} \) respectively such that \( \mathrm{B} \in \overline{\mathrm{AC}}, \mathrm{AB}=60 \mathrm{~cm} ., \mathrm{BC}=80 \mathrm{~cm} \). Find the resultant of this system of forces.
Physics Jan 21, 2025
If \( \overrightarrow{\mathrm{F}}_{1}, \overrightarrow{\mathrm{~F}}_{2} \) are two unlike parallel forces act at the two points \( \mathrm{A}, \mathrm{B} \) respectively such that \( \mathrm{AB}=12.5 \mathrm{~cm},, \mathrm{~F}_{1}=80 \) dyne, \( \mathrm{F}_{2}=30 \) dyne, find the resultant of the two forces. ABCD is a rectangle in which \( \mathrm{AB}=30 \mathrm{~cm}, \mathrm{BC}=40 \mathrm{~cm} \). forces of magnitudes 15,30 , 15,30 gm.wt. act along \( \overrightarrow{\mathrm{BA}}, \overrightarrow{\mathrm{BC}}, \overrightarrow{\mathrm{DC}}, \overrightarrow{\mathrm{DA}} \) respectively. Prove that this system of forces is equivalent to a couple and find the magnitude of its moment , then find two forces acting at A and C perpendicular to \( \overrightarrow{\mathrm{AC}} \) such that the system is in equilibrium.
Physics Jan 21, 2025
b) Find the equation of the straight line which makes with the positive direction of \( X \)-axis appositive angle of measure \( 135^{\circ} \) and intercepts from the positive part of \( y \)-axis apart of length 5 length units.
Geometry Jan 21, 2025
4. \( 3,736 \div 3=r \)
Arithmetic Jan 21, 2025
3. \( 2,999 \div 9=q \) \( q= \)
Arithmetic Jan 21, 2025
1. \( 451 \div 7=p \)
Arithmetic Jan 21, 2025
Solve these simultaneous equations. i \( y=3 x+1 \) and \( 5 x=y+3 \) ii \( x=4 y-2 \) and \( y+x=8 \)
Algebra Jan 21, 2025
\( y ^ { \prime } + y \tan x = y ^ { 3 } \sec ^ { 4 } \)
Calculus Jan 21, 2025
Omari buys a house for \( £ 190,000 \). The value of the house appreciates by \( 5.1 \% \) every year. How much is the house worth after 6 years? Round your answer to the nearest penny.
Arithmetic Jan 21, 2025
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