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3 years ago

5. A pole has to be erected at a point on the boundary of a circular park of diameter 13 metres in

Mathematics

1 answer:

lesya [120]3 years ago

4 0

Answer:

Thus, it is possible to erect a pole at a point p on the boundary of the park at distances 5m and 12m respectively from gates B and A.

Step-by-step explanation:

Let P be the required location of pole .

A and B are the two gates.

Let the distance of pole at p from gate be 'x' meters

i.e. PB = x m

•°• AP = (x + 7)m and AB = 13 m

•°• AP² + BP² = AB² => (x +7)² + x =13²

Rejecting x =-12, we get x = 5

•°• PB = 5m

and

AP = 12m

(I hope this helped :)

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castortr0y [4]

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What two positive real numbers whose product is 21 have the smallest possible sum?

GalinKa [24]

Answer:

$x=\sqrt{21}$

$y=\sqrt{21}$

Step-by-step explanation:

Let x and y are the two positive real numbers

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$x y=21$

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The sum of the two numbers is f(x) =x+y

Replace y with 21/x

$f(x) =x+\frac{21}{x}$

we need to find smallest possible sum , so we take derivative using power rule

$f'(x)= 1-\frac{21}{x^2}$

when sum is minimum then the derivative is equal to 0

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$0=\frac{x^2-21}{x^2}$

multiply both sides by x^2

$x^2-21=0$

$x^2=21$

Take square root on both sides

$x=\sqrt{21}$

$y=\frac{21}{x}$

$y=\frac{21}{\sqrt{21}}$

$y=\sqrt{21}$

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4 years ago

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Answer:

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Step-by-step explanation:

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