<span>1.2555⋅<span>10^<span>−<span>6
</span></span></span></span>Explanation:
<span><span><span>(1.08⋅<span>20<span>−3</span></span>)</span><span>(9.3⋅<span>10<span>−3</span></span>)</span>=<span>1.08<span><span>(20)</span>3</span></span>⋅<span>9.3<span><span>(10)</span>3</span></span>=<span><span>1.08⋅9.3</span><span>8⋅<span>106</span></span></span>=1.2555</span><span>⋅<span>10<span>−6</span></span></span></span>
The formula for the surface area of a sphere is 4πr^2
This can be used in the following way, getting the diameter at 18.3:
18.3/2 = 9.15
Saying PI is 3.14 you can do this:
SA = 4*3.14*9.15^2 = 1051.6 m^2
Formula for volume is:
(4/3)πr^3
V = (4/3)*3.14*9.15^3 = 3207.2 m^3
<u>Question 8</u>
a^2 + 7a + 12
= (a+3)(a+4)
When factorising a quadratic, the product of the two factors should equal the constant term (12), and the sum of the two factors should equal the linear term (7). To find the two factors, list out the factors of 12 (1x12, 2x6, 3x4) and identify the pair that adds up to 7 (3+4).
An alternative method if you get stuck during your exam would be to solve it algebraically using the quadratic formula and then write it in the factorised form.
a = (-7 +or- sqrt(7^2 - 4(1)(12)) / 2(1)
= (-7 +or- sqrt(1))/2
= -3 or -4
These factors are the negative of the values that would go in the brackets when written in factorised form, as when a = -3 the factor (a+3) would equal 0. (If it were positive 3 instead, then in the factorised form it would be a-3).
<u>Question 10</u>
-3(x - y)/9 + (4x - 7y)/2 - (x + y)/18
Rewrite each fraction with a common denominator so you can combine the fractions into one.
= -6(x - y)/18 + 9(4x - 7y)/18 - (x + y)/18
= (-6(x - y) + 9(4x - 7y) - (x + y)) /18
Expand the brackets and collect like terms.
= (-6x + 6y + 36x - 63y - x - y)/18
= (29x - 58y)/18
= 29/18 x - 29/9 y
It would 144 sq ft
2*24= 48
48-4=44
50*2=100
100+44=144
B.
X-17=-5
Add 17 to both sides
-5+17=12
