Answer:
98% is almost 100%, so we can see that the number of problems on the test can only be 1 or 2 more than 86.
The number of problems on the test is 87
Step-by-step explanation:
Careful; (dy/dx)^2 = x^2 cos^2(x) + 2x sin x cos x + sin^2(x).
<span>So, the arc length equals </span>
<span>∫(x = 0 to 2π) √[1 + (x^2 cos^2(x) + 2x sin x cos x + sin^2(x))] dx </span>
<span>= ∫(x = 0 to 2π) √[1 + x^2 cos^2(x) + x sin(2x) + sin^2(x)] dx, via double angle identity. </span>
<span>Let Δx = (2π - 0)/10 = π/5. </span>
<span>Using Simpson's Rule with n = 10, this integral approximately equals </span>
<span>((π/5)/3) * [f(0) + 4 f(π/5) + 2 f(2π/5) + 4 f(3π/5) + 2 f(4π/5) + 4 f(π) + 2 f(6π/5) + 4 f(7π/5) + 2 f(8π/5) + 4 f(9π/5) + f(2π)], </span>
<span>where f(x) = √[1 + x^2 cos^2(x) + x sin(2x) + sin^2(x)]. </span>
<span>------- </span>
<span>I hope this helps!</span>
Answer:
AB = BC = 2√2
Step-by-step explanation:
Start by focusing on the 45 degree angle. The unknown AB is the side adjacent to this 45 degree angle, and the hypotenuse is known to be 4.
Thus,
cos 45 degrees = adj / hyp = AB / 4, or
AB = 4 cos 45 degrees = 4 (1 / √2) =
4 √2
----------- * --------- = 2√2
√2 √2
Since this is a 45-45-90 triangle, the two shorter sides are equal, and so BC = 2√2 also.
Answer:97.1
Step-by-step explanation:
Let same number of hours = x,
since the salary earned is also the same, then
Salary of supervisor A = $25x
Salary of supervisor B = $20(30)+$30(x-30)
Equating
25x=600+30(x-30)
30x-25x=900-600
5x=300
x=60 hours
Check:
Salary of supervisor A = 25*60=1500
Salary of supervisor B = 20*30+30*(60-30)=600+900=1500, ok.
