Mathematics, 25.05.2020 20:59, lareynademividp0a99r

Eli was swimming upstream in a river and lost a plastic bottle at bridge A. He noticed the loss after swimming 10 minutes , so immediately started to swim downstream to catch it. He caught it at bridge B, which was 1 mile away from bridge A. What was the rate of water flow in miles per hour?

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answered: Guest

a. geometricb. g[h] = (3/4)·g[h-1]; g[1] = 384c. g[h] = 384·(3/4)^(h-1)d. g[12] ≈ 16.2183 gallonse. g[12] ≈ 64.8732 quarts

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt

answered: Guest

$r(x)=-\frac{1}{50}x^2+14x$

step-by-step explanation:

let's assume

number of candles set =x

price of of x candles =p(x)

we are given

a candle maker prices one set of scented candles at $10 and sells an average of 200 sets each week

so, we get point as (200,10)

$x=200,p=10$

he finds that when he reduces the price by $1, he then sells 50 more candle sets each week

so, we can find slope

$m=-\frac{1}{50}$

now, we can use point slope form of line

$p(x)=mx+b$

now, we can plug values

$p(x)=-\frac{1}{50}x+b$

we can use point

$x=200,p=10$

and find b

$10=-\frac{1}{50}\times 200+b$

$10=-4+b$

$b=14$

now, we can plug it back

and we get

$p(x)=-\frac{1}{50}x+14$

now, we can find revenue

we know that

revenue = price*quantity

so, we get

$r(x)=x\times p(x)$

$r(x)=x\times (-\frac{1}{50}x+14)$

$r(x)=-\frac{1}{50}x^2+14x$

answered: Guest

30,40,50 is correct answer

Which set of side lengths can be used to form a right triangle?

answered: Guest

mariah is studying the life cycle of the monarch butterfly. she must choose one stage in the cycle to present in science class: egg, caterpillar, chrysalis, or adult. she plans to make her choice randomly using a custom spinner divided into four sections. first, however, she spins the spinner 50 times to see the frequencies it generates.

stage times landed on

egg 10

caterpillar 12

chrysalis 15

adult 13

step-by-step explanation:

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Eli was swimming upstream in a river and lost a plastic bottle at bridge A. He noticed the loss afte...