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1 year ago

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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A positive real number is 2 less than another. When 4 times the larger is added to the square of the smaller, the result is 49.

Kobotan [32]

Answer:

The numbers are

$-2+3\sqrt{5}$ and $3\sqrt{5}$

Step-by-step explanation:

Let

x -----> the smaller positive real number

y -----> the larger positive real number

we know that

A positive real number is 2 less than another

$x=y-2$

$y=x+2$ ----> equation A

When 4 times the larger is added to the square of the smaller, the result is 49

$4y+x^2=49$ ----> equation B

substitute equation A in equation B

$4(x+2)+x^2=49$

solve for x

$x^2+4x-41=0$

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$x^2+4x-41=0$

$a=1\\b=4\\c=-41$

substitute in the formula

$x=\frac{-4\pm\sqrt{4^{2}-4(1)(-41)}} {2(1)}$

$x=\frac{-4\pm\sqrt{180}} {2}$

$x=\frac{-4\pm6\sqrt{5}} {2}$

$x=-2\pm3\sqrt{5}$

The positive real number is

$x=-2+3\sqrt{5}$

Find the value of y

$y=x+2$

$y=-2+3\sqrt{5}+2$

$y=3\sqrt{5}$

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3 years ago

Which statements about the graph of the function y=(1/3)

Elena-2011 [213]

Answer: The range of the function is all real numbers is true.

Explanation: the graph of y = 1/3 is just a horizontal line at y = 1/3. so it’s not increasing or decreasing (it’s staying the same). there is no x-intercept, and the y-intercept is (0, 1/3). the range is all the possible y values, and there are infinite possible y values, so it is all real numbers.

hope this helps!

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3 years ago

32% as a fraction in lowest terms

TiliK225 [7]

32% means 32/100

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A; 8/25.

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2 years ago

By using the table in the handbook, the present value of $12,000 for six years compounded at 6 percent semiannually is

denis23 [38]

Take a look at the attachment to see the solution.
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3 years ago

In ΔBCD, \overline{BD} BD is extended through point D to point E, m∠CDE = (6x-13)^{\circ}(6x−13) ∘ , m∠BCD = (2x+10)^{\circ}(2x+

AveGali [126]

Answer:

m∠CDE = 35°

Step-by-step explanation:

The exterior angle CDE is equal to the sum of the opposite interior angles, BCD and DBC. So, you have ...

6x -13 = (2x+10) +(x +1)

3x -24 = 0 . . . . . . . . . . . . subtract the right side, simplify

x -8 = 0 . . . . . . . . . . . . . . divide by 3

x = 8 . . . . . . . . . . . . . . . . . add 8

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