Answer:x=
−9
/2
y^2+928
Step-by-step explanation:
Dan takes about 8 minutes to run a mile
Yoko payed around $1.75
The <em>approximate</em> solution of the equation shown in the picture is x ≈ 39 / 8 (Right choice: B).
<h3>How to find an approximate solution of a one-variable equation</h3>
The solution of the equation is between x = 4 and x = 5. Now we begin by evaluating each side of the expression (f(x) = x² - 5 · x + 4, g(x) = 2 / (x - 1)) at the average of x = 4 and x = 5.
x = (4 + 5) / 2
x = 4.5
f(4.5) = 4.5² - 5 · 4.5 + 1
f(4.5) = - 5 / 4
g(4.5) = 2 / (4.5 - 1)
g(4.5) = 4 / 7
The solution of the equation is between x = 4.5 and x = 5, then we evaluate at the average:
x = (4.5 + 5) / 2
x = 4.75
f(4.75) = 4.75² - 5 · 4.75 + 1
f(4.75) = - 3 / 16
g(4.75) = 2 / (4.75 - 1)
g(4.75) = 8 / 15
The solution of the equation is between x = 4.75 and x = 5, then we evaluate at the average:
x = (4.75 + 5) / 2
x = 4.875
f(4.875) = 4.875² - 5 · 4.875 + 1
f(4.875) = 25 / 64
g(4.875) = 2 / (4.875 - 1)
g(4.875) = 16 / 31
The <em>approximate</em> solution of the equation shown in the picture is x ≈ 39 / 8 (Right choice: B).
To learn more on successive approximations: brainly.com/question/27191494
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Answer:
Step-by-step explanation:
The Fundamental Theorem of Calculus states that:
![\displaystyle \frac{d}{dx}\left[ \int_a^x f(t)\, dt \right] = f(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%5B%20%5Cint_a%5Ex%20f%28t%29%5C%2C%20dt%20%20%5Cright%5D%20%3D%20f%28x%29)
Where <em>a</em> is some constant.
We can let:
By substitution:
Taking the derivative of both sides results in:
![\displaystyle g'(s) = \frac{d}{ds}\left[ \int_6^s g(t)\, dt\right]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20g%27%28s%29%20%3D%20%5Cfrac%7Bd%7D%7Bds%7D%5Cleft%5B%20%5Cint_6%5Es%20g%28t%29%5C%2C%20dt%5Cright%5D)
Hence, by the Fundamental Theorem:
