a factory bottles 511 bottles of juice in 7 minutes. find the factory's unit rate of bottles per minute

Mathematics

2 answers:

ELEN [110]3 years ago

6 0

The answer would be 73. if you don't believe me then divide 511 by 7 or multiply 73 by 7. your welcome

ziro4ka [17]3 years ago

6 0

Answer: The factory bottles 73 bottles of juice per minute.

Step-by-step explanation: Given that a factory bottles 511 bottles of juice in 7 minutes.

We are to find the factory's unit rate of bottles per minute.

We will be using the UNITARY method to solve the given problem.

We have

in 7 minutes, number of bottles of juice bottle by the factory = 511.

So, in 1 minute, the number of bottles of juice bottle by the factory is given by

$n=\dfrac{511}{7}=73.$

Thus, the factory bottles 73 bottles of juice per minute.

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a cyclist rides his bike at a speed of 27 miles per hour. what is the speed in feet per second? how many feet will the cyclist t

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Step-by-step explanation:

4 0

3 years ago

Integration: How would I get to this answer?

Scrat [10]

Given that $y$ attains a maximum at $x=1$ , it follows that $y'=0$ at that same point. So integrating once gives

$\displaystyle\int\frac{\mathrm d^2y}{\mathrm dx^2}\,\mathrm dx=\int-8x\,\mathrm dx$
$\dfrac{\mathrm dy}{\mathrm dx}=-4x^2+C_1$
$\implies -4(1)^2+C_1=0\implies C_1=4$

and so the first derivative is $y'=-4x^2+4$ .

Integrating again, you get

$\displaystyle\int\frac{\mathrm dy}{\mathrm dx}\,\mathrm dx=\int(-4x^2+4)\,\mathrm dx$
$y=-\dfrac43x^3+4x+C_2$

You know that this curve passes through the point (2, -1), which means when $x=2$ , you have $y=-1$ :

$-1=-\dfrac43(2)^3+4(2)+C_2$
$\implies C_2=\dfrac53$

and so

$y=-\dfrac43x^3+4x+\dfrac53$