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2 years ago

Find the value of the geometric series1000 + 1000(1.03) + 1000(1.03)2 + . . . + 1000(1.03)9

Mathematics

1 answer:

valentinak56 [21]2 years ago

4 0

Answer:

$\boxed{\sf \ \ \ 11,464 \ \ \ }$

Step-by-step explanation:

hello

we need to compute the following

$\sum\limits^9_{i=0} {1000(1.03)^i}=1000\dfrac{1.03^{10}-1}{1.03-1}=11463.879...$

hope this helps

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The admission fee at a movie theater is $5 for children and $9 for adults. If 3200 people go to the movies and $24000 is collect

Usimov [2.4K]

For this problem, let x be the number of children and y for adults. Formulate the equations: 1st equation, x + y = 3,200 and 2nd equation 5x + 9y = 24,000. Re-arrange 1st equation into x = 3200 - y. Then, substitute into 2nd equation, 5(3,200-y) + 9y = 24,000. Then, solve for y. The 16,000 - 5y + 9y = 24000. Final answer is, y = 2000 adults went to watch the movie.

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2 years ago

Tom went on a bike to the store 3 miles away. If it took Tom 1/2 of an hour to get there and 2/3 of an hour to get back , what w

anastassius [24]

Answer:

5.14 mi/h

Step-by-step explanation:

To find the average speed, we simply find the total distance traveled by Tom and divide that by the total time the entire journey took him.

Average speed = (total distance traveled) / (total time taken)

TOTAL DISTANCE TRAVELED

He traveled 3 miles to and 3 miles fro. Hence:

3 + 3 = 6 miles

TOTAL TIME TAKEN

He spent ½ hr to go and ⅔ hr to return back. Hence:

½ + ⅔ = 7/6 hr

Therefore, the average speed is:

v = 6 / (7/6)

v = 36 / 7 = 5.14 mi/h

Tom's average speed was 5.14 mi/h.

8 0

2 years ago

The radius of a right circular cone is increasing at a rate of 1.4 in/s while its height is decreasing at a rate of 2.1 in/s. At

kow [346]

Given:

$\dfrac{dr}{dt}=1.4\text{ in/s}$

$\dfrac{dh}{dt}=-2.1\text{ in/s}$

To find:

The rate of change in volume at $r=120\text{ in. and }175\text{ in.}$

Solution:

We know that, volume of a cone is

$V=\dfrac{1}{3}\pi r^2h$

Differentiate with respect to t.

$\dfrac{dV}{dt}=\dfrac{1}{3}\pi\times \left[(r^2\dfrac{dh}{dt}) + h(2r\dfrac{dr}{dt})\right]$

Substitute the given values.

$\dfrac{dV}{dt}=\dfrac{1}{3}\times \dfrac{22}{7}\times \left[(120)^2(-2.1) +175(2)(120)(1.4)\right]$

$\dfrac{dV}{dt}=\dfrac{22}{21}\times \left[-30240+58800\right]$

$\dfrac{dV}{dt}=\dfrac{22}{21}\times 28560$

$\dfrac{dV}{dt}=29920$

Therefore, the volume of decreased by 29920 cubic inches per second.

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2 years ago

−15x+4≤109 OR −6x+70>−2

Xelga [282]

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