1. Anwser=53.3 (do 40*3 then anwser x 4)
2anwser=120
3a + b = 54...when b = 9
3a + 9 = 54
3a = 54 - 9
3a = 45
a = 45/3
a = 15 <===
Answer:
the roots are {-4/3, 4/3}
Step-by-step explanation:
Begin the solution of 11=6|-2z| -5 by adding 5 to both sides:
11=6|-2z| -5 becomes 16 = 6|-2z|.
Dividing both sides by 12 yields
16/12 = |-z|
There are two cases here: first, that one in which z is positive and second the one in which z is negative.
If z is positive, 4/3 = -z, and so z = -4/3, and:
If z is negative, 4/3 = z
Thus the roots are {-4/3, 4/3}
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>
