Type the correct answer in the box. If necessary, use / for the fraction bar.

A motorboat travels 275 kilometers in 5 hours going upstream. It travels 405 kilometers going downstream in the same amount of t

VladimirAG [237]

Step-by-step explanation:

$275 \times 5 = 1375$

The rate of the motorboat on still water is 1375

$405 \times 5 = 2025$

The current rate of the motorboat is 2025

4 0

2 years ago

If one person recruits five people and each recruited person recruits 5 more, and so on, 15 cycles; how many people would that b

jek_recluse [69]

Answer:

y=5^x

5^15= 30517578125 people

Step-by-step explanation:

x=# of cycles= 15 cycles

y= #of people recruited = what we're figuring out

Plug in 15 for x in the equation y=5^x

y= 5^15= 30517578125 people

3 0

2 years ago

The radius of a cone is decreasing at a constant rate of 7 inches per second, and the volume is decreasing at a rate of 948 cubi

inessss [21]

Answer:

The height of cone is decreasing at a rate of 0.085131 inch per second.

Step-by-step explanation:

We are given the following information in the question:

The radius of a cone is decreasing at a constant rate.

$\displaystyle\frac{dr}{dt} = -7\text{ inch per second}$

The volume is decreasing at a constant rate.

$\displaystyle\frac{dV}{dt} = -948\text{ cubic inch per second}$

Instant radius = 99 inch

Instant Volume = 525 cubic inches

We have to find the rate of change of height with respect to time.

Volume of cone =

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

Instant volume =

$525 = \displaystyle\frac{1}{3}\pi r^2h = \frac{1}{3}\pi (99)^2h\\\\\text{Instant heigth} = h = \frac{525\times 3}{\pi(99)^2}$

Differentiating with respect to t,

$\displaystyle\frac{dV}{dt} = \frac{1}{3}\pi \bigg(2r\frac{dr}{dt}h + r^2\frac{dh}{dt}\bigg)$

Putting all the values, we get,

$\displaystyle\frac{dV}{dt} = \frac{1}{3}\pi \bigg(2r\frac{dr}{dt}h + r^2\frac{dh}{dt}\bigg)\\\\-948 = \frac{1}{3}\pi\bigg(2(99)(-7)(\frac{525\times 3}{\pi(99)^2}) + (99)(99)\frac{dh}{dt}\bigg)\\\\\frac{-948\times 3}{\pi} + \frac{2\times 7\times 525\times 3}{99\times \pi} = (99)^2\frac{dh}{dt}\\\\\frac{1}{(99)^2}\bigg(\frac{-948\times 3}{\pi} + \frac{2\times 7\times 525\times 3}{99\times \pi}\bigg) = \frac{dh}{dt}\\\\\frac{dh}{dt} = -0.085131$

Thus, the height of cone is decreasing at a rate of 0.085131 inch per second.

3 0

2 years ago

HELP ASAP

Ludmilka [50]

The answer is a. Because when word phrases say “a number”, they are referring to the variable. For instance, x is the variable so x is “a number”.

8 0

2 years ago

A punch recipe calls for 1/2 gallon of ginger ale, 1/2 qt of

Blababa [14]

Answer: 14

Step-by-step explanation:

1/2 gallon =2 quarts, so add the 2 quarts and the 1 quart of ginger ale, plus the one pint of lemonade and this makes 14 cups of punch

8 0

2 years ago