Given that,
The diameter of a tennis ball, d = 2.7 inches
Radius, r = 1.35 inches
The dimensions of the storage shed is 14 feet wide, 15 feet long, and 10 feet high.
Volume of the shed is, V = lbh
![V=14\times 15\times 10\\\\V=2100\ \text{feet}^3](https://tex.z-dn.net/?f=V%3D14%5Ctimes%2015%5Ctimes%2010%5C%5C%5C%5CV%3D2100%5C%20%5Ctext%7Bfeet%7D%5E3)
We can convert radius from inches to feet :
1 foot = 12 inches
Radius, r = 0.1125 feet
Let there are x number of tennis balls that can fit in the shed. So,
![x\times V_b=V_s\\\\\text{Where}\ V_b\ \text{and}\ V_s\ \text{volume of ball and shed}\\\\x=\dfrac{V_s}{\dfrac{4}{3}\pi r^3}\\\\x=\dfrac{2100}{\dfrac{4}{3}\pi \times (0.1125)^3}](https://tex.z-dn.net/?f=x%5Ctimes%20V_b%3DV_s%5C%5C%5C%5C%5Ctext%7BWhere%7D%5C%20V_b%5C%20%5Ctext%7Band%7D%5C%20V_s%5C%20%5Ctext%7Bvolume%20of%20ball%20and%20shed%7D%5C%5C%5C%5Cx%3D%5Cdfrac%7BV_s%7D%7B%5Cdfrac%7B4%7D%7B3%7D%5Cpi%20r%5E3%7D%5C%5C%5C%5Cx%3D%5Cdfrac%7B2100%7D%7B%5Cdfrac%7B4%7D%7B3%7D%5Cpi%20%5Ctimes%20%280.1125%29%5E3%7D)
x = 352105.75 balls
or
x = 352106 balls
Hence, 352106 balls can fit in the storage shed.
Answer:
Solution are
i) ![x = 0, \pi, \frac{3\pi}{2} , 2\pi](https://tex.z-dn.net/?f=x%20%3D%200%2C%20%5Cpi%2C%20%5Cfrac%7B3%5Cpi%7D%7B2%7D%20%2C%202%5Cpi)
Step-by-step explanation:
1) (sinx)(cosx) =0
sin2x/2 =0
2x =0, 2pi, 3pi, 4pi
Hence ![x = 0, \pi, \frac{3\pi}{2} , 2\pi](https://tex.z-dn.net/?f=x%20%3D%200%2C%20%5Cpi%2C%20%5Cfrac%7B3%5Cpi%7D%7B2%7D%20%2C%202%5Cpi)
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2) ![cos2x + 2 cos x + 1 = 0\\2cos^2 x +2cosx +1 =0\\(cosx+1)^2 =0\\cosx =-1\\x=\pi](https://tex.z-dn.net/?f=cos2x%20%2B%202%20cos%20x%20%2B%201%20%3D%200%5C%5C2cos%5E2%20x%20%2B2cosx%20%2B1%20%3D0%5C%5C%28cosx%2B1%29%5E2%20%3D0%5C%5Ccosx%20%3D-1%5C%5Cx%3D%5Cpi)
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Take an example: The salary per hour:
Assume x (variable) is the number of hours worked and assume THAT THE RATE PER HOUR IS $10, then:
If you work x hours at the hourly rate of$10, you will generate an income,
say, y that is equal the number of hours worked by the rate per hour, that is:
y = 10.x. The more hour(x) you work, the more income(y) you get.
Hence we created a relationship between y and x , or in English, between the earning and the number of hours worked.
Moreover y depends on x, if there is no x, there is no y and if x increases, y increases. However x is an INDEPENDENT variable because you can
give to x any number & y will follow
I don’t know the rest, but I think the 1st and 3rd ones are true! I hope this helps some, I’m sorry if it’s incorrect!