To solve for the time it reach the maximum height, you must solve the first derivative of the function and equate it to zero
<span>h(t) = −4.9t^2 + 14.7t + 1</span>
dh/ dt = -9.8t + 14.7
then equate to zero
-9.8t + 14.7 = 0
solve for t
t = 1.5 s
then the maximum height is when t = 1.5
<span>h(t) = −4.9t^2 + 14.7t + 1
h(1.5) = </span><span>−4.9(1.5)^2 + 14.7(1.5) + 1
h(1.5) = 12.025 m
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1. Natasha invests £250 in a building society account. At the end of the year her account is
credited with 2% interest. How much interest had her £250 earned in the year?
Solution: Interest = 2% of £250
= 2/100 x £250
answer = £5
2. Alan invests £140 in an account that pays r% interest. After the first year he receives £4.20 interest. What is the value of r, the rate of interest?
r/100 x £140 = £4.20
r = 100 x 4.20 / 140
= 420/140
= 3%
So the interest rate is 3%
surface area (S) of a right rectangular solid is:
S = 2*L*W + 2*L*H + 2*W*H (equation 1)
where:
L = length
W = width
H = height
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you have:
L = 7
W = a
H = 4
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formula becomes:
S = 2*7*a + 2*7*4 + 2*a*4
simplify:
S = 14*a + 56 + 8*a
combine like terms:
S = 22*a + 56
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answer is:
S = 22*a + 56 (equation 2)
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to prove, substitute any value for a in equation 2:
let a = 15
S = 22*a + 56 (equation 2)
S = 22*15 + 56
S = 330 + 56
S = 386
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since a = 15, then W = 15 because W = a
go back to equation 1 and substitute 15 for W:
S = 2*L*W + 2*L*H + 2*W*H (equation 1)
where:
L = length
W = width
H = height
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you have:
L = 7
W = 15
H = 4
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equation 1 becomes:
S = 2*7*15 + 2*7*4 + 2*15*4
perform indicated operations:
S = 210 + 56 + 120
S = 386
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surface area is the same using both equations so:
equations are good.
formula for surface area of right rectangle in terms of a is:
S = 22*a + 56
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