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EastWind [94]
2 years ago
15

obtain the value of X for which (X+1),(X-5),(X-2) is a geometric progression.hence find the sum of the first 12 terms of the pro

gression.​
Mathematics
1 answer:
Viktor [21]2 years ago
5 0

If <em>x</em> + 1, <em>x</em> - 5, and <em>x</em> - 2 are in a geometric progression, then there is some constant <em>r</em> for which

<em>x</em> - 5 = <em>r</em> (<em>x</em> + 1)

==>   <em>r</em> = (<em>x</em> - 5) / (<em>x</em> + 1)

and

<em>x</em> - 2 = <em>r</em> (<em>x</em> - 5)

==>   <em>r</em> = (<em>x</em> - 2) / (<em>x</em> - 5)

Then

(<em>x</em> - 5) / (<em>x</em> + 1) = (<em>x</em> - 2) / (<em>x</em> - 5)

Solve for <em>x</em> :

(<em>x</em> - 5)² = (<em>x</em> - 2) (<em>x</em> + 1)

<em>x</em> ² - 10<em>x</em> + 25 = <em>x</em> ² - <em>x</em> - 2

-9<em>x</em> = -27

<em>x</em> = 3

It follows that the ratio between terms is

<em>r</em> = (3 - 5) / (3 + 1) = -2/4 = -1/2

Now, assuming <em>x</em> + 1 = 4 is the first term of the G.P., the <em>n</em>-th term <em>a(n)</em> is given by

<em>a(n)</em> = 4 (-1/2)ⁿ⁻¹

The sum of the first 12 terms - denoted here by <em>S</em> - is then

<em>S</em> = 4 (-1/2)⁰ + 4 (-1/2)¹ + 4 (-1/2)² + … + 4 (-1/2)¹¹

Solve for <em>S</em> :

<em>S</em> = 4 [(-1/2)⁰ + (-1/2)¹ + (-1/2)² + … + (-1/2)¹¹]

(-1/2) <em>S</em> = 4 [(-1/2)¹ + (-1/2)² + (-1/2)³ + … + (-1/2)¹²]

==>   <em>S</em> - (-1/2) <em>S</em> = 4 [(-1/2)⁰ - (-1/2)¹²]

==>   3/2 <em>S</em> = 4 (1 - 1/4096)

==>   <em>S</em> = 8/3 (1 - 1/4096)

==>   <em>S</em> = 1365/512

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HOW MANY BASEBALLS CAN FIT INTO THE TRACTOR TRAILER. THE TRAILER DIMENSIONS ARE 301.5"L X 96.99"W X 105.04"H AND CIRCUMFERENCE R
Shkiper50 [21]
Volume of tractor = length x width x height = 301.5 x 96.99 x 105.04 = 3,071,630.624

For baseballs of 9 inches:
9=2\pi r \\  \\ r= \frac{9}{2\pi}

Volume = \frac{4}{3} \pi r^3= \frac{4}{3} \pi \left( \frac{9}{2\pi} \right)^3=12.31

Number of 9 inches baseballs = \frac{3,071,630.624}{12.31} = 249,513

For baseballs of 9.25 inches:
9.25=2\pi r \\  \\ r= \frac{9.25}{2\pi}

Volume = \frac{4}{3} \pi r^3= \frac{4}{3} \pi \left( \frac{9.25}{2\pi} \right)^3=13.37

Number of 9.25 inches baseballs = \frac{3,071,630.624}{13.36} = 229,824

Therefore, the tractor can contain between 229,824 and 249,513 baseballs.
8 0
3 years ago
Plssss help (ZOOM IN TO SEE FULL PIC)
MA_775_DIABLO [31]

Answer:

d and e

Step-by-step explanation:

IV must have a pos x value and a negative y value

we can eliminate everything except d e & f

f is wrong bc it has a positive 3 value

5 0
2 years ago
Please help me out!!!!
svetoff [14.1K]

Answer:

b= 70

Step-by-step explanation:

The sum of the opposite interior angles of a triangle is equal to exterior angle.

a+b = 140

We know that a = b since PQ = RQ  The angles opposite the equal sides in an isosceles triangle are equal

b+b = 140

2b =140

Divide by 2

2b/2 =140/2

b= 70


6 0
3 years ago
What's the answer????
katrin2010 [14]
A
C
D
E
F

B should be the obvious no-no
7 0
3 years ago
I need help with this I’ll mark you as branliest
Leni [432]

Answer:

y=3x

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
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