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\end{tabular} Part V Evaluate the following integral. (5 scores per question. The total is 10 scores.) 17. ∫12(x3)dx.
Score
Part VI Solve the following questions. (4 scores per question. The total is 8 scores.) 19. Consider y=31x3−x+1 on the interval [0,3], find the absolute maximum and minimum values of y .
\begin{tabular}{|l|}
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\end{tabular} Part V Evaluate the following integral. (5 scores per question. The total is 10 scores.) 18. ∫−11(e2x−2+x1)dx.
EXERCICE 1:
le plan est rapporté a un repère orthonormé (o;i;j). 1. Donner une représentation paramétrique de la droite (D) passant par le point A(2;−1) et de vecteur directeur u(2;1). 2. Donner une équation cartésienne de la droite (Δ) passant par le point B(−1;1) et de vecteur directeur vˉ(1;3). 3. Soit (D′) la droite définie par sa représentation paramétrique (D′):{x=2−ty=2+2t,(t∈R), et ( Δ′) la droite définie par l'équation cartésienne (Δ′):x−y−3=0.
a- le point E(1;4) est-il un point de la droite (D′) ?
b-monter que (D′) et ( Δ′) sont sécantes.
c-déterminer les coordonnées du point I, point d'intersection de ( D′ ) et ( Δ′ ). 4. a-déterminer une équation cartésienne de la droite (D1) qui passe par le point A′(2;3) et parallèle à la droite ( Δ′ ).
b-déterminer une équation cartésienne de la droite (Δ1) qui passe par le point A′(2;3) et parallèle à l'axe des abscisses. 5. Construire dans le repère (0,i,j) les droites (D′),(Δ′) et (Δ1).
2. In an experiment to determine the water hardness of tap water, a researcher measured three 50 mL aliquots of water samples and to each sample he added 10 mL of pH 10 ammonia/ammonium chloride buffer and two drops of eriochrome black T indicator and the colour changed to wine red. The resulting solutions were then separately titrated against 0.05 M sodium-EDTA solution from the burette until a final endpoint colour change. The data obtained was recorded in a table as shown below.
\begin{tabular}{|l|l|l|l|}
\hline Titration & 1 & 2 & 3 \\
\hline final reading /mL & 10.70 & 10.65 & 10.60 \\
\hline Initial reading /mL & 0.00 & 0.00 & 0.00 \\
\hline Titre value /mL & & & \\
\hline
\end{tabular}
a) What is the expected endpoint colour change?
b) Calculate the average titre of the results?
c) Write a balance equation of reaction between calcium ions and EDTA
d) Calculate the number of moles of EDTA used in each titration and the average number of moles for the whole process.
e) What is the concentration of Ca2+ (expressed as ppmCaCO3 ) in the sample?
An aircraft is climbing at a 30 degree angle to the horizontal. How fast is the aircraft gaining altitude if its speed is 500mi/hr ? Express your answer as mi/hr and round it into the nearest whole number. Input only the numerical value of the answer without the unit.
Which statement describes how the graph of a function, h(x), and its inverse, h−1(x), are related?
The line y=−x is the perpendicular bisector of each segment connecting a point on h(x) to the corresponding point on h−1(x).
The line y=x is the perpendicular bisector of each segment connecting a point on h(x) to the corresponding point on h−1(x).
The graph of the inverse of h(x) is a reflection over the line y=0 of the graph of h(x).
The y-axis is the perpendicular bisector of each segment connecting a point on h(x) to the corresponding point on h−1(x).