Given:
The slope of the line joining points (3,2) and (0,a) is -1.
To find:
The value of a.
Solution:
If a line passes through two points
and
, the slope of a line is:
![m=\dfrac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
The slope of the line joining points (3,2) and (0,a) is -1. So,
![\dfrac{a-2}{0-3}=-1](https://tex.z-dn.net/?f=%5Cdfrac%7Ba-2%7D%7B0-3%7D%3D-1)
![\dfrac{a-2}{-3}=-1](https://tex.z-dn.net/?f=%5Cdfrac%7Ba-2%7D%7B-3%7D%3D-1)
Multiply both sides by -3.
![a-2=-1(-3)](https://tex.z-dn.net/?f=a-2%3D-1%28-3%29)
![a-2=3](https://tex.z-dn.net/?f=a-2%3D3)
![a=3+2](https://tex.z-dn.net/?f=a%3D3%2B2)
![a=5](https://tex.z-dn.net/?f=a%3D5)
Therefore, the value of a is 5.
STEP 1:
find the difference between the total miles of the trip (762 miles) and the miles already traveled (510 miles)
= 762 - 510
= 252 miles left of trip
STEP 2:
divide miles left from step 1 by 3 days
= 252 ÷ 3 days
= 84 miles per day
ANSWER: She needs to travel 84 miles each of the 3 days to complete the trip.
Hope this helps! :)
Answer:
y(t) = 2.5 e⁶ᵗ + 2.5 e⁻⁶ᵗ
Or
y(t) = 5 e⁻⁶ᵗ
Step-by-step explanation:
y(t) = c₁ e⁶ᵗ + c₂ e⁻⁶ᵗ
Let us find our value for y(t) that satisfies the conditions
1) y" - 36y = 0
y" = (d²y/dt²)
y(t) = c₁ e⁶ᵗ + c₂ e⁻⁶ᵗ
y' = (dy/dt) = 6c₁ e⁶ᵗ - 6c₂ e⁻⁶ᵗ
y" = (d/dt)(dy/dt) = 36c₁ e⁶ᵗ + 36c₂ e⁻⁶ᵗ
y" - 36y = 36c₁ e⁶ᵗ + 36c₂ e⁻⁶ᵗ - 36(c₁ e⁶ᵗ + c₂ e⁻⁶ᵗ) = 36c₁ e⁶ᵗ + 36c₂ e⁻⁶ᵗ - 36c₁ e⁶ᵗ - 36c₂ e⁻⁶ᵗ = 0.
The function satisfies this condition.
2) y(0) = 5
y(t) = c₁ e⁶ᵗ + c₂ e⁻⁶ᵗ
At t = 0
y(0) = c₁ e⁰ + c₂ e⁰ = 5
c₁ + c₂ = 5 (e⁰ = 1)
3) lim t→+[infinity] y(t)=0
y(t) = c₁ e⁶ᵗ + c₂ e⁻⁶ᵗ
y(t) = c₁ e⁶ᵗ + c₂ e⁻⁶ᵗ = 0 as t→+[infinity]
c₁ e⁶ᵗ = - c₂ e⁻⁶ᵗ as t→+[infinity]
c₁ = - c₂ e⁻¹²ᵗ as t→+[infinity]
e⁻¹²ᵗ = 0 as t→+[infinity]
c₁ = c₂ or c₁ = 0
Recall c₁ + c₂ = 5
If c₁ = 0, c₂ = 5
If c₁ = c₂, c₁ = c₂ = 2.5
y(t) = c₁ e⁶ᵗ + c₂ e⁻⁶ᵗ = 2.5 e⁶ᵗ + 2.5 e⁻⁶ᵗ
Or
y(t) = 5 e⁻⁶ᵗ
Answer: 5a+b
Step-by-step explanation:
Add zero
5a+b+0
5a+b
20% was added to the price of jeans to make it $42