Answer:
Step-by-step explanation:
A
No 24 is not the best number to use for the LCD, although it will work. 12 is much better because it is smaller.
B
Factor each number into it's primes.
24 =<u> 2*2*2</u>*3
32 = <u>2*2*2</u>*2*2
The highest common factor is 2*2*2 = 8
C
9/10 - 3/10 = 6/10 The denominator remains the same. The numerators get subtracted.
6/10 = 3/5 Two goes into both numerator and denominator of the answer. Therefore you can divide both 6 an 10 by 2
Answer:
11/6
Step-by-step explanation:
<u>Step 1: Convert to Improper fractions</u>
3 1/3 = 3*3/3 + 1/3 = 9/3 + 1/3 = 10/3
1 1/2 = 1*2/2 + 1/2 = 2/2 + 1/2 = 3/2
<u>Step 2: Make common denominators</u>
10/3 * 2/2 = 20/6
3/2 * 3/3 = 9/6
<u>Step 3: Subtract</u>
20/6 - 9/6
11/6
Answer: 11/6
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
Y intercept = when x = 0
Plug in x = 0
0 + 3y = 6
3y = 6, y = 2
Solution: a, (0,2)
