X^2+3×-7=5x-8
X^2-2x+1=0
(X-1)(x-1)=0
X=1 x=1
Y=1^2+3*1-7
Y=1+3-7
Y=4-7
Y=-3
×=1 y=-3
Solution = (1,-3)
Answer= one solution
With ϕ ≈ 1.61803 the golden ratio, we have 1/ϕ = ϕ - 1, so that
![I = \displaystyle \int_0^\infty \frac{\sqrt[\phi]{x} \tan^{-1}(x)}{(1+x^\phi)^2} \, dx = \int_0^\infty \frac{x^{\phi-1} \tan^{-1}(x)}{x (1+x^\phi)^2} \, dx](https://tex.z-dn.net/?f=I%20%3D%20%5Cdisplaystyle%20%5Cint_0%5E%5Cinfty%20%5Cfrac%7B%5Csqrt%5B%5Cphi%5D%7Bx%7D%20%5Ctan%5E%7B-1%7D%28x%29%7D%7B%281%2Bx%5E%5Cphi%29%5E2%7D%20%5C%2C%20dx%20%3D%20%5Cint_0%5E%5Cinfty%20%5Cfrac%7Bx%5E%7B%5Cphi-1%7D%20%5Ctan%5E%7B-1%7D%28x%29%7D%7Bx%20%281%2Bx%5E%5Cphi%29%5E2%7D%20%5C%2C%20dx)
Replace 
:
Split the integral at x = 1. For the integral over [1, ∞), substitute 
:
The integrals involving tan⁻¹ disappear, and we're left with
The 3rd or 1st one I'm not sure which one but u have an idea of what it might be
Answer:
d
Step-by-step explanation:
The denominator of f(x) cannot be zero as this would make f(x) undefined.
Equating the denominator to zero and solving gives the value that x cannot be and if the numerator is non zero for this value then it is a vertical asymptote.
x + 3 = 0 ⇒ x = - 3 ← equation of vertical asymptote
The amount of shampoo required by Morgan each week to bathe her dog = 2 oz
So
The amount of shampoo required by Morgan in 7 days to bathe her dog = 2 oz
The amount of shampoo remaining after 4 weeks = 34 oz
So the amount of shampoo remaining after (4 * 7) days = 34 oz
The amount of shampoo remaining after 28 days = 34 oz
The amount of shampoo that Morgan uses in 28 days = (2/7) * 28 oz
= 2 * 4 oz
= 8 oz
Then
8 oz of shampoo is required by Morgan in = 28 days
Then
34 oz of shampoo will be used in = (28/8) * 34 days
= 7 * 17 days
= 119 days
So
The total number of
days before the bottle becomes empty = 119 + 8 oz
= 127 days
