It already is rounded to the nearest hundredth
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>
Answer:
The 84th term of the arithmetic sequence -5,15,35, ... is 1675.
Step-by-step explanation:
The arithmetic sequence -5,15,35, ... increases by 20 per term. Add 20 to the prior term to find the new term. Do this 83 times from -5, and you reach 1675.
Answer:
They are congruent.
Step-by-step explanation:
We know this for the fact that angle D and angle A are the same.
Angle B and angle A are the same
The line AB and DE are the same.
Not sure about transformations but I think it was transformed around the origin.
Not 100 percent about the last part.
Hope this helps.
Differentiate the given solution:
Now, given that <em>x</em> (<em>π</em>/4) = √2/2 … (I'm assuming there are symbols missing somewhere) … you have
Similarly, given that <em>x'</em> (<em>p</em>/4) = 0, you have
From this result, it follows that
So the particular solution to the DE that satisfies the given conditions is
