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
3 hours is 180 minutes.
She rested for 20 additional minutes, thus it will take her 200 minutes.
Answer:
y = -5x - 21
Step-by-step explanation:
Given in the question,
equation of a parallel line
y = -5x + 6
point through which it passes
(-4,-1)
Step1
Find the gradient of the equation given, as it is parallel so it will have same gradient
equation of straight line
y = mx + c
where m is gradient
c is y intercept
y = -5x + 6
m =-5
Step2
Find y-intercept
-1 = -5(-4) + c
-1 = 20 + c
c = -20 - 1
c = -21
Step3
form the equation
y = -5x - 21
Answer:
336 ways
Step-by-step explanation:
The digits are 1, 2, 2, 4, 5, 5, 6, and 2 that is total eight digits.
The number 654-5222 contains 7 digits.
So, we have find The number of permutations for choosing 7 digits from 8 digits given above.
This can be done in following ways
= 
= 336 ways
Answer:
The answer to your question is 7 times
Step-by-step explanation:
Data
Percent of accuracy = 35%
Times she is at bat = 20
Times she hit the ball = ?
Process
1.- Use proportions to solve this problem
20 times will be the 100% because is the total number of times she is at bat.
20 times ------------------ 100%
x ------------------ 35%
x = (35 x 20) / 100
x = 700 / 100
x = 7
2.- Conclusion
From 20 times she is at bat, she will hit the ball 7 times.
