The area of a circle is given by the formula A = πr² where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))². If the diameter of the logo increases by 70% the radius (and, consequently, the total area) increases by \( \frac{70\text{%}}{2} \) = 35%

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

3 + (4 + 3) ÷ 4 x 5 - 2²
P: 3 + (7) ÷ 4 x 5 - 2²
E: 3 + 7 ÷ 4 x 5 - 4
MD: 3 + \( \frac{7}{4} \) x 5 - 4
MD: 3 + \( \frac{35}{4} \) - 4
AS: \( \frac{12}{4} \) + \( \frac{35}{4} \) - 4
AS: \( \frac{47}{4} \) - 4
AS: \( \frac{47 - 16}{4} \)
\( \frac{31}{4} \)
7\(\frac{3}{4}\)

To multiply terms with radicals, multiply the coefficients and radicands separately:

8\( \sqrt{9} \) x 8\( \sqrt{6} \)
(8 x 8)\( \sqrt{9 \times 6} \)
64\( \sqrt{54} \)

Now we need to simplify the radical:

64\( \sqrt{54} \)
64\( \sqrt{6 \times 9} \)
64\( \sqrt{6 \times 3^2} \)
(64)(3)\( \sqrt{6} \)
192\( \sqrt{6} \)

An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.

To fill a 20 gallon tank exactly halfway you'll need 10 gallons of fuel. Each fuel can holds 2 gallons so:

cans = \( \frac{10 \text{ gallons}}{2 \text{ gallons}} \) = 5