Answer:
a solution is 1/2 *tan⁻¹ (2*y) = - tan⁻¹ (x²) + π/4
Step-by-step explanation:
for the equation
(1 + x⁴) dy + x*(1 + 4y²) dx = 0
(1 + x⁴) dy = - x*(1 + 4y²) dx
[1/(1 + 4y²)] dy = [-x/(1 + x⁴)] dx
∫[1/(1 + 4y²)] dy = ∫[-x/(1 + x⁴)] dx
now to solve each integral
I₁= ∫[1/(1 + 4y²)] dy = 1/2 *tan⁻¹ (2*y) + C₁
I₂= ∫[-x/(1 + x⁴)] dx
for u= x² → du=x*dx
I₂= ∫[-x/(1 + x⁴)] dx = -∫[1/(1 + u² )] du = - tan⁻¹ (u) +C₂ = - tan⁻¹ (x²) +C₂
then
1/2 *tan⁻¹ (2*y) = - tan⁻¹ (x²) +C
for y(x=1) = 0
1/2 *tan⁻¹ (2*0) = - tan⁻¹ (1²) +C
since tan⁻¹ (1²) for π/4+ π*N and tan⁻¹ (0) for π*N , we will choose for simplicity N=0 . hen an explicit solution would be
1/2 * 0 = - π/4 + C
C= π/4
therefore
1/2 *tan⁻¹ (2*y) = - tan⁻¹ (x²) + π/4
Answer:
$1.69
Step-by-step explanation:
Half a dollar = $0.50
Eight dimes = $0.80
Six nickels = $0.30
Nine pennies = $0.09
Total = $0.50 + $0.80 + $0.30 + $0.09 = $1.69
Answer:
Jim reached a greater depth by one foot, as he started 12 feet below the surface.
Step-by-step explanation:
Jim
12 feet+17 feet = 29
29-3 feet (rose 3 feet) = 26
26+8= 34 feet
Carla
0 feet (surface)+ 19 feet= 19
19-3 feet= 16
16+17= 33 feet
Answer:
Option Y is correct.
Step-by-step explanation:
We are given the table representing the relation between new students and returning students for difference classes.
It is required to form the relative frequency table for the given situation.
So, relative frequency table is obtained by dividing the valued by the total number of values in the data set.
<em>Thus, we will get the relative frequency table by dividing the given table values by 500.</em>
Hence, we will get the following table,
New Students Returning Students Total
10th 0.01 0.34 0.35
11th 0.006 0.324 0.33
12th 0.004 0.316 0.32
Total 0.02 0.98 1
Thus, option Y is correct.
<span>X+(X+2)=32
2X+2=32
2X=32-2
2X=30
X=30/2
X=15 ANSWER FOR THE FIRST ODD NUMBER.
15+2=17 FOR THE OTHER ODD NUMBER.
15*17=255 ANSWER FOR THE PRODUCT OF THESE 2 ODD NUMBERS.</span>
