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Question 44011

posted 10 months ago

\sqrt[3]{-8}=-2
\sqrt[4]{-16}=\text { not real }

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Question 44017

posted 10 months ago

Create a linear function of the form:
g(x)=m x+b \text { where }\{b, m \in R \mid m \neq \pm 1, b \neq 0\} \text { and a quadratic function of the form }
h(x)=a(x-h)^{2}+k, \text { where }\{a, h, k \in R \mid a \neq \pm 1, h \neq 0, k \neq 0\}
\text { Sketch your functions } y=g(x), y=h(x), y=g(x)+h(x), y=\frac{g(x)}{h(x)}
\text { Calculate } h(g(1)) \text { and } g(h(1)) \text { showing the full process. }

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Question 44015

posted 10 months ago

a) Create any quadratic function of the form f(x) = ax? + bx +c, where
\{a, b, c \in \mathbb{R} \mid a \neq \pm 1, b \neq 0, c \neq 0\} \text {. Calculate the average rate of change over the interval }
-2 \leq x \leq 3
Estimate the instantaneous rate of change of f(x) at x = -3, using the methods of this course
How does the instantaneous rate of change differ from part b) with the instantaneous rates of
\text { change at } f(x) \text { at } x=4 \text { and } f(x) \text { at } x=-\frac{b}{2 a} ?

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Question 44016

posted 10 months ago

Give three different examples of types of functions (as covered in Grade 11 and/or Grade 12)you know that do not have an instantaneous rate of change. State where your functions do not have an instantaneous rate of change and explain why this is the case.

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Question 44023

posted 10 months ago

If 1= Inx?, then:
x=\pm \sqrt{e}
x=\sqrt{e}
x=-1 \text { or } x=1
x=\frac{1}{2}
x=\pm \frac{1}{2}

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Question 44024

posted 10 months ago

\text { Consider: } A=\left[\begin{array}{ccc} 2 & 3 & 5 \\ 1 & -2 & -2 \end{array}\right] C=\left[\begin{array}{ccc} -5 & 11 & 4 \\ 2 & -1 & 3 \end{array}\right]
Compute: 3A– 4C
\left[\begin{array}{ccc} 6 & 9 & 15 \\ 3 & -6 & -6 \end{array}\right]
\left[\begin{array}{ccc} 20 & -44 & -16 \\ -8 & 4 & -12 \end{array}\right]
\left[\begin{array}{ccc} 26 & -35 & -1 \\ -5 & -2 & -18 \end{array}\right]
\left[\begin{array}{ccc} -26 & 35 & 1 \\ 5 & 2 & 18 \end{array}\right]
Cannot be computed.

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Question 44025

posted 10 months ago

\text { If } y=\frac{\ln x^{2}}{x^{2}}, \text { then } \frac{d y}{d x}=\ldots
\frac{1}{x^{2}}
\frac{2 x}{x^{2}}
\frac{x^{2}\left(\frac{2}{x}\right)-2 x \ln x^{2}}{x^{4}}
2 x\left(1-\ln x^{2}\right)
None of the above.

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Question 44020

posted 10 months ago

\text { If } y=e^{x^{2}+3 x} \text {, then } \frac{d y}{d x}=
e^{x^{2}+3 x}
None of the above
\frac{e^{x+3 x}}{(2 x+3)}
e^{x^{2}+3 x}(2 x+3)
x^{2} e^{x^{2}+3 x}+3 x e^{x^{2}+3 x}

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Question 44035

posted 10 months ago

A producer grower is purchasing fertilizer containing three nutrients: A, B and C. The minimum weekly requirements are 80 units of A, 120 of B, and 240 of C. There are two popular blends of fertilizer on the market. Blend I, costing R8 a bag, contains 2 units of A, 6of B, and 4 of C. Blend II, costing R10 a bag, contains 2 units of A, 2 of B, and 12 of C.
Write down the constraints in terms of x and y.
Represent the constraints on graph paper. Show the feasible region clearly onthe graph.
Write down the cost function
How many bags of each blend should the grower buy each week to minimize the cost of meeting the nutrient requirements?
5 What is the minimum cost?
What is the minimum cost?

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Question 44026

posted 10 months ago

\text { If } \log _{a} p=\frac{1}{x} \text { then } x=\ldots
\log _{p} a
\log _{a} \frac{1}{p}
-\log _{a} p
-\log _{p} a
None of the above.

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