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Butoxors [25]
3 years ago
15

1. The length of the hypotenuse in a right triangle whose other two sides have lengths 3 and 4 2. The value of the Boolean expre

ssion that evaluates whether the length of the above hypotenuse is 5 3. The area of a disk of radius 10 4. The value of the Boolean expression that checks whether a point with coordinates (5, 5) is inside a circle with center (0,0) and radius 7.
Mathematics
1 answer:
nadya68 [22]3 years ago
6 0

Answer:

For the hypotenus, the value is false

Step-by-step explanation:

For the point inside a circle = d = \sqrt{(xp -xc)^{2}  + (yp -yc)^{2} }  =

\sqrt{(5-0)^{2} + (5-0)^{2}  }  = \sqrt{25 + 25} = 7.071

Since 7.071 > 7, then the boolean answer is false

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Identify whether the series sigma notation infinity i=1 15(4)^i-1 is a convergent or divergent geometric series and find the sum
const2013 [10]

Answer:  The correct option is

(d) This is a divergent geometric series. The sum cannot be found.

Step-by-step explanation: The given infinite geometric series is

S=\sum_{i=1}^{\infty}15(4)^{i-1}.

We are to identify whether the given geometric series is convergent or divergent. If convergent, we are to find the sum of the series.

We have the D' Alembert's ratio test, states as follows:

Let, \sum_{i=1}^{\infty}a_i is an infinite series, with complex coefficients a_i and we consider the following limit:

L=\lim_{i\rightarrow \infty}\dfrac{a_{i+1}}{a_i}.

Then, the series will be convergent if  L < 1 and divergent if  L > 1.

For the given series, we have

a_i=15(4)^{i-1},\\\\a_{i+1}=15(4)^i.

So, the limit is given by

L\\\\\\=\lim_{i\rightarrow \infty}\dfrac{a_{i+1}}{a_i}\\\\\\=\lim_{i\rightarrow \infty}\dfrac{15(4)^i}{15(4)^{i-1}}\\\\\\=\lim_{i\rightarrow \infty}\dfrac{15(4)^i}{15(4)^{i}4^{-1}}\\\\\\=\dfrac{1}{4^{-1}}\\\\=4>1.

Therefore, L >1, and so the given series is divergent and hence we cannot find the sum.

Thuds, (d) is the correct option.

7 0
3 years ago
Read 2 more answers
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