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dexar [7]
3 years ago
14

Can anyone pls help me to solve question 2 f and g and pls provide me a explanation I’m with that questions for three days

Mathematics
1 answer:
zvonat [6]3 years ago
5 0

Answer:

  f)  a[n] = -(-2)^n +2^n

  g)  a[n] = (1/2)((-2)^-n +2^-n)

Step-by-step explanation:

Both of these problems are solved in the same way. The characteristic equation comes from ...

  a[n] -k²·a[n-2] = 0

Using a[n] = r^n, we have ...

  r^n -k²r^(n-2) = 0

  r^(n-2)(r² -k²) = 0

  r² -k² = 0

  r = ±k

  a[n] = p·(-k)^n +q·k^n . . . . . . for some constants p and q

We find p and q from the initial conditions.

__

f) k² = 4, so k = 2.

  a[0] = 0 = p + q

  a[1] = 4 = -2p +2q

Dividing the second equation by 2 and adding the first, we have ...

  2 = 2q

  q = 1

  p = -1

The solution is a[n] = -(-2)^n +2^n.

__

g) k² = 1/4, so k = 1/2.

  a[0] = 1 = p + q

  a[1] = 0 = -p/2 +q/2

Multiplying the first equation by 1/2 and adding the second, we get ...

  1/2 = q

  p = 1 -q = 1/2

Using k = 2^-1, we can write the solution as follows.

The solution is a[n] = (1/2)((-2)^-n +2^-n).

 

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A) The hypotenuse is the longest side of the triangle .In the figure EG is the hypotenuse.The given angle is <G=40 degrees.The side adjacent is FG= 10 units.

The question is asking us to find the trigonometry ratio which will  help us find EG.We can use cos  as cos is ratio of adjacent and hypotenuse.

cos 40=\frac{10}{Hypotenuse EG.}

B) Cos  40 =0.766.

Substituting tan40 value we have:

0.766=\frac{10}{EG}

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C)Sum of angles in  triangle is 180.

<E+<F+<G=180

<E+90+40=180

<E+130=180

<E=50 degrees.

D) Tan  40=\frac{EF}{10}

EF=8.39

E) Area of triangle EFG= \frac{1}{2}x base x height.

A rea of the triangle = \frac{1}{2}x8.39x13.05

Area= 54.75 square units.





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