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Keith_Richards [23]
3 years ago
10

Sara jumps off a diving board that is 6 feet above the surface of the water her height above the surface of the water h in feet

is a function of time t in seconds as modeled by the quadratic function h(t)=-2t^2 + t + 6 how many seconds did it take sara to hit the surface of the water after she jumped off the diving board
Mathematics
1 answer:
Flauer [41]3 years ago
7 0
Well when she hits the water h=0 so

2t^2-t-6=0  factor

2t^2-4t+3t-6=0

2t(t-2)+3(t-2)=0

(2t+3)(t-2)=0, since t>0

t=2 seconds...

However it should be noted that h(t)=-2t^2+t+6 implies that

v(t)=dh/dt=-4t+1 and

a(t)=dv/dt=-4

Since this is a free fall equation, this would suggest that the acceleration due to gravity is -4, whether that is supposed to be -4ft/s^2 or -4m/s^2, it certainly is not on this planet! :D  If it is -4ft/s^2 it could be on the Moon or if it is -4m/s^2 it could be on Mars.
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Use​ Newton's method to find an approximate solution of ln(x)=10-x. Start with x_0 =9 and find x_2 .
vova2212 [387]

Answer:

x₂ = 7.9156

Step-by-step explanation:

Given the function  ln(x)=10-x with initial value x₀ = 9, we are to find the second approximation value x₂ using the Newton's method. According to Newtons method xₙ₊₁ = xₙ -  f(xₙ)/f'(xₙ)

If f(x) = ln(x)+x-10

f'(x) = 1/x + 1

f(9) = ln9+9-10

f(9) = ln9- 1

f(9) = 2.1972 - 1

f(9) = 1.1972

f'(9) = 1/9 + 1

f'(9) = 10/9

f'(9) = 1.1111

x₁ = x₀ -  f(x₀)/f'(x₀)

x₁ = 9 -  1.1972/1.1111

x₁  = 9 - 1.0775

x₁  = 7.9225

x₂ = x₁ -  f(x₁)/f'(x₁)

x₂ = 7.9225 -  f(7.9225)/f'(7.9225)

f(7.9225) = ln7.9225 + 7.9225 -10

f(7.9225) = 2.0697 + 7.9225 -10

f(7.9225) = 0.0078

f'(7.9225) = 1/7.9225 + 1

f'(7.9225) = 0.1262+1

f'(7.9225) = 1.1262

x₂ = 7.9225 - 0.0078/1.1262

x₂ = 7.9225 - 0.006926

x₂ = 7.9156

<em>Hence the approximate value of x₂ is 7.9156</em>

7 0
3 years ago
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