It took 20,000 workers to build the Taj Mahal in 20 years. How many workers would be required to build it in 10 years?
2 answers:
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A good place to start is to set to y. That would mean we are looking for
to be an integer. Clearly,
, because if y were greater the part under the radical would be a negative, making the radical an imaginary number, not an integer. Also note that since
is a radical, it only outputs values from
, which means y is on the closed interval:
.
With that, we don't really have to consider y anymore, since we know the interval that is on.
Now, we don't even have to find the x values. Note that only 11 perfect squares lie on the interval , which means there are at most 11 numbers that x can be which make the radical an integer. All of the perfect squares are easily constructed. We can say that if k is an arbitrary integer between 0 and 11 then:
Which is strictly positive so we know for sure that all 11 numbers on the closed interval will yield a valid x that makes the radical an integer.
Answer:
Area of a square is length * length
Area of a rectangle is length * breadth
In the question, the area of the square is 36
And the area of the rectangle is the area of the square
To find the area of the rectangle, multiply 1(1/3) by the area of the square(36)
Area of rectangle becomes, 1(1/3) * 36 = (4/3) * 36 = 48cm2
To find the perimeter of the shape, we must find the perimeter of the rectangle - perimiter of the square
Since area of square is length * length, the length of the square is 6cm
The breadth of the rectangle is equal to the length of the square, hence, b = 6cm
Since, length * breadth = 48
l * 6 = 48
l = 8
Perimeter of the shape = 4 * perimeter of rectangle - perimter of square
Perimeter of rectangle = 2(l+b)
Perimeter of sqaure = 4l
Our answer = 4 * 2(6+8) - 4(6)
= 4 * 28 - 36
= 88cm
Step-by-step explanation: