Respuesta :
Answer:
let the two number be x and y.
Given: the product of two numbers is 450.
then: [tex]x\times y =450[/tex] ......[1]
Also from the given condition that; the first number is half the second number. Also, x>y.
i.e, [tex]y=\frac{1}{2}x[/tex]
Substitute this in equation [1];
[tex]x \times \frac{1}{2}x =450[/tex]
or
[tex]\frac{1}{2}x^2 = 450[/tex] [∴[tex]x^a \times x^b =x^{a+b}[/tex]]
Multiply both sides by 2; we get
[tex]x^2 =450 \times 2[/tex]
or
[tex]x^2=900[/tex]
or
[tex]x=\sqrt{900} =30[/tex]
Now, substitute this x value in [1], to solve for y;
[tex]30 \times y=450[/tex]
Divide by 30 from both the sides, we get;
[tex]y = \frac{450}{30}=15[/tex]
Therefore, the equation [tex]\frac{1}{2}x^2 = 450[/tex] which can be used to find the value of x.
The greater number is x = 30.
The equation is used to find x is;
[tex]\rm x^2=900[/tex]
The value of the greater number x is 30.
Given
The product of the two numbers is 450.
The first number is half the second number.
Let the first number be x and the second number be y.
The product of the two numbers is 450.
[tex]\rm x\times y = 450[/tex]
The first number is half the second number.
[tex]\rm x = \dfrac{1}{2} y[/tex]
Substitute the value of x in equation 1 from equation 2
[tex]\rm x \times y = 450\\\\x \times \dfrac{1}{2}x = 450\\\\x^2 = 450 \times 2\\\\x^2=900\\\\x=30[/tex]
Substitute the value of x in equation 1
[tex]\rm x\times y=450\\\\30 \times y = 450\\\\y = \dfrac{450}{30}\\\\y = 15[/tex]
Hence, the value of the greater number x is 30.
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