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love history [14]
3 years ago
7

during the fall a pumpkin patch advertises four pumpkin for $11.oo which equation below respresents this proportional relationsh

ip
Mathematics
1 answer:
ArbitrLikvidat [17]3 years ago
4 0

Answer:

11x4=44

Step-by-step explanation:

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If the area of AABC is D, give the expressions that complete the equation for the measure of ZB?
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Given:

The figure of triangle ABC.

The area of the triangle ABC is D.

m\angle B=\sin ^{-1}(\dfrac{m}{n})

To find:

The value of m and n in the given expression.

Solution:

Let h be the height of the triangle ABC.

Area of a triangle is:

Area=\dfrac{1}{2}\times base\times h

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Area=\dfrac{1}{2}\times a\times h

The area of the triangle ABC is D.

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2D=ah

\dfrac{2D}{a}=h                  ...(i)

In a right angle triangle,

\sin \theta =\dfrac{Perpendicular}{Hypotenuse}

\sin B =\dfrac{h}{c}

\sin B =\dfrac{1}{c}\times \dfrac{2D}{a}              [Using (i)]

\sin B =\dfrac{2D}{ac}

m\angle B =\sin ^{-1}\dfrac{2D}{ac}            ...(ii)

We have,

m\angle B=\sin ^{-1}(\dfrac{m}{n})          ...(iii)

On comparing (ii) and (iii), we get

m=2D

n=ac

Therefore, the required values are m=2D, n=ac.

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