7.) (x, y) —> (1/2*x, 1/2*y)
<span>, y+2 = (x^2/2) - 2sin(y)
so we are taking the derivative y in respect to x so we have
dy/dx use chain rule on y
so y' = 2x/2 - 2cos(y)*y'
</span><span>Now rearrange it to solve for y'
y' = 2x/2 - 2cos(y)*y'
0 = x - 2cos(y)y' - y'
- x = 2cos(y)y' - y'
-x = y'(2cos(y) - 1)
-x/(2cos(y) - 1) = y'
</span><span>we know when f(2) = 0 so thus y = 0
so when
f'(2) = -2/(2cos(0)-1)
</span><span>2/2 = 1
</span><span>f'(2) = -2/(2cos(0)-1)
cos(0) = 1
thus
f'(2) = -2/(2(1)-1)
= -2/-1
= 2
f'(2) = 2
</span>
So what you need to start with is taking the x from both sides as adding 12 to them. Then, you move the 27 over 4 decimals.
1.50 that should be it and i dont know how to show my work on a computer SORRY.
Let
x------> amount of <span> big marbles in the box
y------> </span>amount of small marbles in the box
R----> amount of small marbles that are red in the box
B----> amount of small marbles that are blue in the box
we know that
x=45+(3/4)*x----> x-(3/4)*x=45----> x/4=45-----> x=180
R+B=y-----> equation 1
R=(2/5)*y---> equation 2
B=(3/5)*y---> equation 3
B=R+24----> equation 4
substitute equation 2 in equation 1
[(2/5)*y]+B=y----> equation 5
substitute equation 2 in equation 4
B=[(2/5)*y]+24----> equation 6
resolve the system
[(2/5)*y]+B=y---> multiply by 5----> 2y+5B=5y----> 3y=5B
B=[(2/5)*y]+24----> multiply by 5----> 5B=2y+120
using a graph tool
see the attached figure
the solution is
B=72
y=120
R=y-B----> R=48
total marbies=x+y-----> 180+120-----> 300
tota; big marbies=180
<span>percent of the marbles are big marbles
</span>if 100%-----------> 300
X----------------> 180
x=180*100/300-----> x=60%
the answer is60%