First, you must know these formula d(e^f(x) = f'(x)e^x dx, e^a+b=e^a.e^b, and d(sinx) = cosxdx, secx = 1/ cosx
(secx)dy/dx=e^(y+sinx), implies <span>dy/dx=cosx .e^(y+sinx), and then
</span>dy=cosx .e^(y+sinx).dx, integdy=integ(cosx .e^(y+sinx).dx, equivalent of
integdy=integ(cosx .e^y.e^sinx)dx, integdy=e^y.integ.(cosx e^sinx)dx, but we know that d(e^sinx) =cosx e^sinx dx,
so integ.d(e^sinx) =integ.cosx e^sinx dx,
and e^sinx + C=integ.cosx e^sinxdx
finally, integdy=e^y.integ.(cosx e^sinx)dx=e^2. (e^sinx) +C
the answer is
y = e^2. (e^sinx) +C, you can check this answer to calculate dy/dx
The slope is : -5/2
The equation is : y=-5/2x + 5
Yes, No, Yes, Yes, No. You fill in (x,y) numbers into the equations and if it cancels out into 4, it would be 4=4. If it doesn’t become 4=4, it’s no.
Lets put everything into decimal form
2.5=2.5
3/4=0.75
107%=1.07
Order:
0.75, 1.07, 2.5
3/4, 107%, 2.5
2800
The math behind it:
800(Mph) x 3(Hours) = 2400(Miles traveled in 3hrs)
800(Mph) x 1/2(or .50hrs) = 400(Miles traveled in 1/2 an hr)
2400(Miles traveled in 3hrs) + 400(Miles traveled in 1/2 an hr) = 2800(Miles traveled in 3 and 1/2hrs)
Hope this helps! :) Have a nice day!
