Explanation

p*e = e*p = p

p + e - \(\frac{pe}{2}\) = p

e - \(\frac{pe}{2}\) = 0

e(\(1 - \frac{p}{2}\)) = 0

e = 0

p*p\(^{-1}\) = e

p - p\(^{-1}\) - \(\frac{pp^{-1}}{2}\) = 0

p\(^{-1}\) - \(\frac{pp}{2}\) = -p

p\(^{-1}\) (1 - \(\frac{p}{2}\)) = -p

p\(^{-1}\) = \(\frac{-p}{1 - \frac{p}{2}}\)

Inverse of -1 \(\to\) p = -1

p\(^{-1}\) = \(\frac{-1}{1 - (\frac{-1}{2})} = \frac{-1}{\frac{3}{2}}\)

= \(\frac{-2}{3}\)

(b) m*7 = m + 7 - \(\frac{7m}{2}\), m*5 = m + 5 - \(\frac{5m}{2}\)

m*7 = m*5, m + 7 - \(\frac{7m}{2}\) = m + 5 - \(\frac{5m}{2}\)

7 - 5 = -\(\frac{5m}{2} + \frac{7m}{2}\)

2 = \(\frac{2m}{2}\)

m = 2

Correct Answer: C. 8

Explanation

The median is the middle number in a set of numbers when arranged in order from least to greatest. In our case we get 3, 6, 7, 9, 11, 14 This set has two middle numbers 7 and 9. From here we need to find the average between these two numbers to find our median: 7+9/2=16/2=8

Correct Answer: A. 105600.00

Explanation

573.06 x 184.25 = 105,586.305

1,05600.00 to four significant figure

What are the Rules for significant figures?

Significant Figures

• All non-zero numbers ARE significant.
• Zeros between two non-zero digits ARE significant.
• Leading zeros are NOT significant.
• Trailing zeros to the right of the decimal ARE significant.
• Trailing zeros in a whole number with the decimal shown ARE significant.

Correct Answer: B. 72°

Correct Answer: B. \(15\pi cm^2\)

Explanation

Curved surface area or a cone \(=\pi rl\)

from the information \(l^2 = 4^2 + 3^2 = 16+9\\

l = \sqrt{25} = 5; ∴ C.S.A\hspace{1mm} = \frac{22}{7}\times 3 \times 5\\

Since \frac{22}{7}=\pi ∴ C.S.A\hspace{1mm} =\hspace{1mm}15\pi\)

Correct Answer: D. 5

Explanation

\(P = \begin{pmatrix} 3 & 4 \\ 2 & x \end{pmatrix}; Q = \begin{pmatrix} 1 & 3 \\ -2 & 4 \end{pmatrix}; R = \begin{pmatrix} -5 & 25 \\ -8 & 26 \end{pmatrix}\)

PQ = \(\begin{pmatrix} 3 & 4 \\ 2 & x \end{pmatrix} \begin{pmatrix} 1 & 3 \\ -2 & 4 \end{pmatrix} = \begin{pmatrix} -5 & 25 \\ 2 - 2x & 6 + 4x \end{pmatrix} = R\)

\(\implies 2 - 2x = -8; -2x = -8 - 2 = -10\)

\(6 + 4x = 26 \implies 4x = 26 - 6 = 20\)

\(\implies x = 5\)

Correct Answer: C. 4\(\frac{1}{2}\)cm

Explanation

l = x; b = x - 1

perimeter = 2(l + b) = 16

l + b = \(\frac{16}{2}\) = 8

l + b = 8

x + x - 1 = 8

2x = 8 + 1

2x = 9

x = \(\frac{9}{2}\)cm

x = 4\(\frac{1}{2}\)

Explanation

(b)(i)

(c)(i) \(2 - 7x - 6x^{2} = 0\)

\(2 + 3 - 7x - 6x^{2} = 3\)

\(5 - 7x - 6x^{2} = 3\)

\(\therefore \text{the roots at y = 3 are } x = -1.4; 0.2\)

(ii) Maximum value of \(y = 5 - 7x - 6x^{2}\) is y = 7.

Correct Answer: C. 30

Correct Answer: (a) 20