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Free_Kalibri [48]
3 years ago
9

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.

Therefore, the correct option is A.

6 0
3 years ago
Read 2 more answers
Stefan sells Jin a bicycle for ​$176 and a helmet for ​$16. The total cost for Jin is ​160% of what Stefan spent originally to b
Elis [28]

Answer:

Stefan originally paid $120 for the bicycle and helmet.

He made $72 by selling them to Jin.

Step-by-step explanation:

Given that:

Selling price of bicycle = $176

Selling price of helmet = $16

Total price = 176+16 = $192

This is 160% of what Stefan paid originally.

Let,

x be the original amount paid by Stefan.

160% of x = 192

\frac{160}{100}x=192\\1.6x=192

Dividing both sides by 1.6

\frac{1.6x}{1.6}=\frac{192}{1.6}\\x=120

Original amount paid by Stefan = $120

Profit = 192 - 120 = $72

Hence

Stefan originally paid $120 for the bicycle and helmet.

He made $72 by selling them to Jin.

3 0
2 years ago
Please help,-----basic algebra. Find the value of x
iren [92.7K]

Answer:

134 degrees

Step-by-step explanation:

what you do, is see that they are alternate interior angles so all you do is subtract 46 from 180 so that makes 134.

5 0
3 years ago
Read 2 more answers
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