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Home Question Bank Math Archive 2025 January 01

Math Questions from Jan 01,2025

Browse the Math Q&A Archive for Jan 01,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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5. Soive the 3 part Open Sentance \[ \begin{array}{l}11=3 x-7=29 \\ \text { Mark only one oval. } \\ \text { No Real Number Solutions } \\ \text { All Real Number Solutions } \\ x=72 \\ x=6,12 \\ x=1.33,7.33\end{array} \] \( \int \frac { d x } { x \sin ^ { 2 } ( x ) } \) 32. \( \sec \theta=-\frac{5}{4} \) and \( \sin \theta>0 \) [B] ABCD is a rhombus in which \( A(5,3), B(6,-2), C(1, m) \) Find the value of \( m \) ? ou are given that \( x=\left(2 x^{2}-x+8\right) y \) Show, by the method of complet- ing the square that \( \frac{(x-1+y)^{2}}{4 y}=\frac{1+2 y-63 y^{2}}{16 y^{2}} \) i) Find the values of \( y \) for which \( 1+2 y-63 y^{2} \geq 0 \). ii) Deduce the least and the greates possible values of the expression \( \frac{x}{2 x^{2}-x+8} \) for all real values of \( x \) Exercice \( \mathbb{Q} \) : Soient \( A B C \) un triangle et \( G=\operatorname{bar}\{(A ;-1) ;(B ;-4) ;(C ; 3)\} \). Soit \( I \) le barycentre des deux points pondérés \( (B ;-4) \) et \( (C ; 3) \). Soit \( K \) le barycentre des deux points pondérés \( (B ;-4) \) et \( (A ;-1) \) 1. Construire les points \( I, K \) et \( \mid G \). 2. Montrer que \( G \) est le milieu du segment \( [A I] \). 3. a- Montrer que \( : \overrightarrow{C G}=\frac{1}{2} \overrightarrow{C A}+2 \overrightarrow{C B} \) et \( \overrightarrow{C K}=\frac{1}{5} \overrightarrow{C A}+\frac{4}{5} \overrightarrow{C B} \). b- Déduire que les points \( C, K \) et \( G \) sont alignés. 4. On considère le point \( F \) tel que \( F= \) bar \( \{(A ;-1),(C ; 3)\} \). Montrer que \( G \in(B F) \). 5. En déduire que les droites \( (A I) ;(C K) \) et \( (B F) \) sont concourantes en un point qu'on déterminera. 6. Déterminer et construire l'ensemble des points \( M \) du plan tels que : \[ \overrightarrow{M A}+4 \overrightarrow{M B}-3 \overrightarrow{M C}\|=\|-\overrightarrow{M A}-4 \overrightarrow{M B} \| \text {. } \] \( \Rightarrow e ^ { x } x - e ^ { x } + 1 = 0 \) \( [3][\mathrm{A}] \) Find the value of \( X \) which satisfies that: \( 3 \tan X-4 \cos ^{2} 60=8 \operatorname{Sin}^{2} 30 \), where \( X \) is an acute angle Mathematics Crade 10 NSC Whelyear Examumexion FY QUESTION 4 \( f(x)=-2 x^{2}+2 \) and \( g(x)=2^{x}+1 \) are the defining equations of graphs of \( f \) and \( g \) respectively. 4.1 Write down an equation for the asymptote of \( g \). 4.2 Sketch the graphs of \( f \) and \( g \) on the same set of axes, clearly showing All intercepts with the axes, twaning points and 5 asymptotes. 4.3 Write down the range of \( f \). 4.4 Determine the maximum value of h if \( h(x)=3^{f(x)} \). 4.5 What transformation does the graph of \( y=f(x) \) undergo in orden to obtain graph of \( y=2 x^{2}-2 \) ? \( [B] \) If \( \overline{A B} \) is a diameter in the circle \( M \), If \( A(8, Y), B(X, 3) \), \( M(5,7) \) Find the value of \( X+Y \)
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