Dy/dx = (ycos(x))/(1 + y²)
(1 + y²)/y dy = cos(x) dx
(1/y + y) dy = cos(x) dx
Integrating:
ln(y) + y²/2 = sin(x) + c
ln(1) + 1/2 = sin(0) + c
c = 1/2
Thus,
ln(y) + y²/2 = sin(x) + 1/2
Answer: 2184
because when you multiply 14 times 12 times 13 you get 2184
Answer:
x-intercept: 
y-intercept: 
Step-by-step explanation:
To find the x-intercept, substitute in
for
and solve for
.


Simplify 2(0): 
Subtract 0 - 3 = -3: 
Subtract 7 from both sides: 
Simplify: 
Divide both sides by -4 

To find the y-intercept, substitute in
for
and solve for
.


Switch sides: 
Simplify -4(0): 
Add 3 to both sides: 
Simplify: 
Divide both sides by 2: 

Answer:
first get the total ratio; 2 + 5 = 7
so the fraction of blue marbles is 5/7
then assume the number of total marbles to be k
then use the expression;
5/7*k = 65
7*5/7 * k = 65*7
5k =455
5/5k = 455/5
k = 91
then calculate the number if red marbles from;
x = 2/7*91
x = 26
Therefore there are 26 red marbles.
Answer:
8624.03
Step-by-step explanation:
(8×1,000)+(6×100)+(2×10)+(4×1)+(3×1/100)
8000+600+20+4+.03
8624.03