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igomit [66]
3 years ago
11

Common denominators for 5/6 and 8/21 help me!!!!!!!!!

Mathematics
1 answer:
Helga [31]3 years ago
4 0
The common denominator would have to be 42
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A rectangular box which is open at the top can be made from an12-by-18-inch piece of metal by cutting a square from each corner
algol [13]

Answer:

h=2.35in, l=13.3in and w=7.3in

Step-by-step explanation:

In order to solve this problem, we must start by drawing a diagram that will represent the prolem. (Look at attached picture)

From the diagram we can see that the length ad the width of the box are found by  using the following expressions:

L=18-2x

W= 12-2x

H=x

next, we can make use of the volume formula of a rectangular prism, which is the following:

V=WLH

so we can substitute the expressions we got before on the formula:

V=x(12-2x)(18-2x)

and for ease of calculation, we can multiply the terms, so we get:

V=x(216-24x-36x+4x^{2})

V=x(4x^{2}-60x+216)

V=4x^{3}-60x^{2}+216x

So now we can find the derivative of the volume:

V'=12x^{2}-120x+216

and set it equal to zero, so we get:

12x^{2}-120x+216=0

and now we can solve. We can start by factoring the left side of the equation, so we get:

12(x^{2}-10x+18)=0

which yields:

x^{2}-10x+18=0

This one can only be solved by using the quadratic formula:

x=\frac{-b\pm \sqrt{-b^{2}-4ac}}{2a}

so we substitute the corresponding values:

x=\frac{-(-10)\pm \sqrt{-(-10)^{2}-4(1)(18)}}{2(1)}

which yields:

x=7.65in or x=2.35in

we keep the 2.35in only, because the 7.65in returns an impossible box, since that would make the width a negative width.

So the 2.35in height would give us the greatest box. Now we can use it to find the height, the width and the length of the box.

Height=x=2.35

W=12-2x=12-2*2.35=7.3in

L=18-2x=18-2(2.35)=13.3in

5 0
3 years ago
As an estimation we are told 5 miles is 8 km. <br> Convert 34.5 km to miles.
rjkz [21]

Answer:

The answer is 21.5625

Step-by-step explanation:

The reason is because it first says 5 miles=8 km so that helps us right there.We divide 34.5 by 8 which will give us 4.3125.Then you have to multiply that by 5 which will give us 21.5625.

8 0
3 years ago
Joannie lent 200$ to her sister. Four years later, her sister repaid her in full with 228$. What a simple annual interest rate d
tatiyna
I believe the interest world be 3.5%
6 0
3 years ago
Read 2 more answers
PLEASE HELP!!! ASAP!! thank you &lt;33 10 points ;)
ahrayia [7]

Answer:

first find the area of the triangle

1/2 base x height

(1/2) 6 x 4 = (1/2) (24) = 12

area of rectangle

base x height

4 x 6 = 24

add them together

24 + 12 = 36

B) 36 inches

hope this helps :)

Step-by-step explanation:

7 0
3 years ago
Michael wants to install flooring in in the fitness room. The flooring cost 20 dollars a square yard. Explain how to find price
Alinara [238K]
It will cost $16.72 because one sqaure yard equals .836 of a meter and then multiply that by 20 and get 16.72
8 0
3 years ago
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