Kayaking Upstream
please help alg 2?
71). Factor the polynomial:
16×2 + 40xy + 25y2
72).Factor the polynomial:
z2 + 3z – 4
73).Factor the polynomial:
h2 – 10h + 24
74).Factor the polynomial:
81uv3 + 3u4
75).Solve:
z2(2z – 1) = 0
77).Solve the inequality:
r2 ≤ 2(r + 4)
81). Factor:
3y2 – 5y + 8
82).Express as a simplified polynomial:
(4a + 5)2
84).Write in scientific notation:
762.20
85).Write in scientific notation:
0.04775
90).Simplify:
m2 = m
97).Lisa Chen invested $24,000, part at 8% and the rest at 7.2%. How much did she invest at each rate if her income from the 8% investment is two thirds that of the 7.2% investment?
100).Tim paddles his kayak 12 km upstream against a 3km/h current and back again in 5 hours and 20 minutes. In that time, how far could he have paddled in still water?
71). Factor the polynomial: 16×2 + 40xy + 25y2
16x^2 + 40xy + 25y^2
(4x)^2 + 2*4x*5y + (5y)^2
(4x + 5y)^2
72).Factor the polynomial: z2 + 3z – 4
z^2 + 3z – 4
(z + 4)(z – 1)
73).Factor the polynomial: h2 – 10h + 24
h^2 – 10h + 24
(h – 4)(h – 6)
74).Factor the polynomial: 81uv3 + 3u4
81uv^3 + 3u^4
3u*(27v^3 + u^3)
75).Solve: z2(2z – 1) = 0
z^2(2z – 1) = 0
2z^3 – z^2 = 0
z = 0
77).Solve the inequality: r2 ≤ 2(r + 4)
r^2 ≤ 2(r + 4)
r^2 ≤ 2r + 8
r^2 – 2r ≤ 8
r^2 – 2r + 1 ≤ 8 + 1
(r – 1)^2 ≤ 9
r – 1 ≤ ±√9
r ≤ 1 ± 3
81). Factor: 3y2 – 5y + 8
3y^2 – 5y + 8
y^2 – (5/3)y = -8/3
y^2 – (5/3)y + (5/6)^2 = -8/3 + (5/6)^2
(y – 5/6)^2 = -8*12/36 + 25/36
(y – 5/6)^2 = -71/36
y – 5/6 = ±√(71/36)
y = -5/6 ± √(71/36)
I’m leaving the polynomial as 3y^2 – 5y + 8.
82).Express as a simplified polynomial: (4a + 5)2
(4a + 5)2
8a + 10
84).Write in scientific notation: 762.20
7.6220 E(2)
85).Write in scientific notation: 0.04775
4.775 X 10^(-2) paper and pencil style
4.775 X E(-2) calculator segmented display style
90). Simplify: m2 = m
m^2 = m
m = ±1
97).Lisa Chen invested $24,000, part at 8% and the rest at 7.2%. How much did she invest at each rate if her income from the 8% investment is two thirds that of the 7.2% investment?
x ::== fraction of $24,000 invested at 8%
(1-x) is the fraction of $24,000 invested at 7.2%
$24,000(0.08)x = (2/3)*$24,000(0.072)(1-x)
(0.08)x = (2/3)*(0.072)(1-x)
(0.08)x = (0.048)(1-x)
x = (1-x)(0.048)/(0.08)
x = (1-x)*6
x/(1-x) = 6, x < 1
and
1/6 = (1-x)/x, x > 0
Lisa Chen invested 6/7 of the $24,000 at 8% and invested 1/7 of the $24,000 at 7.2%.
100).Tim paddles his kayak 12 km upstream against a 3km/h current and back again in 5 hours and 20 minutes. In that time, how far could he have paddled in still water?
Suppose that Tim’s kayaking work rate is constant upstream and downstream.
w ::== Tim’s kayaking speed in in km/hr in still water at that work rate
u ::== hours Tim spends paddling upstream
u*(w-3) = 12
12 = (16/3)*(w+3)
12 = (16/3)*(w+3)
(w+3) = 12/(16/3)
w + 3 = 36/16
w + 3 = 9/4
w = 9/4 – 3
w = 9/4 – 12/4
w = -3/4
But a negative speed (work rate) is inconsistent with the statement that Tim paddled upstream.
Conclusion: The supposition that Tim’s kayaking work rate was constant upstream and downstream is false, and Question 100). does not provide enough information for its solution.
My Brother Kayaking Upstream
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