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Mathematics

1 answer:

MaRussiya [10]3 years ago

6 0

Answer: 6773.27

Step-by-step explanation: volume formula for the cone is pie(radius)^2(height/3) just plug in your information into the formula and viola

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Alabama Instruments Company has set up a production line to manufacture a new calculator. The rate of production of these calcul

anyanavicka [17]

Answer:

5536 calculators

Step-by-step explanation:

We integrate the function dx/dt to obtain the number of new calculators between beginning of the 3rd week and end of week 4. Note that beginning of 3rd week is the same as end of 2nd week. So, $\int\limits^4_2 {\frac{dx}{dt} } \, dx$ = $\int\limits^4_2 {5000 (1 - \frac{100}{(t +12)^{2} }) } \, dx$

Let u = t + 12, then $\frac{du}{dt}$ = 1. So, du = dt. We also change the limits of our integration. So, when t = 2, u = 2 + 12 = 14 and when t = 4, u = 4 + 12 = 16

Then $\int\limits^4_2 {5000(1 -\frac{100}{(t+12)^{2} } )} \, dx$ = ∫₁₄¹⁶ ${5000(1 -\frac{100}{u^{2} } )} \, du = 5000[ u + \frac{100}{u} ]$ ₁₄¹⁶ = $5000[16 + \frac{100}{16} - (14 + \frac{100}{14} )] = 5000 [16 - 14 + \frac{100}{16} - \frac{100}{14} ] = 5000 [2 + \frac{100}{16} - \frac{100}{14} ] = 5535.7$