Answer:
The first store
Step-by-step explanation:
Given data
Let us find the unit cost on each sale
A price for pineapples is $5 for two pineapples
Unit cost per pineapple
=5/2
=$2.5 per pineapple
price for pineapple is $8 for four pineapples
Unit cost
=8/4
=$2 per pineapple
Hence the first store offers the lowest price per pineapple $2.5
Answer: 35
Explanation: If patty has $21, and $3 is the price for 5 hat pins, then: 21/3=7, so she can buy 7 packages which cost $3 and contain 5 pins, and because the question asked the number of pins, we will multiply 7 • 5 and that equals 35
Answer:
Step-by-step explanation:
Jim drank 2 and 4/5 orange juice
2and 4/5=14/5 orange juice
jack drank 1and 1/10 less than Jim= 11/10 less than Jim
I introduce the whole numbers into the fractions
we will convert the number 14/5 into a fraction that has the denominator 10, by multiplying by 2 both numerator and denominator
(14/5 )*2=28/10
Now we can find out how much juine Jack drank
28/10- 11/10= 17/10
so Jack drank 17/10 orange juice , the fraction can be written also as
1 and 7/10
Answer:
The dimensions that minimize the cost of materials for the cylinders have radii of about 3.628 cm and heights of about 7.256 cm.
Step-by-step explanation:
A cylindrical can holds 300 cubic centimeters, and we want to find the dimensions that minimize the cost for materials: that is, the dimensions that minimize the surface area.
Recall that the volume for a cylinder is given by:

Substitute:

Solve for <em>h: </em>

Recall that the surface area of a cylinder is given by:

We want to minimize this equation. To do so, we can find its critical points, since extrema (minima and maxima) occur at critical points.
First, substitute for <em>h</em>.

Find its derivative:

Solve for its zero(s):
![\displaystyle \begin{aligned} (0) &= 4\pi r - \frac{600}{r^2} \\ \\ 4\pi r - \frac{600}{r^2} &= 0 \\ \\ 4\pi r^3 - 600 &= 0 \\ \\ \pi r^3 &= 150 \\ \\ r &= \sqrt[3]{\frac{150}{\pi}} \approx 3.628\text{ cm}\end{aligned}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cbegin%7Baligned%7D%20%280%29%20%26%3D%204%5Cpi%20r%20%20-%20%5Cfrac%7B600%7D%7Br%5E2%7D%20%5C%5C%20%5C%5C%204%5Cpi%20r%20-%20%5Cfrac%7B600%7D%7Br%5E2%7D%20%26%3D%200%20%5C%5C%20%5C%5C%204%5Cpi%20r%5E3%20-%20600%20%26%3D%200%20%5C%5C%20%5C%5C%20%5Cpi%20r%5E3%20%26%3D%20150%20%5C%5C%20%5C%5C%20r%20%26%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7B150%7D%7B%5Cpi%7D%7D%20%5Capprox%203.628%5Ctext%7B%20cm%7D%5Cend%7Baligned%7D)
Hence, the radius that minimizes the surface area will be about 3.628 centimeters.
Then the height will be:
![\displaystyle \begin{aligned} h&= \frac{300}{\pi\left( \sqrt[3]{\dfrac{150}{\pi}}\right)^2} \\ \\ &= \frac{60}{\pi \sqrt[3]{\dfrac{180}{\pi^2}}}\approx 7.25 6\text{ cm} \end{aligned}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Cbegin%7Baligned%7D%20h%26%3D%20%5Cfrac%7B300%7D%7B%5Cpi%5Cleft%28%20%5Csqrt%5B3%5D%7B%5Cdfrac%7B150%7D%7B%5Cpi%7D%7D%5Cright%29%5E2%7D%20%20%5C%5C%20%5C%5C%20%26%3D%20%5Cfrac%7B60%7D%7B%5Cpi%20%5Csqrt%5B3%5D%7B%5Cdfrac%7B180%7D%7B%5Cpi%5E2%7D%7D%7D%5Capprox%207.25%206%5Ctext%7B%20cm%7D%20%20%20%5Cend%7Baligned%7D)
In conclusion, the dimensions that minimize the cost of materials for the cylinders have radii of about 3.628 cm and heights of about 7.256 cm.