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andrew11 [14]
2 years ago
9

A baker has 41.6 pounds of flour in a large bag. She wants to divide the flour into equal portions that weigh 2.6 pounds each. H

ow many portions can the baker make from the original amount of flour?
​
Mathematics
1 answer:
olga nikolaevna [1]2 years ago
3 0

41.6/2.6 = 16

therefore into 16 parts

hope it helps...!!!

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A metal cylinder can with an open top and closed bottom is to have volume 4 cubic feet. Approximate the dimensions that require
Aleksandr-060686 [28]

Answer:

r\approx 1.084\ feet

h\approx 1.084\ feet

\displaystyle A=11.07\ ft^2

Step-by-step explanation:

<u>Optimizing With Derivatives </u>

The procedure to optimize a function (find its maximum or minimum) consists in :

  •  Produce a function which depends on only one variable
  •  Compute the first derivative and set it equal to 0
  •  Find the values for the variable, called critical points
  •  Compute the second derivative
  •  Evaluate the second derivative in the critical points. If it results positive, the critical point is a minimum, if it's negative, the critical point is a maximum

We know a cylinder has a volume of 4 ft^3. The volume of a cylinder is given by

\displaystyle V=\pi r^2h

Equating it to 4

\displaystyle \pi r^2h=4

Let's solve for h

\displaystyle h=\frac{4}{\pi r^2}

A cylinder with an open-top has only one circle as the shape of the lid and has a lateral area computed as a rectangle of height h and base equal to the length of a circle. Thus, the total area of the material to make the cylinder is

\displaystyle A=\pi r^2+2\pi rh

Replacing the formula of h

\displaystyle A=\pi r^2+2\pi r \left (\frac{4}{\pi r^2}\right )

Simplifying

\displaystyle A=\pi r^2+\frac{8}{r}

We have the function of the area in terms of one variable. Now we compute the first derivative and equal it to zero

\displaystyle A'=2\pi r-\frac{8}{r^2}=0

Rearranging

\displaystyle 2\pi r=\frac{8}{r^2}

Solving for r

\displaystyle r^3=\frac{4}{\pi }

\displaystyle r=\sqrt[3]{\frac{4}{\pi }}\approx 1.084\ feet

Computing h

\displaystyle h=\frac{4}{\pi \ r^2}\approx 1.084\ feet

We can see the height and the radius are of the same size. We check if the critical point is a maximum or a minimum by computing the second derivative

\displaystyle A''=2\pi+\frac{16}{r^3}

We can see it will be always positive regardless of the value of r (assumed positive too), so the critical point is a minimum.

The minimum area is

\displaystyle A=\pi(1.084)^2+\frac{8}{1.084}

\boxed{ A=11.07\ ft^2}

8 0
2 years ago
In which quadrant is ( 5,4 ) is located<br>this is hw and i wanna get a good grade plz helpp!!!!
Andre45 [30]
(5,4)

On a system of 2 perpendicular axis with O as origine, the pair (5,4) means:

5 is the distance from the origin O and situated on x-axis (on the right of O)
4 is the distance from the origin O and situated on y-axis (above O)

Then the pair (5,4) is situated in the 1st Quadrant

8 0
3 years ago
What is the difference between squaring and taking the square root ?
wel

Answer:

Squares are the numbers, generated after multiplying a value by itself. Whereas square root of a number is value which on getting multiplied by itself gives the original value.

Step-by-step explanation:

Hence, both are vice-versa methods. For example, the square of 2 is 4 and the square root of 4 is 2.

8 0
2 years ago
Last year, the numbers of skateboards produced per day at a certain factory were normally distributed with a mean of 20,500 skat
alisha [4.7K]

Answer:

This can be solved by using the empirical rule for a normal distribution.

Step-by-step explanation:

A. The number of skateboards given is one standard deviation above the mean. Approximately 68% of the data points lie within the range plus and minus one standard deviation of the mean. Therefore the required percentage is:

68 + 16 = 84%.

B. The given number of skateboards is two standard deviations above the mean. Approximately 95% of the data points lie within the range plus and minus two standard deviations of the mean. Therefore the required percentage is:

5/2 = 2.5%

C.The given number of skateboards is one standard deviations below the mean. Therefore the required percentage is:

16%.

8 0
3 years ago
Guys... Whats 2+2 :DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
Elis [28]

Answer:

4

Step-by-step explanation:

ok

6 0
2 years ago
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