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2 years ago

2) The area of a rectangular pool is 1260 ft. Find the dimensions of the rectangle, if one

1 answer:

5 0

Two equations

W*L=1260

3W+48=L

Solve

L=1260/W

3W+48=1260/W

3W^2+48W=1260

3W^2+48W-1260=0

Divide by 3

W^2+16W-420=0

Factor

(W-14) (W+30)

W=14

L=90

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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

Help will make you as brain plssss

saul85 [17]

Answer:

answer is 19.

Step-by-step explanation:

see picture for explanation.

hope it helps you.

7 0

3 years ago

Read 2 more answers

The Wildcats in leopards are on evenly matched football teams when they play there is a .5 probability that the Wildcats win if

aliya0001 [1]

Answer:

P( x = 2) = 0.4

Or 40%

Step-by-step explanation:

Given that wildcat has 0.5 probability of winning if they play nine times

Probability = possible outcomes ÷ required outcome

The required outcome = 9

Probability = 0.5

Let calculate the possible outcomes

Possible outcomes = 0.5 × 9 = 4.5 games

the probability that the Wildcats win two of the games will be

P( x = 2) = 2/4.5 = 0.44

Or 44%

8 0

2 years ago

Amy is baking her famous pies to sell at the Town Fall Festival. She uses 32.5 cups of flour for every 10 cups of sugar in order

Vinil7 [7]

We can use the equation:

f = 3.25s

3.25 is the cups of flour used for every cup of sugar.

Where 'f' represents flour and 's' represents sugar.

6 0

3 years ago

B) Amount Rs 5760, Interest Rs 1526

Crazy boy [7]

Given :

Amount, A = 5760 Rs.

Interest in the amount, I = 1526 Rs.

To Find :

We need to find the % rate of interest.

Solution :

Let, us assume it is simple interest.

So,

$Interest = \dfrac{price \times rate \times time}{100}\\\\1526 = \dfrac{5760 \times r \times m}{100}\\\\r = \dfrac{152600}{5760m}\\\\r = \dfrac{26.5}{m}$

Hence, this is the required solution.

6 0

3 years ago