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hammer [34]
1 year ago
13

55. The sum of an infinite geometric series is five times the value of the first term. What is the common ratio of the series?

Mathematics
1 answer:
myrzilka [38]1 year ago
8 0

Answer:

r = 4/5

Step-by-step explanation:

Formula

Sum of an infinite geometric series = a / (1 - r)

Givens

Sum = 5*a

a = a

r = ?

Solution

5a = a/(1 - r)                   Divide both sides by a

5a/a = a / (a * (1 - r)       The a's on the right cancel

5 = 1 / (1 - r)                    Multiply both sides by 1 - r

5*(1 - r) = 1*(1 - r)/(1 - r)   The 1 - r s on the right cancel

5*(1 - r) = 1                     Remove the brackets.

5 - 5r = 1                        Subtract 5 from both sides

5-5 - 5r = 1 - 5               Combine

-5r = - 4                          Divide by - 5

r = 4/5  

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How do u do b??????????
horrorfan [7]

the assumption being that the first machine is the one on the left-hand-side and the second is the one on the right-hand-side.

the input goes to the 1st machine and the output of that goes to the 2nd machine.

a)

if she uses and input of 6 on the 2nd one, the result will be 6² - 6  = 30, if we feed that to the 1st one the result will be √( 30 - 5) = √25 = 5, so, simply having the machines swap places will work to get a final output of 5.

b)

clearly we can never get an output  of -5 from a square root, however we can from the quadratic one, the 2nd machine/equation.

let's check something, we need a -5 on the 2nd, so

\bf \underset{final~out put}{\stackrel{y}{-5}}=x^2-6\implies 1=x^2\implies \sqrt{1}=x\implies 1=x

so if we use a "1" as the output on the first machine, we should be able to find out what input we need, let's do that.

\bf \underset{first~out put}{\stackrel{y}{1}}=\sqrt{x-5}\implies 1^2=x-5\implies 1=x-5\implies 6=x

so if we use an input of 6 on the first machine, we should be able to get a -5 as final output from the 2nd machine.

\bf \stackrel{first~machine}{y=\sqrt{\boxed{6}-5}}\implies y=\sqrt{1}\implies y=1 \\\\\\ \stackrel{second~machine}{y = \boxed{1}^2-6}\implies y = 1-6\implies y = -5

5 0
3 years ago
Find the product. -3x^ 3(-2x^ 2 + 4x + 7)
larisa86 [58]

Answer:

w

Step-by-step explanation:

w is the answer to all ur problems

8 0
3 years ago
Read 2 more answers
Math help please show work thanks
katrin2010 [14]

Answer:

Total material needed = 9.5 square feet

Step-by-step explanation:

Dimensions  of I = 2. 5feet x 1 feet

    Area = 2.5 square feet

Dimensions of S :

                      Top part = 1 feet x 1 feet

                         Area of top part = 1 square feet

                      Bottom part = 1 feet x 2.5 feet

                          Area of bottom part = 2.5 square feet

  Total Area of S = 2.5 + 1  = 3.5  square feet

Total material needed = Area of I + Area of S + Area of S

                                  = 2.5 + 3.5 + 3.5

                                  = 9.5 square feet.

4 0
3 years ago
O
never [62]

Answer:

○ B. 525\:square\:units

Step-by-step explanation:

All sides meet at right angles, so when split up, you have this:

525 = 98 + 21 + 154 + 252 = 7 \times 14 + 3 \times 7 + 11 \times 14 + 9 \times 28

I am joyous to assist you anytime.

8 0
3 years ago
One method of slowing the growth of an insect population without using pesticides is to introduce into the population a number o
mezya [45]

Answer:

I don't know while not enquire from others

8 0
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