so basically what you would have to do is set up your numbers. it would look something like this. 68
× 49
-------------
and would then multiply 9 by 8, 9 by 6. put it down below the line while making sure to carry the numbers if need be. then do the same with the 4 times 8, and 4 by 6.
Answer:
The volume of paint that covers the whole car is
gallons or one and a quarter gallons.
Step-by-step explanation:
Let the volume of paint required to cover whole car be 'x'.
Given:
Volume of paint to cover one-fifth of a car = one-fourth of a gallon.
We use unitary method to determine the volume of paint required.
∵ One-fifth of a car requires paint = ![\frac{1}{4}\ gal](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%5C%20gal)
∴ Whole volume of car requires paint = ![\frac{\frac{1}{4}}{\frac{1}{5}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cfrac%7B1%7D%7B4%7D%7D%7B%5Cfrac%7B1%7D%7B5%7D%7D)
![=\frac{1}{4}\times \frac{5}{1}\\=\frac{5}{4}\\=1\frac{1}{4}\ gal](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B4%7D%5Ctimes%20%5Cfrac%7B5%7D%7B1%7D%5C%5C%3D%5Cfrac%7B5%7D%7B4%7D%5C%5C%3D1%5Cfrac%7B1%7D%7B4%7D%5C%20gal)
Therefore, the volume of paint that covers the whole car is
gallons or one and a quarter gallons.
<span>y'' + 5y' + 6y = 2e^t is a second order differential equation with solution y = Ae^mt + Be^nt + p(t); where m and n are the roots of the quadratic equation x^2 + 5x + 6 = 0, and p(t) is the particular solution.
x = -2 and x = -3
y = Ae^-2t + Be^-3t + p(t)
For the particular solution, Ke^t + 5Ke^t + 6Ke^t = 2e^t
12K = 2
K = 1/6
Therefore, solution is </span>
<span>y = Ae^-2t + Be^-3t + 1/6 e^t
</span>
Let x be the amount Amy used
Let 3x be the amount Mary used
Let 20-2 be the total amount used
3x + x = 20-2
4x=18
x=4.5
Amy use 4.5 yards of material.
Hope this helped!