All categories

3 years ago

What is the sum of the infinite geometric series? -3-3/2-3/4-3/8-3/16-....

Mathematics

2 answers:

Natali5045456 [20]3 years ago

6 0

Answer:

- 6

Step-by-step explanation:

The sum to infinity of a geometric series is calculated as

S( infinity ) = $\frac{a}{1-r}$

where a is the first term and r the common ratio

Here a = - 3 and r = - $\frac{3}{2}$ ÷ - 3 = $\frac{1}{2}$ , thus

S( infinity ) = $\frac{-3}{1-\frac{1}{2} }$ = $\frac{-3}{\frac{1}{2} }$ = - 6

larisa86 [58]3 years ago

3 0

Answer:

s infinite =-6

Step-by-step explanation:

You might be interested in

Use the Midpoint Rule with n = 5 to estimate the volume V obtained by rotating about the y-axis the region under the curve y = 1

velikii [3]

Using the shell method, the volume is given exactly by the definite integral,

$2\pi\displaystyle\int_0^1x(1+9x^3)\,\mathrm dx$

Splitting up the interval [0, 1] into 5 subintervals gives the partition,

[0, 1/5], [1/5, 2/5], [2/5, 3/5], [3/5, 4/5], [4/5, 5]

with left and right endpoints, respectively, for the $i$ -th subinterval

$\ell_i=\dfrac{i-1}5$

$r_i=\dfrac i5$

where $1\le i\le5$ . The midpoint of each subinterval is

$m_i=\dfrac{\ell_i+r_i}2=\dfrac{2i-1}{10}$

Then the Riemann sum approximating the integral above is

$2\pi\displaystyle\sum_{i=1}^5m_i(1+9{m_i}^3)\frac{1-0}5$

$\dfrac{2\pi}5\displaystyle\sum_{i=1}^5\left(\frac{2i-1}{10}+9\left(\frac{2i-1}{10}\right)^4\right)$

$\dfrac{2\pi}{5\cdot10^4}\displaystyle\sum_{i=1}^5\left(16i^4-32i^3+24i^2+1992i-999\right)=\frac{112,021\pi}{25,000}\approx\boxed{14.08}$

(compare to the actual value of the integral of about 14.45)

3 0

3 years ago

A model ship uses the scale 1 inch : 10 feet. If the model is 9.5 inches long, the ship is ____ feet long

Debora [2.8K]

Answer:

i got 95 inches

Step-by-step explanation:

5 0

2 years ago

a rectangular prism has a length of 2 3/4 feet, a width of 4 1/2 feet, and a height of 6 inches. what is the volume of the prism

Nataliya [291]

Answer:

10692 cubic inches

Step-by-step explanation:

Since we are told to give the units in inches, let's convert the two values which are in feet.

1 ft= 12 inches

thus,

length 2.75 ft. = 33inch

breadth 4.5 ft. = 54 inch

and height is 6 inches.

Volume of a cube= length × width × height

= 33 × 54 × 6

= 10692 cubic inches

7 0

2 years ago

Factor 36x^2 + 11x-12 please hurry

xz_007 [3.2K]

Answer:

The answer is

Step-by-step explanation:

36x² + 11x - 12

To factor the expression rewrite 11x as a difference

That's

36x² + 27x - 16x - 12

<u>Factor out 9x from the expression</u>

9x( 4x + 3) - 16x - 12

<u>Factor out - 4 from the expression</u>

9x( 4x + 3) - 4( 4x + 3)

Factor out 4x + 3 from the expression

We have the final answer as

Hope this helps you

5 0

3 years ago

Read 2 more answers

PLEASE HELP ME!!!!!!! SEE BOTH PICTURES!!!!

Natali [406]

I think both answers are C.

(-8,-4) and (-5,-2)

other one

Fix the compass at points P and T

3 0

3 years ago