A factory produce bicycles at a rate of 110+0.5t^2-0.9t bicycles per week (t in weeks)

Mathematics

1 answer:

klasskru [66]3 years ago

3 0

Answer:

221

Step-by-step explanation:

Day 8 is the first day of the second week.

Day 21 is the last day of week 3.

We need to know the n umber of bicycles made from t = 1 to t = 3

The function is b(t) = 110 + 0.5t^2 - 0.9t, where t is in weeks.

We need to integrate the function with the limits of 1 to 3.

$\int_{1}^{3} (110 + 0.5t^2 - 0.9t) dt$

$\int_{1}^{3} (110 + \dfrac{t^2}{2} - \dfrac{9t}{10}) dt$

$= 110t + \dfrac{t^3}{6} - \dfrac{9t^2}{20} \Biggr|_{1}^{3}$

$= 330.45 - 109.72$

$= 220.7333$

Answer: 221

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Ajax is 5 and 1 fourth feet tall. His sister is 3 eighths foot shorter than Ajax How tall is Ajax Sister?

user100 [1]

Answer:

$4\frac{3}{4}$ feet tall

Step-by-step explanation:

Ajax is "5 and 1 fourth feet tall", which can be written as the mixed number $5\frac{1}{4}$ .

His sister is "3 eighths foot shorter", so she's 3/8 feet shorter than 5 1/4.

So, this is just a subtraction problem:

$5\frac{1}{4} -\frac{3}{8}$

To solve this, we want to convert 5 1/4 into an improper fraction, which is: $\frac{21}{4}$ . Now, we want to find a common denominator. In this case, that common denominator is 8, so $\frac{21}{4} =\frac{42}{8}$ .

Finally, we subtract 3/8 from 42/8: $\frac{42}{8} -\frac{3}{8} =\frac{39}{8}$ . So, Ajax's sister is 39/8 feet. Converting this into a mixed number, we have: 39/8 = 4 $\frac{6}{8} =4\frac{3}{4}$ .