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Saudi Arabia
Evaluate \( x^{2}-(x y-y) \) for \( x \) satisfying \( \frac{4(x+4)}{7}=2 x+8 \) and \( y \) satisfying \( -5 y-9=3 y+15 \)
Algebra Jan 30, 2025
b. \( 5(x-4)-(2 x-6)=5(x-4) \)
Algebra Jan 30, 2025
16) The radius and height of a cylinder are in the ratio \( 5: 7 \), and its volume is \( 550 \mathrm{in}^{3} \) What is the radius of the cylinder, in inches? A. \( \sqrt{5} \) B. \( \sqrt{7} \) C. 5 D. 7
Geometry Jan 29, 2025
Q2-Evaluate the integrals: (a) \( \int \sin ^{11} x \cdot \cos ^{5} x \cdot d x \)
Calculus Jan 29, 2025
A particle \( P \) moves in a straight line. It starts at a point \( O \) on the line and at time \( t \) after leaving \( O \) it has a velocity \( v=6t^{2}-30t+24 \). i) Find the set of values of \( t \) for which the acceleration of the particle is negative. \ii) Find the distance between the two positions at which \( P \) is at instantaneous rest. \iii) Find the two positive values of \( t \) at which \( P \) passes through \( O \).
Calculus Jan 29, 2025
A vehicle is moving in a straight line. The velocity \( v \mathrm{~m}^{-1} \) at time \( t \) s after the vehicle starts is given by \( v=A\left(t-0.05 t^{2}\right) \) for \( 0 \approx t \approx 15 \) and \( v=\frac{B}{t^{2}} \) for \( t \geqslant 15 \), where \( A \) and \( B \) are constants. The distance travelled by the vehicle between \( t=0 \) and \( t=15 \) is 225 m. i) Find the value of \( A \) and show that \( B=3375 \). \ii) Find an expression in terms of \( t \) for the total distance travelled by the vehicle when \( t \geqslant 15 \). \iii) Find the speed of the vehicle when it has travelled a total distance of 315 m.
Calculus Jan 29, 2025
Two particles \( A \) and \( R \) start to move at the same instant from a point \( O \). The particles move in the same direction along the same straight line. The acceleration of \( A \) at time \( t \) s after starting to move is \( a \mathrm{~ms} \mathbf{s}^{-2} \), where \( a=0.05-0.0002t \). i) Find \( A^{\text{'} } \) s velocity when \( t=200 \) and when \( t=500 \). \ii) Find the distance between \( A \) and \( B \) when \( t=500 \).
Physics Jan 29, 2025
21. \( \left(\frac{3}{5}+\frac{1}{4}\right) \times \frac{2}{3} \)
Arithmetic Jan 29, 2025
2. You know that \( \frac{1}{7}=0 . \overline{142857} \). Can you predict what the decimal expansions of \( \frac{2}{7}, \frac{3}{7} \) ratio \( \frac{4}{7}, \frac{5}{7}, \frac{6}{7} \) are, without actually doing the long division? If so, how? [Hint : Study the remainders while finding the value of \( \frac{1}{7} \) carefully.]
Arithmetic Jan 29, 2025
EXERCISE 1.3 1. Write the following in decimal form and say what kind of decimal expansion ead multiplication has: \( \begin{array}{llll}\text { (i) } \frac{36}{100} & \text { (ii) } \frac{1}{11} & \text { (iii) } 4 \frac{1}{8} & \text { commutative, } \\ \begin{array}{llll}\text { (iv) } \frac{3}{13} & \text { (v) } \frac{2}{11} & \text { (vi) } \frac{329}{400} & \text { irrational. }\end{array}\end{array} \begin{array}{l}\text { number (that i }\end{array} \)
Arithmetic Jan 29, 2025
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