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JulijaS [17]
3 years ago
14

A maple tree loses 384 leaves during the first week of fall, and 3/2 as many each successive week. At the end of 7 weeks, all th

e leaves have fallen. How many leaves fell from the tree?
Mathematics
1 answer:
Ksenya-84 [330]3 years ago
4 0

Answer:

12,354 leaves

Step-by-step explanation:

Leaves fallen from a maple tree = \sum_{n=0}^{6}  = 384(\frac{3}{2} )^{n}

At the end of 7 weeks

= 384 + 384(1.5) + 384(1.5)² + 384(1.5)³ + 384(1.5)⁴ + 384(1.5)⁵ + 384(1.5)⁶

= 12,354 leaves

12,354 leaves fell from the tree.

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Step-by-step explanation:

Please note I have attached an edited version of your sketch to aid my solution. Now this question can be solved in multiple ways. Here, we shall see one of them. Looking at the original sketch, we can see that the figure is actually a combination of a Triangle (Figure 1 in my sketch) and a rectangle (Figure 2 in my sketch). So we can simply find the sides of a Triangle and the sides of a Rectangle and add them. Perimeter on Figure 1:The Perimeter of a Triangle is given by the Sum of the three sides as:

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Perimeter on Sketched Figure:The perimeter of the total figure will be two sides of the triangle and the three sides of the rectangle (as the one adjacent between Fig. 1 and 2 can not be taken into account). Thus we need to find 5 different sides and add them together. Now since the figure is on a graph paper, we can read of the size of some sides, thus the left side of the triangle is  units and the base of the triangle is also  units. Now to find the last unknown side we can take Pythagorian theorem, since our triangle is a Right triangle, (i.e. one angle is 90°). Pythagoras states that the squared of the hypotenuse of a right triangle is equal to the sum of the squares of the other two legs of the triangle (where the hypotenuse side is always across the 90° angle. So here we can say that: where  is the hypotenuse and our unknown side. So plugging in values and solving for   we have: units.

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