Answer:
It will leave the sprinkler at speed of ![v_2=613.87m/sec](https://tex.z-dn.net/?f=v_2%3D613.87m%2Fsec)
Step-by-step explanation:
We have given internal diameter of the garden hose ![d_1=0.740in=1.8796cm](https://tex.z-dn.net/?f=d_1%3D0.740in%3D1.8796cm)
So radius ![r_1=\frac{d_1}{2}=\frac{1.8796}{2}=0.9398cm](https://tex.z-dn.net/?f=r_1%3D%5Cfrac%7Bd_1%7D%7B2%7D%3D%5Cfrac%7B1.8796%7D%7B2%7D%3D0.9398cm)
So area ![A_1=\pi r_1^2=3.14\times 0.9398^2=2.7733cm^2](https://tex.z-dn.net/?f=A_1%3D%5Cpi%20r_1%5E2%3D3.14%5Ctimes%200.9398%5E2%3D2.7733cm%5E2)
Water in the hose has a speed of 4 ft/sec
So ![v_1=4ft/sec=121.92cm/sec(As\ 1ft/sec\ =30.48cm/sec)](https://tex.z-dn.net/?f=v_1%3D4ft%2Fsec%3D121.92cm%2Fsec%28As%5C%201ft%2Fsec%5C%20%3D30.48cm%2Fsec%29)
Number of holes n = 36
Diameter of each hole ![d_2=0.1397cm](https://tex.z-dn.net/?f=d_2%3D0.1397cm)
So radius ![r_2=0.0698cm](https://tex.z-dn.net/?f=r_2%3D0.0698cm)
So area ![A_2=\pi r^2=3.14\times 0.0698^2=0.0153cm^2](https://tex.z-dn.net/?f=A_2%3D%5Cpi%20r%5E2%3D3.14%5Ctimes%200.0698%5E2%3D0.0153cm%5E2)
From continuity equation
![A_1v_1=nA_2v_2](https://tex.z-dn.net/?f=A_1v_1%3DnA_2v_2)
![2.7733\times 121.92=36\times 0.0153\times v_2](https://tex.z-dn.net/?f=2.7733%5Ctimes%20121.92%3D36%5Ctimes%200.0153%5Ctimes%20v_2)
![v_2=613.87m/sec](https://tex.z-dn.net/?f=v_2%3D613.87m%2Fsec)
15. 2x-5=-20
2x=-15; Add positive 5 on both sides to isolate x.
x=
; Divide 2 on both sides to find the value of x.
17.
=-9
9x=-36; Multiply positive 4 on both sides of the equation.
x==-4; Divide 9 on both sides of the equation to find the value of x.
Pay attention here because I'm adding an extra letter to our circle to help keep track of the values in our formula. OUTSIDE of the intercepted arc I'm adding the point E. So the major arc is arc BEG and the minor arc is arc BG. The formula then for us is ∠
![BFG= \frac{1}{2}(arcBEG-arcBG)](https://tex.z-dn.net/?f=BFG%3D%20%5Cfrac%7B1%7D%7B2%7D%28arcBEG-arcBG%29%20)
. We just don't have values for the arcs yet. If the measure of the central angle is 4x+238, then the measure of arcBG is also 4x+238. Around the outside of the circle is 360°. So we will use it in an expression. ArcBEG=360-(4x+238). Fitting that into our formula we have
![2x+146= \frac{1}{2}[(360-4x-238)-(4x+238)]](https://tex.z-dn.net/?f=2x%2B146%3D%20%5Cfrac%7B1%7D%7B2%7D%5B%28360-4x-238%29-%284x%2B238%29%5D%20)
. Doing all the simplifying inside there we have
![2x+146= \frac{1}{2}(122-4x-4x-238)](https://tex.z-dn.net/?f=2x%2B146%3D%20%5Cfrac%7B1%7D%7B2%7D%28122-4x-4x-238%29%20)
and
![2x+146= \frac{1}{2}(-8x-116)](https://tex.z-dn.net/?f=2x%2B146%3D%20%5Cfrac%7B1%7D%7B2%7D%28-8x-116%29%20)
. Multiply both sides by 2 to get rid of the fraction: 4x+292=-8x-116. Combine like terms to get 12x = -408 and divide to solve for x. x = -34. Fourth choice down from the top.
Answer:
2.78hrs
Step-by-step explanation:
Volume of water in the pool =πr2h
V = 3.142 * 2.5² *1.7
V = 33.38m³
Emptying the pool out at 12m³ per hour
= 33.38/12
= 2.78hrs
Assignment: ![\bold{Solve \ Equation: \ 7^2 \ + \ 4^3 \ \div 2^5}](https://tex.z-dn.net/?f=%5Cbold%7BSolve%20%5C%20Equation%3A%20%5C%207%5E2%20%5C%20%2B%20%5C%204%5E3%20%5C%20%5Cdiv%202%5E5%7D)
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Answer: ![\boxed{\bold{51}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cbold%7B51%7D%7D)
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Explanation: ![\downarrow\downarrow\downarrow](https://tex.z-dn.net/?f=%5Cdownarrow%5Cdownarrow%5Cdownarrow)
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[ Step One ] Apply PEMDAS Order Of Operations
Note: ![\bold{PEMDAS: \ Parenthesis, \ Exponents, \ Multiply, \ Divide, \ Add, \ Subtract}](https://tex.z-dn.net/?f=%5Cbold%7BPEMDAS%3A%20%5C%20Parenthesis%2C%20%5C%20Exponents%2C%20%5C%20Multiply%2C%20%5C%20Divide%2C%20%5C%20Add%2C%20%5C%20Subtract%7D)
![\bold{7^2: \ 49}](https://tex.z-dn.net/?f=%5Cbold%7B7%5E2%3A%20%5C%2049%7D)
[ Step Two ] Rewrite Equation
![\bold{49+64\div \:2^5}](https://tex.z-dn.net/?f=%5Cbold%7B49%2B64%5Cdiv%20%5C%3A2%5E5%7D)
[ Step Three ] Calculate Exponents
![\bold{4^3: \ 64}](https://tex.z-dn.net/?f=%5Cbold%7B4%5E3%3A%20%5C%2064%7D)
[ Step Four ] Rewrite Equation
![\bold{49+64\div \:2^5}](https://tex.z-dn.net/?f=%5Cbold%7B49%2B64%5Cdiv%20%5C%3A2%5E5%7D)
[ Step Five ] Calculate Exponents
![\bold{2^5: \ 32}](https://tex.z-dn.net/?f=%5Cbold%7B2%5E5%3A%20%5C%2032%7D)
[ Step Six ] Rewrite Equation
![\bold{49+64\div \:32}](https://tex.z-dn.net/?f=%5Cbold%7B49%2B64%5Cdiv%20%5C%3A32%7D)
[ Step Seven ] Divide
![\bold{64\div \:32: \ 2}](https://tex.z-dn.net/?f=%5Cbold%7B64%5Cdiv%20%5C%3A32%3A%20%5C%202%7D)
[ Step Eight ] Rewrite Equation
![\bold{49+2}](https://tex.z-dn.net/?f=%5Cbold%7B49%2B2%7D)
[ Step Nine ] Add
![\bold{51}](https://tex.z-dn.net/?f=%5Cbold%7B51%7D)
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