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Luden [163]
4 years ago
15

the coordinates for the endpoints of a line segment are (-5,13) and (-9,21). find the coordinates for the midpoint of the line s

egment. a. (-7, 17) b. (-4, 4) c. (-2, 4) d. (4, 17)
Mathematics
1 answer:
dedylja [7]4 years ago
8 0
The midpoint of AB where A(x_A;\ y_A) and B(x_B;\ y_B)

\left(\dfrac{x_A+x_B}{2};\ \dfrac{y_A+y_B}{2}\right)

A(-5;\ 13);\ B(-9;\ 21)

The midpoint of AB: \left(\dfrac{-5+(-9)}{2};\ \dfrac{13+21}{2}\right)=\left(\dfrac{-14}{2};\ \dfrac{34}{2}\right)=(-7;\ 17)

Answer: A. (-7, 17)

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Check the picture below.

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3. In a single growing season at the Smith Family Orchard, the average yield per apple tree is 150 apples when the number of tre
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Answer:

<em><u>A.10000</u></em>

<em><u>B.25 more trees must be planted</u></em>

Step-by-step explanation:

⇒Given:

  • The intial average yield per acre y_{i} = 150
  • The initial number of trees per acre  t_{i} = 100
  • For each additional tree over 100, the average yield per tree decreases by 1 i.e , if the number trees become 101 , the avg yield becomes 149.
  • Total yield = (number of trees per acre)*(average yield per acre)

<em>A.</em>

⇒If the total trees per acre is doubled , which means :

total number of trees per acre t_{f} = 2*t_{i} = 200

the yield will decrease by : t_{f} - y_{i}

y_{f}= 150-100= 50

⇒total yield = 50*200=10000

<em>B.</em>

⇒to maximize the yield ,

let's take the number of trees per acre to be 100+y ;

and thus the average yield per acre = 150 - y;

total yield = (100+y)*(150-y)\\=15000+50y-y^{2} \\

this is a quadratic equation. this can be rewritten as ,

     ⇒   =15000+50y-y^{2}\\=15000+625 - (625 - 50y +y^{2})\\=15625 - (y-25)^{2}

In this equation , the total yield becomes maximum when y=25;

<u><em>⇒Thus the total number of trees per acre = 100+25 =125;</em></u>

                 

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