Math

Problem 66101

Simplify: a. $5x - 2 - 3x$ ; b. $5x - (2 - 3x)$ . What are the simplified forms?

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Problem 66102

Simplify the expression: -5(2 x-4) + 11 x - 10 = ?

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Problem 66103

Find the equations of the line perpendicular and parallel to $y=-\frac{9}{8} x+1$ through the point $(8,-3)$ .

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Problem 66104

Determine if the lines $8 x+6 y=8$ , $4 y=-3 x+5$ , and $y=-\frac{3}{4} x+7$ are parallel, perpendicular, or neither.

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Problem 66105

The integral that represents the area of the region enclosed by $f(x)=x^{3}-x$ and the $x$ -axis is $\int_{0}^{1}\left(x^{3}-x\right) d x$ $\int_{-1}^{1}\left(x-x^{3}\right) d x$ $\int_{-1}^{1}\left(x^{3}-x\right) d x$ $2 \int_{0}^{1}\left(x-x^{3}\right) d x$

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Problem 66106

3. Multiply: (a) $3.2 \times 6$ (b) $2.85 \times 8$ (c) $7.49 \times 23$ (e) $0.426 \times 23$ (e) $5.82 \times 2.5$ (g) $1.026 \times 1000$ (4) $0.008 \times 1000$ (1) $1.832 \times 17.35$ (k) $0.057 \times 0.06$ (h) $16.92 \times 105.4$ (a) If a bag of paddy weighs 75.25 kg , what is the weight of 150 bags? (b) 1.25 m of cloth is required to make 1 shirt. What is the length of cloth requir make 8 shirts?

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Problem 66107

9. ${ }^{7}$ (a) If the two angles of a triangle are $50^{\circ}$ and $75^{\circ}$ , find the third ang. b) If $2 x^{\circ}, 4 x^{\circ}$ and $6 x^{\circ}$ are the three angles of a triangle, find the valuer is find the angles. (c) If the three angles of a triangle are $x^{\circ},(x+20)^{\circ}$ and $(x-50)^{\circ}$ , find x . Also, find the angles. (d) If the two opposite interior angles of a triangle are $30^{\circ}$ and $55^{\circ}$ exterior angle of a triangle.
10. त(3) In a right angled triangle, one acute angle is $40^{\circ}$ . Find the other atexes that triangle. (b) In an equilateral triangle, one angle is $60^{\circ}$ . Find the remaining anglo (c) In an isosceles triangle, one base angle is $45^{\circ}$ . Find the another bases
स'(d) If one angle of an isosceles triangle is equal to the sum of remaining angles, find the size of each angle.
11. (a) In a $\triangle A B C, \angle A=\angle B=65^{\circ}$ , find $\angle C$ .

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Problem 66108

Attempt All Questions
1. Dichromate ion $\left(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}\right)$ in acidic solution is a good oxidizing agent. Which of the following oxidations can be accomplished with dichromate ion in acidic solution? Explain a. $\mathrm{Sn}^{2+}(\mathrm{aq})$ to $\mathrm{Sn}^{4+}(\mathrm{aq})$ b. $\mathrm{Ag}(\mathrm{s})$ to $\mathrm{Ag}^{+}(\mathrm{aq})$
2. For each of the following cell diagrams a. $\operatorname{Pt}(\mathrm{s})\left|\mathrm{Fe}^{2+}(\mathrm{aq}), \mathrm{Fe}^{3+}(\mathrm{aq}) \|\left|\mathrm{Ag}^{+}(\mathrm{aq})\right| \mathrm{Ag}(\mathrm{s})\right.$ b. $\mathrm{Pt}(\mathrm{s})\left|\mathrm{Mn}^{2+}(\mathrm{aq}), \mathrm{MnO}_{4}^{-}(\mathrm{aq})\right|\left|\mathrm{Cu}^{2+}(\mathrm{aq})\right| \mathrm{Cu}(\mathrm{s})$ i. calculate the $E_{\text {cell }}^{o}$ ii. what is the change in Gibbs free energy? iii. is the cell reaction spontaneous or nonspontaneous? Explain.
3. Will the following reaction $\mathrm{Cr}_{2} \mathrm{O}_{7}^{2 \cdot}(\mathrm{aq})+14 \mathrm{H}^{+}+6 \mathrm{Ag}(\mathrm{~s}) \longrightarrow 2 \mathrm{Cr}^{3+}(\mathrm{aq})+6 \mathrm{Ag}^{+}(\mathrm{aq})+7 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) E_{\text {cell }}=-0.023 \mathrm{~V}$ be spontaneous if $\left[\mathrm{Cr}_{2} \mathrm{O}_{7}{ }^{2-}\right]=[\mathrm{Ag}+]=0.675 \mathrm{M},\left[\mathrm{Cr}^{3+}\right]=0.6 \mathrm{M}$ and $\mathrm{pH}=2$ ? Explain.
4. Define the following terms a) Oxidation b) Oxidizing agent c) Salt bridge d) Liquid junction e) Standard electrode potential

