D=number of drinks
p=number of bags of popcorn
75=6d+8p
100.50=12d+10p
multiply first equation by -2 and add to first
-49.50=-6p
divide -6
8.25=p
sub
100.50=12d+10p
100.50=12d+82.50
minus 82.50
18=12d
divide 12
1.50=d
$1.50 per drink
YOU BETTER READ AND LEARN AND NOT JUST USE THIS TO PASS, LEARN
So you would plug in 0 for a from the beginning since this is numerical slope definition of a derivative
Answer:
dddddddddddddddddddddddd could be rewritten as d^24 because d*d*d*d*d*d*d... = d^24
Step-by-step explanation:
When we multiply all of the d's together we get .
The answer is (1/2)xe^(2x) - (1/4)e^(2x) + C
Solution:
Since our given integrand is the product of the functions x and e^(2x), we can use the formula for integration by parts by choosing
u = x
dv/dx = e^(2x)
By differentiating u, we get
du/dx= 1
By integrating dv/dx= e^(2x), we have
v =∫e^(2x) dx = (1/2)e^(2x)
Then we substitute these values to the integration by parts formula:
∫ u(dv/dx) dx = uv −∫ v(du/dx) dx
∫ x e^(2x) dx = (x) (1/2)e^(2x) - ∫ ((1/2) e^(2x)) (1) dx
= (1/2)xe^(2x) - (1/2)∫[e^(2x)] dx
= (1/2)xe^(2x) - (1/2) (1/2)e^(2x) + C
where c is the constant of integration.
Therefore,
∫ x e^(2x) dx = (1/2)xe^(2x) - (1/4)e^(2x) + C