The answer will be (10,2) because of the substitution method.
Answer:
y=-9x+5
Step-by-step explanation:
Answer:
![6 + 2=8 \\so... +2 + +6 = +8\\](https://tex.z-dn.net/?f=6%20%2B%202%3D8%20%5C%5Cso...%20%2B2%20%2B%20%2B6%20%3D%20%2B8%5C%5C)
Step-by-step explanation:
So the thing about adding of integers is that is both nos. are positive then you can simply add it and same with negative too.But with negative and positive we should subtract but that is for later.Luckily we have 2 positive integers so we do it like this:
+6 is the same as 6 and +2 is the same as 2 so we...
rule:add the numbers and add the sign.
![6 + 2=8\\so... +2 + +6 = +8](https://tex.z-dn.net/?f=6%20%2B%202%3D8%5C%5Cso...%20%2B2%20%2B%20%2B6%20%3D%20%2B8)
Answer:
![x = \frac{\sqrt 3}{ 3}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B%5Csqrt%203%7D%7B%203%7D)
Step-by-step explanation:
Given
See attachment for complete question
First, we calculate the water pipe length (AC):
![AC^2 = AB^2 + BC^2](https://tex.z-dn.net/?f=AC%5E2%20%3D%20AB%5E2%20%2B%20BC%5E2)
![AC^2 = 1^2 + x^2](https://tex.z-dn.net/?f=AC%5E2%20%3D%201%5E2%20%2B%20x%5E2)
![AC^2 = 1 + x^2](https://tex.z-dn.net/?f=AC%5E2%20%3D%201%20%2B%20x%5E2)
![AC = \sqrt{1 + x^2](https://tex.z-dn.net/?f=AC%20%3D%20%5Csqrt%7B1%20%2B%20x%5E2)
The cost of laying across water is twice (2 times) laying on land.
So, the total cost (C) is:
![C = 2 * \sqrt{1 + x^2} + 1 * (4 - x)](https://tex.z-dn.net/?f=C%20%3D%202%20%2A%20%5Csqrt%7B1%20%2B%20x%5E2%7D%20%2B%201%20%2A%20%284%20-%20x%29)
![C = 2 \sqrt{1 + x^2} + (4 - x)](https://tex.z-dn.net/?f=C%20%3D%202%20%5Csqrt%7B1%20%2B%20x%5E2%7D%20%2B%20%284%20-%20x%29)
Differentiate
![C' = \frac{2x}{\sqrt{1 + x^2}} - 1](https://tex.z-dn.net/?f=C%27%20%3D%20%5Cfrac%7B2x%7D%7B%5Csqrt%7B1%20%2B%20x%5E2%7D%7D%20-%201)
To find the most economical cost, we simply minimize C' by equating C' to 0
![C' = 0](https://tex.z-dn.net/?f=C%27%20%3D%200)
![\frac{2x}{ \sqrt{1 + x^2}}-1 = 0\\](https://tex.z-dn.net/?f=%5Cfrac%7B2x%7D%7B%20%5Csqrt%7B1%20%2B%20x%5E2%7D%7D-1%20%3D%200%5C%5C)
![\frac{2x}{ \sqrt{1 + x^2}}=1](https://tex.z-dn.net/?f=%5Cfrac%7B2x%7D%7B%20%5Csqrt%7B1%20%2B%20x%5E2%7D%7D%3D1)
Cross multiply
![2x= \sqrt{1 + x^2}](https://tex.z-dn.net/?f=2x%3D%20%5Csqrt%7B1%20%2B%20x%5E2%7D)
Take square of both sides
![4x^2 = 1+x^2](https://tex.z-dn.net/?f=4x%5E2%20%3D%201%2Bx%5E2)
Collect like terms
![4x^2 -x^2= 1](https://tex.z-dn.net/?f=4x%5E2%20-x%5E2%3D%201)
![3x^2= 1](https://tex.z-dn.net/?f=3x%5E2%3D%201)
Solve for ![x^2](https://tex.z-dn.net/?f=x%5E2)
![x^2 = \frac{1}{3}](https://tex.z-dn.net/?f=x%5E2%20%3D%20%5Cfrac%7B1%7D%7B3%7D)
Solve for x
![x = \sqrt{\frac{1}{3}}](https://tex.z-dn.net/?f=x%20%3D%20%5Csqrt%7B%5Cfrac%7B1%7D%7B3%7D%7D)
![x = \frac{1}{\sqrt 3}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B1%7D%7B%5Csqrt%203%7D)
Rationalize:
![x = \frac{1}{\sqrt 3} * \frac{\sqrt 3}{\sqrt 3}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B1%7D%7B%5Csqrt%203%7D%20%2A%20%5Cfrac%7B%5Csqrt%203%7D%7B%5Csqrt%203%7D)
![x = \frac{\sqrt 3}{ 3}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B%5Csqrt%203%7D%7B%203%7D)