Answer:
Penelope can read 6 pages in 5 minutes.
Step-by-step explanation:
You would use the equation 1.2x = P
P=how many pages x=how many minutes
1.2(5) = 6
She can read 6 pages in 5 minutes
Answer: Estimate : 1000 Exact : 942.83
Step-by-step explanation:
The estimate is 1000 because 96.8 is rounded to 100 and 9.74 is rounded to 10, so 100 times 10 is 1000. If you wanted the exact, then the exact is 942.83200, If you simplify this total, then the final answer is 942.83.
A subsidiary or intermediate theorem in an argument or proof.
Source: Wikipedia
Answer:
It would be 1/4 or 25%
Step-by-step explanation:
done this before
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
