Math

Problem 66001

Determine if the following line pairs are parallel, perpendicular, or neither:
Line 1: $y=-\frac{2}{3} x-8$ , Line 2: $6 x-4 y=-6$ , Line 3: $3 y=-2 x+2$ .

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Problem 66002

Simplify the expression: $5(b^{-3})^{4}$ and expand it to include only positive exponents.

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Problem 66003

Find the limit as $x$ approaches 2 for the expression $\frac{x^{2}+x-6}{x^{2}-4}$ .

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Problem 66004

Simplify the expression: $-3(8mn^{2})^{0}$ and express with positive exponents.

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Problem 66005

1. The net ionic equation for the reaction between sodium thiosulphate and hydrochloric acid is given as $\mathrm{S}_{2} \mathrm{O}_{3}^{2-}(\mathrm{aq})+2 \mathrm{H}^{+}(\mathrm{aq}) \longrightarrow \mathrm{S}(\mathrm{~s})+\mathrm{SO}_{2}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l})$
To prove that this reaction follows first order kinetics, a student varied the concentration of $\mathrm{S}_{2} \mathrm{O}_{3}{ }^{2-}$ while keeping that of $\mathrm{H}^{+}$ constant $(10 \mathrm{~mL}$ of 2 M HCl $)$ and observed the rate of appearance of $\mathrm{S}(\mathrm{s})$ with time. Starting with 50 mL of $0.15 \mathrm{M} \mathrm{S}_{2} \mathrm{O}_{3}{ }^{2-}$ , he generated the results shown in table 1 .
Table 1: Results for the clock reaction between $\mathrm{S}_{2} \mathrm{O}_{3}{ }^{2-}$ and $\mathrm{H}^{+}$ \begin{tabular}{|l|l|l|l|l|} \hline Beaker & Vol. $\mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3} / \mathrm{mL}$ & Vol. $\mathrm{H}_{2} \mathrm{O} / \mathrm{mL}$ & { $\left[\mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}\right] / \mathrm{M}$ } & Time/s \\ \hline A & 50.0 & 0.0 & 0.15 & 22.5 \\ \hline B & 40.0 & 10.0 & & 27.3 \\ \hline C & 30.0 & 20.0 & & 35.1 \\ \hline D & 40.0 & 30.0 & & 60.0 \\ \hline E & 10.0 & 40.0 & & 159.1 \\ \hline \end{tabular} a) Copy and complete table 1. b) Plot a graph of $\ln \left[\mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}\right]$ (M) against time (s).

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Problem 66006

Section C(One Questions) (15 Marks) Let the rate of increase of bacteria is proportional to its size it is found that a culture of 300 bacteria has increased to 6 hundrod affer 90 minutes. (a) Express the population after $t$ hours as a function of $f$ . (b) How many bacteria are there in 5 hours? (c) How many hours and minutes will it take the culture to reach 20,000 bacteria. ( 3 marks

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Problem 66007

4. Evaluale mathematically $\lim _{x \rightarrow 0} \frac{x}{\sqrt{x+4-2}}$

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Math

Problem 66001

Determine if the following line pairs are parallel, perpendicular, or neither:
Line 1: $y=-\frac{2}{3} x-8$ , Line 2: $6 x-4 y=-6$ , Line 3: $3 y=-2 x+2$ .

Problem 66002

Simplify the expression: $5(b^{-3})^{4}$ and expand it to include only positive exponents.

Problem 66003

Find the limit as $x$ approaches 2 for the expression $\frac{x^{2}+x-6}{x^{2}-4}$ .

Problem 66004

Simplify the expression: $-3(8mn^{2})^{0}$ and express with positive exponents.

Problem 66005

Problem 66006

Problem 66007

4. Evaluale mathematically $\lim _{x \rightarrow 0} \frac{x}{\sqrt{x+4-2}}$

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Math

Problem 66001

Determine if the following line pairs are parallel, perpendicular, or neither: Line 1: y=−23x−8y=-\frac{2}{3} x-8y=−32​x−8, Line 2: 6x−4y=−66 x-4 y=-66x−4y=−6, Line 3: 3y=−2x+23 y=-2 x+23y=−2x+2.

Problem 66002

Simplify the expression: 5(b−3)45(b^{-3})^{4}5(b−3)4 and expand it to include only positive exponents.

Problem 66003

Find the limit as xxx approaches 2 for the expression x2+x−6x2−4\frac{x^{2}+x-6}{x^{2}-4}x2−4x2+x−6​.

Problem 66004

Simplify the expression: −3(8mn2)0-3(8mn^{2})^{0}−3(8mn2)0 and express with positive exponents.

Problem 66005

Problem 66006

Problem 66007

4. Evaluale mathematically lim⁡x→0xx+4−2\lim _{x \rightarrow 0} \frac{x}{\sqrt{x+4-2}}limx→0​x+4−2​x​

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Determine if the following line pairs are parallel, perpendicular, or neither:
Line 1: $y=-\frac{2}{3} x-8$ , Line 2: $6 x-4 y=-6$ , Line 3: $3 y=-2 x+2$ .

Simplify the expression: $5(b^{-3})^{4}$ and expand it to include only positive exponents.

Find the limit as $x$ approaches 2 for the expression $\frac{x^{2}+x-6}{x^{2}-4}$ .

Simplify the expression: $-3(8mn^{2})^{0}$ and express with positive exponents.

4. Evaluale mathematically $\lim _{x \rightarrow 0} \frac{x}{\sqrt{x+4-2}}$