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Problem 66109

1. What is hydrodynamic voltammetry? State two (2) applications of voltammetry.
2. What is the potential of a cell consisting of a silver electrode dipped in silver nitrate solution with $[\mathrm{Ag}+]=0.01 \mathrm{M}$ and a standard calomel reference electrode $\left(\mathrm{E}_{\mathrm{ref}}=+0.242\right.$ V). Neglect liquid-junction potential.
3. Briefly describe a simple electrochemical cell used in potentiometric analysis. Write a cell diagram for this cell.
4. Calculate the ionic strengths of the following solutions A) 0.20 M NaCl and $0.30 \mathrm{M} \mathrm{Na}_{2} \mathrm{SO}_{4}$ B) $0.1 \mathrm{M} \mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}$

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Problem 66110

5. Calculate the activity coefficients of sodium and chloride ions for a 0.04 M NaCl solution
6. What is an electrode of the first kind? Write a general Nernst equation for this indicator electrode.
7. A solution of $0.25 \mathrm{M} \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}$ and $0.35 \mathrm{M} \mathrm{Cr}^{3+}$ has a pH of 2.0 . What is the $\mathrm{E}_{\text {cell }}$ of this half-cell?
8. In an acidic solution, $\mathrm{O}_{2}(\mathrm{~g})$ oxidizes $\mathrm{Cr}^{2+}(\mathrm{aq})$ to $\mathrm{Cr}^{3+}(\mathrm{aq})$ . The $\mathrm{O}_{2}(\mathrm{~g})$ is reduced to $\mathrm{H}_{2} \mathrm{O}(\mathrm{l})$ . $E_{\text {cell }}^{o}$ for this reaction is +1.653 V . What is the electrode potential for the $\mathrm{Cr}^{3+} / \mathrm{Cr}^{2+}$ half-cell?

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Problem 66111

5. Calculate the activity coefficients of sodium and chloride ions for a 0.04 M NaCl solution
6. What is an electrode of the first kind? Write a general Nernst equation for this indicator electrode.
7. A solution of $0.25 \mathrm{M} \mathrm{Cr}_{2} \mathrm{O}_{7}{ }^{2-}$ and $0.35 \mathrm{M} \mathrm{Cr}^{3+}$ has a pH of 2.0 . What is the $\mathrm{E}_{\text {cell }}$ of this half-cell?

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Problem 66112

6. What is an electrode of the first kind? Write a general Nernst equation for this indicator electrode.
7. A solution of $0.25 \mathrm{M} \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}$ and $0.35 \mathrm{M} \mathrm{Cr}^{3+}$ has a pH of 2.0 . What is the $\mathrm{E}_{\text {cell }}$ of this halfcell?

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Math

Problem 66101

Simplify: a. $5x - 2 - 3x$ ; b. $5x - (2 - 3x)$ . What are the simplified forms?

Problem 66102

Simplify the expression: -5(2 x-4) + 11 x - 10 = ?

Problem 66103

Find the equations of the line perpendicular and parallel to $y=-\frac{9}{8} x+1$ through the point $(8,-3)$ .

Problem 66104

Determine if the lines $8 x+6 y=8$ , $4 y=-3 x+5$ , and $y=-\frac{3}{4} x+7$ are parallel, perpendicular, or neither.

Problem 66105

The integral that represents the area of the region enclosed by $f(x)=x^{3}-x$ and the $x$ -axis is $\int_{0}^{1}\left(x^{3}-x\right) d x$ $\int_{-1}^{1}\left(x-x^{3}\right) d x$ $\int_{-1}^{1}\left(x^{3}-x\right) d x$ $2 \int_{0}^{1}\left(x-x^{3}\right) d x$

Problem 66106

Problem 66107

Problem 66108

Problem 66109

Problem 66110

Problem 66111

Problem 66112

6. What is an electrode of the first kind? Write a general Nernst equation for this indicator electrode.
7. A solution of $0.25 \mathrm{M} \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}$ and $0.35 \mathrm{M} \mathrm{Cr}^{3+}$ has a pH of 2.0 . What is the $\mathrm{E}_{\text {cell }}$ of this halfcell?

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Math

Problem 66101

Simplify: a. 5x−2−3x5x - 2 - 3x5x−2−3x; b. 5x−(2−3x)5x - (2 - 3x)5x−(2−3x). What are the simplified forms?

Problem 66102

Simplify the expression: -5(2 x-4) + 11 x - 10 = ?

Problem 66103

Find the equations of the line perpendicular and parallel to y=−98x+1y=-\frac{9}{8} x+1y=−89​x+1 through the point (8,−3)(8,-3)(8,−3).

Problem 66104

Determine if the lines 8x+6y=88 x+6 y=88x+6y=8, 4y=−3x+54 y=-3 x+54y=−3x+5, and y=−34x+7y=-\frac{3}{4} x+7y=−43​x+7 are parallel, perpendicular, or neither.

Problem 66105

Problem 66106

Problem 66107

Problem 66108

Problem 66109

Problem 66110

Problem 66111

Problem 66112

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Simplify: a. $5x - 2 - 3x$ ; b. $5x - (2 - 3x)$ . What are the simplified forms?

Find the equations of the line perpendicular and parallel to $y=-\frac{9}{8} x+1$ through the point $(8,-3)$ .

Determine if the lines $8 x+6 y=8$ , $4 y=-3 x+5$ , and $y=-\frac{3}{4} x+7$ are parallel, perpendicular, or neither.