Advertisements
Advertisements
प्रश्न
Find two numbers whose mean proportional is 16 and the third proportional is 128.
Advertisements
उत्तर
Let x and y be two numbers
Their mean proportion = 16
and third proportion = 128
∴ `sqrt(xy)` = 16
⇒ xy = 256
⇒ x = `(256)/y` ....(i)
and `y^2/x` = 128
⇒ x = `y^2/(128)` ....(ii)
From (i) and (ii)
`(256)/y = y^2/(128)`
⇒ y3 = 256 x 128
= 32768
⇒ y3 = (32)3
⇒ y = 32
∴ x = `(256)/y`
= `(256)/(32)`
= 8
∴ Numbers are 8, 32.
APPEARS IN
संबंधित प्रश्न
a, b, c are in continued proportion. If a = 3 and c = 27 then find b.
If p, q and r in continued proportion, then prove the following:
(p2 - q2)(q2 + r2) = (q2 - r2)(p2 + q2)
If a, b, c and dare in continued proportion, then prove that
`sqrt (("a + b + c")("b + c + d")) = sqrt "ab" + sqrt "bc" + sqrt "cd"`
What number must be added to each of the numbers 6, 15, 20 and 43 to make them proportional?
Show that the following numbers are in continued proportion:
48, 60, 75
If a, b, c are in continued proportion, prove that: `(a + b)/(b + c) = (a^2(b - c))/(b^2(a - b)`.
If a, b, c are in continued proportion, prove that: (a + b + c) (a – b + c) = a2 + b2 + c2
Are 30, 40, 45, and 60 in proportion?
The America’s famous Golden Gate bridge is 6480 ft long with 756 ft tall towers. A model of this bridge exhibited in a fair is 60 ft long with 7 ft tall towers. Is the model, in proportion to the original bridge?
If x + y + z = 0, the value of `x/(y + z)` is ______.
