Make x the subject of \[\begin{array} { l } y = \ln \left( 3 + e ^ { 2 x } \right) \\ \text { A) } x = \frac { \ln \left( 3 - e ^ { y } \right) } { 2 } \\ \text { R) } x = \frac { e ^ { y } - 3 } { 2 } \\ \text { C) } x = \frac { y - \ln 3 } { 2 } \\ \text { n) } x = \frac { y } { 2 \ln 3 } \\ \text { F) } x = \ln \sqrt { e ^ { y - 3 } } \end{array}\]

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Exam 2: Non-Linear Equations

A firm's average cost function is given by $A C = \frac { 800 } { Q } + 2 Q + 18$ Find, to the nearest whole number, the value of Q at the lowest point on the graph of AC plotted against Q, in the interval, 0 c Q c 30.

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Question 1

Correct Answer:

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B

Given the supply and demand functions P = QS2 + 10QS + 30 P = - QD2 - 8QD + 200 Calculate the equilibrium price, correct to 2 decimal places.

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(Multiple Choice)

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Question 2

Correct Answer:

Verified

D

$\text { If } a=\frac{2 \sqrt{x}}{y^{3}} \text { and } b=3 x^{4} y \text {, simplify } \frac{4 b}{a^{2}} \text {. }$

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Question 3

Correct Answer:

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A

Find the solutions of the quadratic equation $2 x ^ { 2 } + 6 d x - d ^ { 2 } = 0$

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Question 4

Make x the subject of y= 3+ A) x= R) x= C) x= n) x= F) x=

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Question 5

The value (in cents)of shares, x years after their flotation on the stock market, is modelled by V = 6e0.8t Find the increase in the value of these shares, to the nearest cent, 4 years and 2 months later.

(Multiple Choice)

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Question 6

If fixed costs are 30, variable costs per unit are Q + 3, and the demand function is P + 2Q = 50 Which of the following gives the formula for the associated profit?

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Question 7

Find the value of k so that the equation x2 - 10x + 2k = 8x - k Has exactly one root.

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Question 8

State the degree of homogeneity of the production function $Q=7 K^{\frac{1}{4}}\left(5 L^{\frac{1}{2}} K^{\frac{1}{2}}+2 K^{\frac{3}{4}}\right)$

(Multiple Choice)

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Question 9

A firm's average cost function is given by $A C = \frac { 800 } { Q } + 2 Q + 18$ Find, to the nearest whole number, the value of Q at the lowest point on the graph of AC plotted against Q, in the interval, 0 c Q c 30.

Given the supply and demand functions P = QS2 + 10QS + 30 P = - QD2 - 8QD + 200 Calculate the equilibrium price, correct to 2 decimal places.

$\text { If } a=\frac{2 \sqrt{x}}{y^{3}} \text { and } b=3 x^{4} y \text {, simplify } \frac{4 b}{a^{2}} \text {. }$

Find the solutions of the quadratic equation $2 x ^ { 2 } + 6 d x - d ^ { 2 } = 0$

Make x the subject of y= 3+ A) x= R) x= C) x= n) x= F) x=

The value (in cents)of shares, x years after their flotation on the stock market, is modelled by V = 6e0.8t Find the increase in the value of these shares, to the nearest cent, 4 years and 2 months later.

If fixed costs are 30, variable costs per unit are Q + 3, and the demand function is P + 2Q = 50 Which of the following gives the formula for the associated profit?

Find the value of k so that the equation x2 - 10x + 2k = 8x - k Has exactly one root.

State the degree of homogeneity of the production function $Q=7 K^{\frac{1}{4}}\left(5 L^{\frac{1}{2}} K^{\frac{1}{2}}+2 K^{\frac{3}{4}}\right)$

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Exam 2: Non-Linear Equations

A firm's average cost function is given by AC=800Q+2Q+18A C = \frac { 800 } { Q } + 2 Q + 18AC=Q800​+2Q+18 Find, to the nearest whole number, the value of Q at the lowest point on the graph of AC plotted against Q, in the interval, 0 c Q c 30.

Given the supply and demand functions P = QS2 + 10QS + 30 P = - QD2 - 8QD + 200 Calculate the equilibrium price, correct to 2 decimal places.

If a=2xy3 and b=3x4y, simplify 4ba2. \text { If } a=\frac{2 \sqrt{x}}{y^{3}} \text { and } b=3 x^{4} y \text {, simplify } \frac{4 b}{a^{2}} \text {. } If a=y32x​​ and b=3x4y, simplify a24b​.

Find the solutions of the quadratic equation 2x2+6dx−d2=02 x ^ { 2 } + 6 d x - d ^ { 2 } = 02x2+6dx−d2=0

Make x the subject of y= 3+ A) x= R) x= C) x= n) x= F) x=

The value (in cents)of shares, x years after their flotation on the stock market, is modelled by V = 6e0.8t Find the increase in the value of these shares, to the nearest cent, 4 years and 2 months later.

If fixed costs are 30, variable costs per unit are Q + 3, and the demand function is P + 2Q = 50 Which of the following gives the formula for the associated profit?

Find the value of k so that the equation x2 - 10x + 2k = 8x - k Has exactly one root.

State the degree of homogeneity of the production function Q=7K14(5L12K12+2K34)Q=7 K^{\frac{1}{4}}\left(5 L^{\frac{1}{2}} K^{\frac{1}{2}}+2 K^{\frac{3}{4}}\right)Q=7K41​(5L21​K21​+2K43​)

Linear Equations

Mathematics of Finance

Differentiation

Partial Differentiation

Integration

Matrices

Linear Prgamming

Dynamics

Filters

A firm's average cost function is given by $A C = \frac { 800 } { Q } + 2 Q + 18$ Find, to the nearest whole number, the value of Q at the lowest point on the graph of AC plotted against Q, in the interval, 0 c Q c 30.

$\text { If } a=\frac{2 \sqrt{x}}{y^{3}} \text { and } b=3 x^{4} y \text {, simplify } \frac{4 b}{a^{2}} \text {. }$

Find the solutions of the quadratic equation $2 x ^ { 2 } + 6 d x - d ^ { 2 } = 0$

State the degree of homogeneity of the production function $Q=7 K^{\frac{1}{4}}\left(5 L^{\frac{1}{2}} K^{\frac{1}{2}}+2 K^{\frac{3}{4}}\right)$