If I can ride a bicycle at the rate of 5 meters per second, how long will it take to ride a distance of 12km at the same rate?

Step 1: Expand $(3x-2)^2$.
$(3x-2)^2 = 9x^2 - 12x + 4$

Step 2: Subtract $(3x-2)$.
$9x^2 - 12x + 4 - (3x - 2) = 9x^2 - 12x + 4 - 3x + 2$

Step 3: Combine like terms.
$9x^2 - 15x + 6$

Step 4: Factor the expression.
$9x^2 - 15x + 6 = 3(3x^2 - 5x + 2) = 3(3x - 2)(x - 1)$
3(3x-2)(x-1)

Step 1: Common denominator is 12.
$\frac{y^2}{4} = \frac{3y^2}{12}, \quad \frac{y}{6} = \frac{2y}{12}$

Step 2: Subtract the fractions.
$\frac{3y^2}{12} - \frac{2y}{12} = \frac{3y^2 - 2y}{12}$
\dfrac{3y^{2-2y}{12}}

Step 1: Expand the numerator.
$(4x + 3)^2 = (4x + 3)(4x + 3) = 16x^2 + 24x + 9$

Step 2: Divide by 7.
$\frac{16x^2 + 24x + 9}{7}$
\dfrac{16x^{2+24x+9}{7}}

Step 1: Expand the numerator.
$(5x + 4)^2 = (5x + 4)(5x + 4) = 25x^2 + 40x + 16$

Step 2: Divide by 37.
$\frac{25x^2 + 40x + 16}{37}$
\dfrac{25x^{2+40x+16}{37}}

Step 1: Write factorials.
$7! = 7 \times 6 \times 5!, \quad 2! = 2 \times 1 = 2$

Step 2: Simplify.
$\frac{7!}{5! \cdot 2!} = \frac{7 \times 6 \times 5!}{5! \cdot 2} = \frac{7 \times 6}{2} = 21$
21

Step 1: Write numerator up to 5!.
$9! = 9 \times 8 \times 7 \times 6 \times 5!$
Denominator: $5! \cdot 2! \cdot 2! = 5! \cdot 2 \cdot 2 = 5! \cdot 4$

Step 2: Simplify.
$\frac{9 \times 8 \times 7 \times 6 \times 5!}{5! \cdot 4} = \frac{9 \times 8 \times 7 \times 6}{4}$

Step 3: Compute step-by-step.
$9 \times 8 = 72$
$72 \times 7 = 504$
$504 \times 6 = 3024$
$3024 \div 4 = 756$
756

Step 1: Pascal's triangle row for $(a + b)^5$ (coefficients: 1, 5, 10, 10, 5, 1).
$(a + b)^5 = 1 \cdot a^5 b^0 + 5 a^4 b^1 + 10 a^3 b^2 + 10 a^2 b^3 + 5 a^1 b^4 + 1 \cdot a^0 b^5$

Step 2: Write the expansion.
$a^5 + 5a^4 b + 10 a^3 b^2 + 10 a^2 b^3 + 5 a b^4 + b^5$
a^{5 + 5a^{4}b + 10a^{3}b^{2} + 10a^{2}b^{3} + 5ab^{4} + b^{5}}

Step 1: Use binomial theorem or Pascal's triangle (same coefficients as ).
$(x + 2)^5 = x^5 + 5 x^4 (2) + 10 x^3 (2)^2 + 10 x^2 (2)^3 + 5 x (2)^4 + (2)^5$

Step 2: Compute powers of 2.
$2^1 = 2, \quad 2^2 = 4, \quad 2^3 = 8, \quad 2^4 = 16, \quad 2^5 = 32$

Step 3: Multiply coefficients.
$5 \times 2 = 10$
$10 \times 4 = 40$
$10 \times 8 = 80$
$5 \times 16 = 80$

Step 4: Full expansion.
$x^5 + 10x^4 + 40x^3 + 80x^2 + 80x + 32$
x^{5 + 10x^{4} + 40x^{3} + 80x^{2} + 80x + 32}

Step 1: Convert m/s to km/h (multiply by $\frac{3600}{1000} = 3.6$).
$340 \times 3.6$

Step 2: Compute.
$340 \times 3 = 1020$
$340 \times 0.6 = 204$
$1020 + 204 = 1224$
Speed = 1224 km/h
1224 km/h

Step 1: Convert distance to metres.
$18.8 \, km = 18.8 \times 1000 = 18800 \, \mathrm{m}$

Step 2: Convert time to seconds.
$1 \, h \, 10 \, min = (60 + 10) \times 60 = 70 \times 60 = 4200 \, \mathrm{s}$

Step 3: Calculate speed.
$\frac{18800 \, m}{4200 \, s} = \frac{188}{42} = \frac{94}{21} \approx 4.476$

Step 4: To 3 significant figures.
4.48 m/s
4.48 m/s