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sesenic [268]
2 years ago
12

What is the sum of the infinite geometric series? mc010-1.jpg

Mathematics
1 answer:
ra1l [238]2 years ago
4 0
You haven't provided the series, therefore, I can only help with the concept.

<u><em>For an infinite geometric series, we have two possibilities for the common ratio (r):</em></u>
for r > 1, the terms in the series will keep increasing infinitely and the only possible logic summation of the series would be infinity
for r < 1, the terms will decrease, therefore, we can formulate a rule to get the sum of the infinite series

<u><em>In an infinite series with r < 1, the summation can be found using the following rule:</em></u>
sum = \frac{a_{1} }{1-r}
where:
a₁ is the first term in the series
r is the common ratio

<u>Example:</u>
For the series:
2 , 1, 0.5 , 0.25 , ....
we have:
a₁ = 2
r = 0.5
Therefre:
sum = \frac{2}{1-0.5} = 4

Hope this helps :)
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Drew creates a table of ordered pairs representing the width and area of a dog pen. Which situation could describe Drew’s plans
Feliz [49]

Answer:

the answer is A :)

Step-by-step explanation:


8 0
2 years ago
Read 2 more answers
F(x)=3x 2 +9f, left parenthesis, x, right parenthesis, equals, 3, x, squared, plus, 9 and g(x)=\dfrac{1}{3}x^2-9g(x)= 3 1 ​ x 2
34kurt

Answer:

f(g(x)) = \frac{1}{3}x^4 - 18x^2 + 252

g(f(x)) = 3x^4 + 18x^2 + 18

<em>f(x) and g(x) and not inverse functions</em>

Step-by-step explanation:

Given

f(x) = 3x^2 + 9

g(x) = \dfrac{1}{3}x^2 - 9

Required

Determine f(g(x))

Determine g(f(x))

Determine if both functions are inverse:

Calculating f(g(x))

f(x) = 3x^2 + 9

f(g(x)) = 3(\frac{1}{3}x^2 - 9)^2 + 9

f(g(x)) = 3(\frac{1}{3}x^2 - 9)(\frac{1}{3}x^2 - 9) + 9

Expand Brackets

f(g(x)) = (x^2 - 27)(\frac{1}{3}x^2 - 9) + 9

f(g(x)) = x^2(\frac{1}{3}x^2 - 9) - 27(\frac{1}{3}x^2 - 9) + 9

f(g(x)) = \frac{1}{3}x^4 - 9x^2 - 9x^2 + 243 + 9

f(g(x)) = \frac{1}{3}x^4 - 18x^2 + 252

Calculating g(f(x))

g(x) = \dfrac{1}{3}x^2 - 9

g(f(x)) = \frac{1}{3}(3x^2 + 9)^2 - 9

g(f(x)) = \frac{1}{3}(3x^2 + 9)(3x^2 + 9) - 9

g(f(x)) = (x^2 + 3)(3x^2 + 9) - 9

Expand Brackets

g(f(x)) = x^2(3x^2 + 9) + 3(3x^2 + 9) - 9

g(f(x)) = 3x^4 + 9x^2 + 9x^2 + 27 - 9

g(f(x)) = 3x^4 + 18x^2 + 18

Checking for inverse functions

f(x) = 3x^2 + 9

Represent f(x) with y

y = 3x^2 + 9

Swap positions of x and y

x = 3y^2 + 9

Subtract 9 from both sides

x - 9 = 3y^2 + 9 - 9

x - 9 = 3y^2

3y^2 = x - 9

Divide through by 3

\frac{3y^2}{3} = \frac{x}{3} - \frac{9}{3}

y^2 = \frac{x}{3} - 3

Take square root of both sides

\sqrt{y^2} = \sqrt{\frac{x}{3} - 3}

y = \sqrt{\frac{x}{3} - 3}

Represent y with g(x)

g(x) = \sqrt{\frac{x}{3} - 3}

Note that the resulting value of g(x) is not the same as g(x) = \dfrac{1}{3}x^2 - 9

<em>Hence, f(x) and g(x) and not inverse functions</em>

4 0
2 years ago
What is the slope of the segment shown for a staircase with 10-inch treads and 7.75-inch risers? As you walk up (or down) the st
s2008m [1.1K]

The formula for slope is

Slope = Rise / Run = Risers / Treads

Slope = 7.75 in /10 in = 0.775

The slope Is 0.775.

The vertical distance is not continuous, thus it is discrete. A discrete function only allows certain points in the interval. When you walk up or down the stairs, the vertical distances are not continuous because of the treads. You cannot stay also mid-air, so it should be discrete. An example of a continuous function would be when you walk up or down an inclined plane. 

8 0
2 years ago
What is the positive solution to this equation? 4x2 + 12x = 135​
Bas_tet [7]

Answer:

127/12

Step-by-step explanation:

4 × 2 + 12x = 135

(1. Simplify 4 x 2 to 8.

8 + 12x = 135

(2. Subtract 88 from both sides.

12x= 135 - 8

(3. Simplify 135 - 8 to 127

12x = 127

(4. Divide both sides by 12

x= 127/12

Decimal Form: 10.583333

I think this is the awnser, but don't quote me on that

4 0
2 years ago
Of the28 golf balls 5/7 are white how many are white
Goshia [24]

Answer:

20 balls are white

Step-by-step explanation:

5/7* 28

7 0
2 years ago
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