Answer:
x ≈ 57.8°
Step-by-step explanation:
The relevant trig relation is the one that relates the side adjacent to the angle to the hypotenuse and the angle:
Cos = Adjacent/Hypotenuse
cos(x) = 8/15
The value of x is found using the inverse cosine function:
x = arccos(8/15)
x ≈ 57.8°
My explanation is attached below.
<span><span><span>(3x−2)/</span><span>(x−1<span>)^2</span></span></span>=<span>A/(<span>x−1) </span></span>+ <span><span>B/x</span><span>(x−1<span>)^2
</span></span></span> =[<span><span>A(x−1)+Bx</span><span>(x−1<span>)] / 2</span></span></span></span>
3x-2=A(x-1)+Bx
3x-2=x(A+B)-A
A+B=3
-A=-2=>A=2
A+B=3=>2+B=3=>B=1
lets check our partial fraction
we have
<span><span><span>2/(<span>x−1) </span></span>+ <span>x/<span>(x−1<span>)^2 </span></span></span>= [<span><span>2(x−1)+x] / </span><span>(x−1<span>)^2
</span></span></span> =(<span><span>3x−2) / </span><span>(x−1<span>)^2</span></span></span></span></span>
Goal= 800 yards.
For every 200 yards he pushes in an hour, he ends up resting and it goes back a 100 yards the next hour after.
so (200-100)+(200-100)+(200-100)+(200-100)+(200-100)+(200-100)+(200).
2 hours + 2 hours + 2 hours + 2 hours + 2 hours + 2 hours + 1 hour = 13 hours.
So it will take 13 hours for Mr. Bean to push up his car up to the gas station.