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Mathematics : Application of Derivatives

Name: Zigya - For The Curious Learner
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Long Answer Type

351.

Find the largest possible area of a right-angled triangle whose hypotenuse is 5 cm long.

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352. A point on the hypotenuse of a triangle is at distance a and b from the sides of the triangle. Show that the maximum length of the hypotenuse is

open parentheses straight a to the power of 2 over 3 end exponent plus straight b to the power of 2 over 3 end exponent close parentheses to the power of 3 over 2 end exponent.

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353. Find the maximum-area of an isosceles triangle inscribed in the ellipse

straight x squared over straight a squared plus straight y squared over straight b squared space equals space 1

with its vertex at one end of the major axis.

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Short Answer Type

354.

Let AP and BQ be two vertical poles at points A and B, respectively. If AP = 16 m. BQ = 22 m and AB = 20 m, then find the distance of a point R on AB from the point A such that RP² + RQ² is minimum.

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Long Answer Type

355.

If length of three sides of a trapezium other than base are equal to 10 cm. then find the area of the trapezium when it is maximum.

172 Views

Short Answer Type

356.

Use differentials to approximate $square root of 25.3 end root.$

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357.

Use differentials to approximate $square root of 0.037 end root$ .

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358.

Use differentials to approximate $square root of 36.6 end root$

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359.

Use differentials to approximate:
$square root of 49.5 end root$

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360.

Use differentials to approximate:
$square root of 0.6 end root$

78 Views