The answer to the first question is 7(3.14)/6.
the answer to the second question is quadrant 2
1. You need to make a proportion
2. Your proportion would be 8 over 10 equals X over 15
3. Your equation would be 10x=15(8)
4. 15x8=125
5. 10x=125
6. you would divide 125 by 10
7. thats your answer
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
By applying z-score formula we got that if a reporter determines a mean order time of 63 minutes then value o Z is 1.19
<h3>What is standard deviation?</h3>
Standard deviation is a number used to tell how measurements for a group are spread out from the average (mean), or expected value
Here given that
The owners of an eyeglass store claim that they fill customers' orders, on average, in 60 minutes with a standard deviation of 15. 9 minutes. Based on a random sample of 40 orders, a reporter determines a mean order time of 63 minutes
mean=μ=60
standard deviation=σ=15.9
number of sample=n=40
Now we can calculate z by z-score formula as
By applying z-score formula we got that if a reporter determines a mean order time of 63 minutes then value o Z is 1.19
To learn more about standard deviation visit :brainly.com/question/12402189