Question: 1 The product of two positive numbers is 15876 and the large one is 9 times the other. Find the numbers.
Question:2
Th sum of the squares of two positive whole numbers is 794. If one of the numbers is 13 , find the other.
Very good explanation.
1 .
a = first number
b = second number
The large one is 9 times the other.
This mean :
b = 9 a
a * b = 15876
a * 9 a = 15876
9 a ^ 2 = 15876 Divide both sides by 9
a ^ 2 = 15876 / 9
a ^ 2 = 1764
a = sqroot ( 1764 )
a = 42
b = 9 a = 9 * 42 = 3789
2.
a = first number
b = second number ( In this case b = 13 )
The sum of the squares of two positive whole numbers is 794.
This mean :
a ^ 2 + b ^ 2 = 794
a ^ 2 + 13 ^ 2 = 794
a ^ 2 + 169 = 794 Subtract 169 to both sides,
a ^ 2 + 169 - 169 = 794 - 169
a ^ 2 = 625
a = sqroot ( 625 ) = 25
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Thanks for a provide a good maths
x y = 15876
y = 9 x
so
9 x^2 = 15876
x^2 = 1764
x = 42
===================
169 + x^2 = 794
x^2 = 625
x = 25
To find the numbers in the first question, we can start by letting one of the numbers be "x." Since the larger number is 9 times the other, we can say that the other number is 9x.
Now, we know that the product of the two numbers is 15876, so we can form an equation:
x * 9x = 15876
Simplifying, we get:
9x^2 = 15876
Dividing both sides by 9, we get:
x^2 = 1764
Taking the square root of both sides, we find:
x = ±42
Since we need to find positive numbers, we take only the positive root:
x = 42
Now, to find the other number, we substitute the value of x into our equation:
Other number = 9 * 42 = 378
Therefore, the two numbers are 42 and 378.
For the second question, we're given that the sum of the squares of two positive whole numbers is 794, and one of the numbers is 13. Let's assume the other number is "x."
We can set up the equation:
13^2 + x^2 = 794
Simplifying, we get:
169 + x^2 = 794
Subtracting 169 from both sides, we have:
x^2 = 625
Taking the square root of both sides, we find:
x = ±25
Since we're looking for a positive number, we take only the positive root:
x = 25
Therefore, the other number is 25.