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lorasvet [3.4K]
3 years ago
12

Please Help! Dimitri bought a cylindrical clay flowerpot that holds approximately 15 gallons of dry soil (1 gallon ≈ 0.15 cubic

feet). The radius of the pot is 9 inches. What is the height of the flowerpot to the nearest tenth of a foot? Show your work.
Mathematics
1 answer:
Alex_Xolod [135]3 years ago
4 0

Answer:

\huge\colorbox{blue}{h$\approx$1.3  foot }

Step-by-step explanation:

we are given volume and redious

but r is in inches and V is in gallons

so we have to convert V into inches unit

\sf\displaystyle 1\: cubic\: foot=1728 \: cubic\: inches

first convert gallon to cubic foot

\sf\displaystyle 15\times 0.15\: (\text{since 1 gallon=0.15 cubic feet}) \\  \displaystyle \:  = 2.25

now convert cubic feet to cubic inches:

\sf\displaystyle 2.25\times 1728 \\  = 3888

now we need a little algebra to figure out h

V_{cylinder}=\pi r^2 h

substitute the value of V and r:

\displaystyle \:  \pi  \times {9}^{2}  \times h = 3888

simplify square:

\displaystyle \:  \pi  \times 81  \times h = 3888

divide both sides by 81:

\displaystyle \:  \frac{ \pi  \times 81  \times h}{81} = \frac{ 3 888}{81} \\ \pi  \times  h = 48

divide both sides by π:

\displaystyle \:  \frac{\pi \times h}{\pi}  =  \frac{48}{\pi}  \\   \: h  \approx 15.3

12 inches = 1 foot

15.3 " =15.3/12

≈1.3 foot

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What is the surface area of the shape DUE AT 10:15 AM
Liono4ka [1.6K]

Answer:

196

Step-by-step explanation:

2 times 14 times 7=196

Hope this helps!

8 0
3 years ago
The point (7, 8) is the solution of which of the following systems of equations?
Alex73 [517]

Option 4

<u>V</u><u>e</u><u>r</u><u>i</u><u>f</u><u>i</u><u>c</u><u>a</u><u>t</u><u>i</u><u>o</u><u>n</u><u>:</u><u>-</u>

\\ \sf\longmapsto x-7y=-49

\\ \sf\longmapsto 7-7(8)=-49

\\ \sf\longmapsto 7-56=-49

\\ \sf\longmapsto -49=-49

And

\\ \sf\longmapsto 10x+9y=142

\\ \sf\longmapsto 10(7)+9(8)=142

\\ \sf\longmapsto 70+72=142

\\ \sf\longmapsto 142+142

Hence verified

8 0
3 years ago
Read 2 more answers
What’s 5/6 divided by 5/2 in fraction form
nadya68 [22]

Answera:The answer is 0.3333333333 repeated

Step-by-step explanation:5/6 is 0.8333333 repeated divided by 5/2 which is 2.5 which when divided is 0.333333333 repeated.

4 0
3 years ago
Read 2 more answers
To find 5, Beau found 22 = 4 and 32 = 9. He said that since 5 is between 4 and 9, 5 is between 2 and 3. Beau thinks a good estim
shusha [124]

Complete question

To find \sqrt{5} , Beau found 2^2 = 4 and 3^2 = 9 . He said that since 5 is between 4 and 9, \sqrt{5}, is between 2 and 3. Beau thinks a good estimate for \sqrt{5} , is \frac{2 + 3}{2} =  2.5 Is his estimate high or low? How do you know?

Answer:

The estimation is high because 5 is very close to 4 so \sqrt{5} will also be very close to \sqrt{4} which is lower than the estimate

In order to get a good estimate

The first step is to choose a number between 2 and 3 let say 2.8 , 2,85 , 2.9 and the square them

i.e

2.1^2 =  4.41

     2.2^2 =  4.84

      2.3^2 =  5.29

From here we can see that \sqrt{5}  lies between 2.2 and 2.3 but is closer to  2.2

So a good estimate for \sqrt{5} is 2.2

Step-by-step explanation:

8 0
3 years ago
I NEED HELP PLEASE, THANKS! :)
Alenkasestr [34]

Answer:

Option A

Step-by-step explanation:

This is a great question!

The first thing we want to do here is to graph the system of " inequalities " -

\begin{bmatrix}2x+9y\le \:100\\ 9x+y\le \:54\end{bmatrix}

As x is ≥ 0, respectively y ≥ 0, it makes things a lot simpler, as it kind of restricts us to quadrant 1, but not entirely.

First change each inequality to " slope - intercept " form, as such -

2x + 10y \leq 100,\\10y \leq 100 - 2x,\\y \leq - 1 / 5x + 10\\----------\\9x + y \leq 54,\\y \leq - 9x + 54

The graphed solutions would be in the attachment. I have colored the region with which the two intersect, and the fact that we are limited to quadrant 1. In this colored region there are 3 major points, ( 5, 9 ), ( 0, 10 ), and ( 6, 0 ). We have to determine which of these are are maximum points, as the minimum are the same. Substitute these values ( ( 5, 9 ), ( 0, 10 ), and ( 6, 0 ) ) into the equation f( x, y ) = 10x + 4y,

f ( x, y ) = 10( 5 ) + 4( 9 ),\\f ( x, y ) = 86 -\\f ( x, y ) = 10( 0 ) + 4( 10 ),\\f ( x, y ) = 40 -\\f ( x, y ) = 10( 6 ) + 4( 0 ),\\f ( x, y ) = 60

( 5, 9 ) resulted in the greatest amount, 86. That would make it our maximum point -

<u><em>Solution = Option A</em></u>

3 0
3 years ago
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