Answer:
given that 
and that 
.
Step-by-step explanation:
The relation between the 
and the 
in this question is given by parametric equations (with 
as the parameter.)
Make use of the fact that:
.
Find 
and 
as follows:
![\begin{aligned} \frac{dx}{dt} &= \frac{d}{dt} [a\, (\cos(t) + \sin(t))] \\ &= a\, (-\sin(t) + \cos(t)) \\ &= a\, (\cos(t) - \sin(t))\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%20%5Cfrac%7Bdx%7D%7Bdt%7D%20%26%3D%20%5Cfrac%7Bd%7D%7Bdt%7D%20%5Ba%5C%2C%20%28%5Ccos%28t%29%20%2B%20%5Csin%28t%29%29%5D%20%5C%5C%20%26%3D%20a%5C%2C%20%28-%5Csin%28t%29%20%2B%20%5Ccos%28t%29%29%20%5C%5C%20%26%3D%20a%5C%2C%20%28%5Ccos%28t%29%20-%20%5Csin%28t%29%29%5Cend%7Baligned%7D)
.
as long as and .
![\begin{aligned} \frac{dy}{dt} &= \frac{d}{dt} [a\, (\sin(t) - \cos(t))] \\ &= a\, (\cos(t) - (-\sin(t))) \\ &= a\, (\cos(t) + \sin(t))\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%20%5Cfrac%7Bdy%7D%7Bdt%7D%20%26%3D%20%5Cfrac%7Bd%7D%7Bdt%7D%20%5Ba%5C%2C%20%28%5Csin%28t%29%20-%20%5Ccos%28t%29%29%5D%20%5C%5C%20%26%3D%20a%5C%2C%20%28%5Ccos%28t%29%20-%20%28-%5Csin%28t%29%29%29%20%5C%5C%20%26%3D%20a%5C%2C%20%28%5Ccos%28t%29%20%2B%20%5Csin%28t%29%29%5Cend%7Baligned%7D)
.
Calculate 
using the fact that 
. Assume that and :
.
Answer- 86 and 49
Step-by-step explanation: 86+49=135
86-49=37
Answer:
D.) 4x + y
Step-by-step explanation:
3x + x + y
Add 3
x and x
.
4
x + y
<span>Let the nickels be x and the dimes be y
x + y = 24
5x + 10y = 185
5x + 5y = 120
5y = 65
y=13
x=11
Answer: 11 nickels and 5 dimes</span>
