x+y =27 sum of two numbers is 27
x=y+3 One of the numbers is three more than the other
substitute x=y+3 into the first equation
(y+3) + y = 27
combine like terms
2y + 3 = 27
subtract 3 from each side
2y = 24
divide by 2
y =12
x = y+3
x = 12+3
x =15
the two numbers are 12 and 15
Answer:
960 is the volume and 80 is the surface area.
Step-by-step explanation:
For the volume you multpliy 12*8*10=960
Then for surface area you multpily 10*8=80
Let t = number of hours
The first candle starts at 8 inches.
It burns at 7/10 inch per hour, so in t hours it burns (7/10)t inches.
After t hours, its length is 8 - (7/10)t
The second candle starts at 6 inches.
It burns at 1/5 inch per hour, so in t hours it burns (1/5)t inches.
After t hours, its length is 6 - (1/5)t
You want the lengths to be equal, so the equation is
8 - (7/10)t = 6 - (1/5)t
Answer:
Chon
Step-by-step explanation:
Answer:
3/5
Step-by-step explanation:
Firstly we will substitue x = 0 and we will realise that we have 0 in denominator. we will use Lhopitals rule.
![\frac{d}{dx} sin(3x)(cos(3x) = 3cos(6x)\\\frac{d}{dx} 5x = 5\\ \lim_{x \to \infty} \frac{3cos(6*x)}{5} = \frac{3cos(0)}{5} = \frac{3}{5}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%20sin%283x%29%28cos%283x%29%20%3D%203cos%286x%29%5C%5C%5Cfrac%7Bd%7D%7Bdx%7D%205x%20%3D%205%5C%5C%20%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B3cos%286%2Ax%29%7D%7B5%7D%20%3D%20%5Cfrac%7B3cos%280%29%7D%7B5%7D%20%3D%20%5Cfrac%7B3%7D%7B5%7D)