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3 years ago

Please help show that the following are TRUE.

Mathematics

1 answer:

mafiozo [28]3 years ago

7 0

Answer:

see below

Step-by-step explanation:

The formula for the sum of an infinite geometric series with first term a1 and common ratio r (where |r| < 1) is ...

sum = a1/(1 -r)

Applying this to the given series, we get ...

a. sum = 5/(1 -3/4) = 5/(1/4) = 20

b. sum = d/(1 -1/t) = d/((t-1)/t) = dt/(t-1)

_____

The derivation of the above formula is in most texts on sequences and series. In general, you write an expression for the difference of the sum (S) and the product r·S. You find all terms of the series cancel except the first and last, and the last goes to zero in the limit, because r^∞ → 0 for |r| < 1. Hence you get ...

S -rS = a1

S = a1/(1 -r)

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Given 3 sides of a triangle - how to tell it right, acute, or obtuse 8,11, 16

user100 [1]

Using Pythagorean theorem, we can justify our answer.
if c^2 = a^2 + b^2 then triangle is right one,
if c^2 > a^2 + b^2 then triangle is obtuse and
if c^2 < a^2 + b^2 then triangle is acute triangle.

Here a=8, b=11 and c=16
Put these values in the equation
16^2 = 8 ^2 + 11^2
256 = 64 +121
256> 185
So here c^2 > a^2 + b^2 Which means triangle is obtuse triangle.

Answer: Obtuse Triangle

6 0

3 years ago

Solve the logarithmic equation . Round the answer to four decimal places . 2^x =25

levacccp [35]

Answer:

x = 4.6439

Step-by-step explanation:

2^x =25

Take the log of each side

log 2^x = log 25

We know that log a^b = b log a

x log 2 = log 25

Divide each side by log 2

x = log 25 / log 2

x =4.643856

Rounding to 4 decimal places

x = 4.6439

8 0

2 years ago

Read 2 more answers

(10

Anni [7]

Given:

The matrix multiplication

$\begin{bmatrix}4&5&6\\1&2&3\end{bmatrix}\begin{bmatrix}10\\20\\30\end{bmatrix}$

To find:

The order of resulting matrix.

Solution:

We know that, if order of first matrix is $m_1\times n_1$ and the order of second matrix is $m_2\times n_2$ , then the order of these two matrices is $m_1\times n_2$ .

We have,

$\begin{bmatrix}4&5&6\\1&2&3\end{bmatrix}\begin{bmatrix}10\\20\\30\end{bmatrix}$

Here, the order of first matrix is $2\times 3$ and the order of the second matrix is $3\times 1$ . So, the order of the second matrix is $2\times 1$ . It is also written are 2 by 1.