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Kenya
If \( a \) and \( b \) are linearly independent and \( p a-(p+q-1) b=0 \) then find \( p, q \)
Algebra Dec 09, 2024
c) Differentiate the implicit function \( y+x y+y^{2}=2 \quad \) (2 Marks) 4. a) Find the points on \( y=x^{4}+4 x^{3}-6 \) at which the gradient is 0 and determine the nature of these points. (8 Marks)
Calculus Dec 09, 2024
\( \begin{array}{l}\text { Let } x, y \text { be orhogonal vectors in a } \\ \text { vector space } \mathrm{V} \text { and }\end{array} \) \( \|x\|=\sqrt{5},\|y\|=\sqrt{7} \) Evaluate \( \|2 x-y\| \)
Pre Calculus Dec 09, 2024
The vectors \( \mathrm{u}, \mathrm{v}, \mathrm{w} \) are linearly independent in a vector space V and suppose that the statement below is true; \( (1+\alpha-\beta) u+\beta v=2 \delta w+v \) Find the value of \( \alpha, \beta, \delta \) Select one:
Algebra Dec 09, 2024
Solve the Matrix equation \( \mathrm{AX}=\mathrm{B} \) where \[ A=\left[\begin{array}{ll}1 & 2 \\ 4 & 3\end{array}\right], B=\left[\begin{array}{cc}0 & 5 \\ -5 & 10\end{array}\right] \]
Algebra Dec 09, 2024
6. Given that \( \cos (2 x+35)^{\circ}=\sin (3 x-10)^{\circ} \) a) Solve for x \( \left.\begin{array}{l}\frac{2 x+35^{\circ}+3 x-10^{\circ}}{}=90 \\ 5 x+25^{\circ}=90-25\end{array} \right\rvert\, \frac{\frac{5 x}{8}=}{x=13} \) b) Hence find \( \tan (2 x+4) \) without tables or calculators. \( (13 \times 2)+4 \) \( 26+4=30 \)
Trigonometry Dec 09, 2024
folve the equation \( 1+\log (2 x-9)=\log (3 x+5)-\log 2 \). 27. COMMERCIAI ARITHMETIC (II)
Algebra Dec 09, 2024
Find the equation of the tangent to the curve \( x^{2}-y^{2}=7 \) at e) 4 Marks) point \( (4,3) \) f) \( \quad \) Differentiate \( y=x \sin ^{-1} x \) with respect to \( x \quad \)
Calculus Dec 09, 2024
5. From a point 20 m away on a level ground the angle of elevation to the bottom of window is \( 27^{\circ} \) and the angle of elevation of the top of the window is \( 32^{\circ} \). Calcula height of the window. (3 marks) \( \begin{array}{l}\operatorname{sinc}\left(v 6=\left(63^{\circ}\right)=B \mathrm{C} / \sin \left(2 t^{\circ}\right)\right. \\ 20^{x} \sin \left(27^{\circ} / \sin (3=10.2 \mathrm{~m}\right. \\ 180-90-32=580 \\ \sin \frac{50}{32}\end{array} \)
Trigonometry Dec 09, 2024
Evaluate \( \int\left(2 x^{3}+1\right)^{7} x^{2} d x \)
Calculus Dec 09, 2024
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