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denpristay [2]
3 years ago
13

The top tree broke and fell over.the remaining tree teunk is 3 feet tall.the tip of the tree rests on the ground 14 feet from th

e base of the trunk.what is the lenght of the broken part of the tree to the nearest tenth of a foot

Mathematics
1 answer:
Bas_tet [7]3 years ago
5 0

Answer:

14.3 feet.

14.3 feet

Step-by-step explanation:

The problem forms a right triangle in which:

The Vertical Leg of the Right Triangle = 3 feet

The Horizontal Leg of the Right Triangle =14 feet

We are to determine the length of the broken part of the tree. This is the Hypotenuse of the Right Triangle,

Using Pythagoras Theorem

Hypotenuse^2=Opposite^2+Adjacent^2\\Hypotenuse^2=14^2+3^2\\Hypotenuse^2=205\\Hypotenuse=\sqrt{205}\\Hypotenuse=14.32\\ \approx 14.3 feet $(to the nearest tenth of a foot).\\Therefore, the lenght of the broken part of the tree to the nearest tenth of a foot is 14.3 feet.

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Suppose that you earned a​ bachelor's degree and now​ you're teaching high school. The school district offers teachers the oppor
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Answer:

Step-by-step explanation:

Answer:

a. The amount that is saved at the expiration of the 5 year period is $22,769.20¢

b. The amount of interest is $2,769.20¢

Step-by-step explanation:

Since the amount that is deposited every year for a period of five years is $4,000 and the rate of the interest is 6.5%. We can always calculate the amount that is saved at the expiration of the five years.

    We will first state the formula for calculating the future value of annuity:-

      Future value of annuity =

                      P[\frac{(1 + r)^{t}-1 }{r}]

   Where P is the amount deposited per year.

   r is the rate of interest

   t is the time or period

 

    and in this case, the actual value of P = $4,000

      rate of interest, r is 6.5% = 0.065

      time, t is 5 years.

   Substituting e, we have:

   Fv of annuity =

                          4,000[\frac{(1 + 0.065)^{5}-1 }{0.065 }]

   = 4,000 × [((1.065)^5)- 1/0.065]

 = 4,000 × [(1.37 - 1)/0.065]

 = 4,000 × (0.37/0.065)

 = 4,000 × 5.6923

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a. Therefore the amount that is saved at the end of the five (5) years is $22,769.20¢

b. To find the interest, we will calculate the amount of deposit made during the period of five years and subtract the sum from the current amount that is saved ($22,769.29¢).

  Since I deposited 4,000 every year for five years, the total amount of deposit I made at the period =

       4,000 × 5 = $20,000

  The amount of interest is then = $22,769.20¢ - $20,000 = $2,769.20¢

3 0
3 years ago
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