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Burka [1]
3 years ago
15

Demonstrate that the digits of a perfect square cannot add to 2, 3, 5, 6, or 8

Mathematics
1 answer:
Lelu [443]3 years ago
5 0
It depends on what did you mean by saying perfect square. If I've understood it correctly, I can help you with a part of your problem. The squares of mod <span>9</span><span> are </span><span><span>1</span><span>,4,7</span></span><span> which are came from </span><span><span>1,2,</span><span>4.</span></span><span> </span>Addition of the given numbers are 2,3,5,6, 8, which are exactly the part of your problem. This number, which is not shown as squares Mod 9, and thus doesn't appear as a sum of digits of a perfect square. I hope you will find it helpful.
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A rectangular prism with a volume of 2 cubic units is filled with cubes with side lengths of 1/4​ unit. How many 1/4 unit cubes
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Answer:

128

Step-by-step explanation:

Method A.

The volume of the prism is 2 cubic units.

Each cube has side length of 1/4 unit.

The volume of each cube is (1/4)^3 cubic unit.

The volume of each cube is 1/64 cubic unit.

To find the number of cubes that fit in the prism, we divide the volume of the prism by the volume of one cube.

(2 cubic units)/(1/64 cubic units) =

= 2/(1/64)

= 2 * 64

= 128

Method B.

Imagine that the prism has side lengths 1 unit, 1 unit, and 2 units (which does result in a 2 cubic unit volume.) Since each cube has side length 1/4 unit, then you can fit 4 cubes by 4 cubes by 8 cubes in the prism. Then the number of cubes is: 4 * 4 * 8 = 128

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The area of a square is simply the side length squared and we are given that the area is 125 so:

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s=5√5

Now using the area equation again, and adding 1 inch to s we have:

A=(s+1)^2, and using s found above we have:

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Here we are required to rewrite the equation ax-by=c, where a,b,c>0 In the slope-intercept form.

The slope-intercept form of ax-by=c is ;

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There a no. of ways to write the equation of a line; however, the most popular of these ways is the slope-intercept form.

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Therefore, the equation ax-by=c can be rewritten thus;

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Consequently, the slope-intercept form of ax-by=c is ;

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