Xy = -900
x + y = 5
x + y = 5
x - x + y = -x + 5
y = -x + 5
xy = -900
x(-x + 5) = -900
x(-x) + x(5) = -900
-x² + 5x = -900
-x² + 5x + 900 = 0
-1(x²) - 1(-5x) - 1(-900) = 0
-1(x² - 5x - 900) = 0
-1 -1
x² - 5x - 900 = 0
x = -(-5) ± √((-5)² - 4(1)(-900))
2(1)
x = 5 ± √(25 + 3600)
2
x = 5 ± √(3625)
2
x = 5 ± 5√(145)
2
x = 2.5 ± 2.5√(145)
x + y = 5
2.5 ± 2.5 √(145) + y = 5
- (2.5 ± 2.5√(145) - (2.5 ± 2.5√(145)
y = 2.5 ± 2.5√(145)
(x, y) = (2.5 ± 2.5√(145), 2.5 ± 2.5√(145))
The two numbers that add up to 5 and multiply to -900 are 2.5 ± 2.5√(145).
Answer:
9.4 secs
Step-by-step explanation:
From Newton's law of cooling;
T(t) = Ts + Do e^-kt
Where;
D0= initial temperature difference
Ts= Temperature of the surroundings
t= time
K = positive constant
Do = 185 - 60 = 125 degrees
167 = 60 + 125 e^-3k
167 - 60 = 125 e^-3k
107/125 = e^-3k
ln(e^-3k) = ln(107/125)
-3k = -0.1555
k = 0.1555/3
k = 0.0518
Substituting the value of k to find the time taken to reach 137 degrees
T(t) = Ts + Do e^-kt
137 = 60 + 125 e^-(0.0518t)
137 - 60 = 125 e^-(0.0518t)
77 = 125 e^-(0.0518t)
e^-(0.0518t)= 77/125
ln [e^-(0.0518t)] = ln(77/125)
-0.0518t = -0.4845
t = 0.4845/0.0518
t = 9.4 secs
If the angle of depression is 28° the complementary angle in the triangle is 62°. With this you can use soh-cah-toa to find the x value.
cos62 = 350/x; multiply both sides by x
cos62 x = 350; divide both sides by cos62
x = 350 / cos62
x = 745.519
x = 746 ft
Hope this helps you!
Answer:
Its B
Step-by-step explanation: