Answer:
9.4
Step-by-step explanation:
We can use the Pythagorean theorem
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
5^2+8^2 = c^2
25 +64 = c^2
89 = c^2
Taking the square root of each side
sqrt(89) = sqrt(c^2)
9.433981132 = c
To the nearest tenth
9.4
Answer:
Exact form : x = +_2 squareroot 11+5
Decimal form : x=11.63324958...,-1.63324958...
Step-by-step explanation: Use the formula (b/2)^2 in order to create a new term. Solve for x by using the term to complete the square.
I hope this helps you out! :)
Answer: The answer will be 28
Step-by-step explanation:
Let
. Then differentiating, we get
![f'(x) = 3x^2 - 2](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%203x%5E2%20-%202)
We approximate
at
with the tangent line,
![f(x) \approx f(x_1) + f'(x_1) (x - x_1) = 10x - 18](https://tex.z-dn.net/?f=f%28x%29%20%5Capprox%20f%28x_1%29%20%2B%20f%27%28x_1%29%20%28x%20-%20x_1%29%20%3D%2010x%20-%2018)
The
-intercept for this approximation will be our next approximation for the root,
![10x - 18 = 0 \implies x_2 = \dfrac95](https://tex.z-dn.net/?f=10x%20-%2018%20%3D%200%20%5Cimplies%20x_2%20%3D%20%5Cdfrac95)
Repeat this process. Approximate
at
.
![f(x) \approx f(x_2) + f'(x_2) (x-x_2) = \dfrac{193}{25}x - \dfrac{1708}{125}](https://tex.z-dn.net/?f=f%28x%29%20%5Capprox%20f%28x_2%29%20%2B%20f%27%28x_2%29%20%28x-x_2%29%20%3D%20%5Cdfrac%7B193%7D%7B25%7Dx%20-%20%5Cdfrac%7B1708%7D%7B125%7D)
Then
![\dfrac{193}{25}x - \dfrac{1708}{125} = 0 \implies x_3 = \dfrac{1708}{965}](https://tex.z-dn.net/?f=%5Cdfrac%7B193%7D%7B25%7Dx%20-%20%5Cdfrac%7B1708%7D%7B125%7D%20%3D%200%20%5Cimplies%20x_3%20%3D%20%5Cdfrac%7B1708%7D%7B965%7D)
Once more. Approximate
at
.
![f(x) \approx f(x_3) + f'(x_3) (x - x_3) = \dfrac{6,889,342}{931,225}x - \dfrac{11,762,638,074}{898,632,125}](https://tex.z-dn.net/?f=f%28x%29%20%5Capprox%20f%28x_3%29%20%2B%20f%27%28x_3%29%20%28x%20-%20x_3%29%20%3D%20%5Cdfrac%7B6%2C889%2C342%7D%7B931%2C225%7Dx%20-%20%5Cdfrac%7B11%2C762%2C638%2C074%7D%7B898%2C632%2C125%7D)
Then
![\dfrac{6,889,342}{931,225}x - \dfrac{11,762,638,074}{898,632,125} = 0 \\\\ \implies x_4 = \dfrac{5,881,319,037}{3,324,107,515} \approx 1.769292663 \approx \boxed{1.769293}](https://tex.z-dn.net/?f=%5Cdfrac%7B6%2C889%2C342%7D%7B931%2C225%7Dx%20-%20%5Cdfrac%7B11%2C762%2C638%2C074%7D%7B898%2C632%2C125%7D%20%3D%200%20%5C%5C%5C%5C%20%5Cimplies%20x_4%20%3D%20%5Cdfrac%7B5%2C881%2C319%2C037%7D%7B3%2C324%2C107%2C515%7D%20%5Capprox%201.769292663%20%5Capprox%20%5Cboxed%7B1.769293%7D)
Compare this to the actual root of
, which is approximately <u>1.76929</u>2354, matching up to the first 5 digits after the decimal place.
Answer:
18793000
Step-by-step explanation: