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1 year ago

What is the least positive integers which , when subtracted 7300 would make a result a perfect square?

Mathematics

1 answer:

ycow [4]1 year ago

7 0

75 is the least positive integers which , when subtracted 7300 would make a result a perfect square

<h3>What is the least positive value?</h3>

So normally the least positive integer of all the numbers is the number 1 but when you talk about least positive integer, often times you are talking about the special function called the ceiling function

<h3>Least positive integer:</h3>

The smallest of the numbers in the set {1, 2, 3, …} is 1.

So, the number 1 is the smallest positive integer.

7300

If we Take Square root of 7300 we have to subtract 75 from 7300 to get a perfect square.

7300-75=7225

(85)^2=7225

75 to be subtracted

√7300 ≥ 85

Perfect Square = 85² = 7225 or (7300-7225 = 75)

75 is the least positive integers which , when subtracted 7300 would make a result a perfect square

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9. The ticket at right has a perimeter of 42 cm.

Liula [17]

Perimeter simply represents the sum of all side lengths of a shape. The length of the missing side of the ticket is 5 cm; the length of gold line on each ticket is 20 cm, and 2 bottles of gold ink are required to draw gold lines on 200 tickets.

I've added the image of the ticket as an attachment.

(a) The missing side length

From the attachment, the 4 unknown side lengths are equal. Represent this side length with L.

So, we have:

$Perimeter =2\times 11 + 4 \times L$

This gives

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Collect like terms

$4 \times L = 42-22$

$4 \times L = 20$

Divide both sides by 4

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There are 4 slant lines and the length of one of the slant lines is 5 cm (as calculated above).

So, the length of the gold line is:

$Gold = 4 \times L$

$Gold = 4 \times 5cm$

$Gold = 20cm$

$n = 200$ --- number of tickets

The length of all gold line in the 200 tickets is:

$Length = 200 \times Gold$

$Length = 200 \times 20cm$

$Length = 4000 cm$

$Length = 4000 \times 0.01m$ ---- convert to meters

$Length = 40m$

Given that:

$Bottle = 20m$ --- 1 bottle for 20 m

The number of bottles (n) is:

$n = \frac{Length}{Bottles}$

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$n = 2$

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