What is the measure of angle DBC?

Given the sequence 1/2 ; 4 ; 1/4 ; 7 ; 1/8 ; 10;.. calculate the sum of 50 terms

miv72 [106K]

Hint :-

Break the given sequence into two parts .
Notice the terms at gap of one term beginning from the first term .They are like $\dfrac{1}{2},\dfrac{1}{4},\dfrac{1}{8}$ . Next term is obtained by multiplying half to the previous term .
Notice the terms beginning from 2nd term , $4,7,10,13$ . Next term is obtained by adding 3 to the previous term .

Solution :- 

We need to find out the sum of 50 terms of the given sequence . After splitting the given sequence ,

$\implies S_1 = \dfrac{1}{2},\dfrac{1}{4},\dfrac{1}{8}$ .

We can see that this is in Geometric Progression where 1/2 is the common ratio . Calculating the sum of 25 terms , we have ,

$\implies S_1 = a\dfrac{1-r^n}{1-r} \\\\\implies S_1 = \dfrac{1}{2}\left[ \dfrac{1-\bigg(\dfrac{1}{2}\bigg)^{25}}{1-\dfrac{1}{2}}\right]$

Notice the term $\dfrac{1}{2^{25}}$ will be too small , so we can neglect it and take its approximation as 0 .

$\implies S_1\approx \cancel{ \dfrac{1}{2} } \left[ \dfrac{1-0}{\cancel{\dfrac{1}{2} }}\right]$

$\\\implies \boxed{ S_1 \approx 1 }$

$\rule{200}2$

Now the second sequence is in Arithmetic Progression , with common difference = 3 .

$\implies S_2=\dfrac{n}{2}[2a + (n-1)d]$

Substitute ,

$\implies S_2=\dfrac{25}{2}[2(4) + (25-1)3] =\boxed{ 908}$

Hence sum = 908 + 1 = 909

7 0

2 years ago

There are 50 deer in a particular

olchik [2.2K]

answered

There are 50 deer in a particular forest. The population is increasing at a rate of 15% per year. Which exponential growth function represents

the number of deer y in that forest after x months? Round to the nearest thousandth.

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dribeiro

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Answer:

The expression that represents the number of deer in the forest is

y(x) = 50*(1.013)^x

Step-by-step explanation:

Assuming that the number of deer is "y" and the number of months is "x", then after the first month the number of deer is:

y(1) = 50*(1+ 0.15/12) = 50*(1.0125) = 50.625

y(2) = y(1)*(1.0125) = y(0)*(1.0125)² =51.258

y(3) = y(2)*(1.0125) = y(0)*(1.0125)³ = 51.898

This keeps going as the time goes on, so we can model this growth with the equation:

y(x) = 50*(1 - 0.15/12)^(x)

y(x) = 50*(1.013)^x

8 0

2 years ago

F(x)=4x4−5x3−2x+6 and g(x)=3x3−4x2−2x+1 . What is f(x)+g(x) ?

igomit [66]

4*4-5*3-2x+6= -x-7/2 slope = 2

3 * 3 - 4 *2 -2x +1= - x - 2/2 slope = -2

2 + -2 = 0

6 0

3 years ago

Glen needs at least $225 for a new audio system. She he already saved $90. He earns $15 per hour at his part-time job. Write and

Nesterboy [21]

Answer:

90+15x=225

Step-by-step explanation:

90 already saved plus 15 an hour equals 225

3 0

2 years ago

Complete the solution of the equation. Find the value of y when x equals 4. -7x + y = -22

xz_007 [3.2K]

-7x + y = -22

-7*4 + y = -22

y = -22 + 28

y = 6

4 0

3 years ago