Math

http://baronsledjoys.tumblr.com/post/93067055294/crowdsourcing-for-calculus-help

This post explains everything!

baronsledjoys, I emailed you like you wanted! Ask if you need more help ok!

breakdown of a free response question from the calc 2013 exam for those who intend to take the exam in the future

Could you break down dy/dx=e^x*y^2 for me?
Anonymous

im guessing you mean integrating it so here it goes:

dy/dx=e^x*y^2

get one side in terms of y and the other in terms of x

dy/y^2 = e^xdx

integrate both sides

-1/y = e^x + C

rearrange to get in terms of y

-y = e^(-x) + C

y = -e^(-x) + C

[this is all assuming that dy/dx=e^x*y^2 = (e^x)(y^2) and not e^(xy^2)]

good resource for linear programming!


lucid-bones:
Help?

Variables:
A grade = A = 1792
B grade = B = 1600
Economy blend = E
Superior blend = S
Profit = P = E+3S (what you want to maximize)
Restrictions:
A grade: (4/16)E + (8/16)S </= 1792 
0.25E + .5S </= 1792
(4 of the 16 ounces in 1 pound of E are from A; 8 of the 16 ounces in one pound of S are from A; the total amount of A cannot exceed 1792 ounces)
B grade: (10/16)E + (2/16)S </= 1600
0.625E + 0.125S </= 1600
(10 of the 16 ounces in E are from B; 2 of the 16 ounces in S are from B; the total amount of B cannot exceed 1600 ounces)
E > 0
S > 0
Solve with substitution:
0.25E + .5S = 1792
.5S = 1792 – 0.25E
S = 3584 – 0.5E
0.625E + 0.125S = 1600
0.625E + (0.125)(3584 – 0.5E) = 1600
0.5625E + 448 = 1600
0.5625E = 1152
E = 2048 ounces —> 2048/16 = 128 packages of economy blend
S = 3584 – (0.5)(2048) = 3584 – 1024 = 2560 ounces —> 2560/16 = 160 packages of superior blend

lucid-bones:

Help?

Variables:

A grade = A = 1792

B grade = B = 1600

Economy blend = E

Superior blend = S

Profit = P = E+3S (what you want to maximize)

Restrictions:

A grade: (4/16)E + (8/16)S </= 1792 

0.25E + .5S </= 1792

(4 of the 16 ounces in 1 pound of E are from A; 8 of the 16 ounces in one pound of S are from A; the total amount of A cannot exceed 1792 ounces)

B grade: (10/16)E + (2/16)S </= 1600

0.625E + 0.125S </= 1600

(10 of the 16 ounces in E are from B; 2 of the 16 ounces in S are from B; the total amount of B cannot exceed 1600 ounces)

E > 0

S > 0

Solve with substitution:

0.25E + .5S = 1792

.5S = 1792 – 0.25E

S = 3584 – 0.5E

0.625E + 0.125S = 1600

0.625E + (0.125)(3584 – 0.5E) = 1600

0.5625E + 448 = 1600

0.5625E = 1152

E = 2048 ounces —> 2048/16 = 128 packages of economy blend

S = 3584 – (0.5)(2048) = 3584 – 1024 = 2560 ounces —> 2560/16 = 160 packages of superior blend

a cafe gives away prizes. Large ones cost the cafe 125 and small prizes costs 40. The cafe cannot spend more than 1500. How many of each prize can be awarded. PLEASE HELP IM KIND OF STUCK ON THIS. THANKS A LOT!!:)
Anonymous

it can give away 4 large prizes and 25 small prizes

(4)(125) = 500

(25)(40) = 1000

500+1000 = 1500

xysciences:

Sine, Cosine, and the resulting unit circle. 

xysciences:

Sine, Cosine, and the resulting unit circle. 

I got a 5 (on the ab exam)! :') i'm in shock because i'm terrible at math.. thanks for the help! :)
Anonymous

Congratulations! I’m glad I could help, and keep up the good work!!

sum 880(1/4)^(i-1); the sum is 1173

sum 880(1/4)^(i-1); the sum is 1173

(-4)[(1-(-6)^7)/(1-(-6))] = -159964

(-4)[(1-(-6)^7)/(1-(-6))] = -159964