All categories

3 years ago

Please show me the work!

Mathematics

1 answer:

Papessa [141]3 years ago

6 0

Answer:

9/2π cm/s

Step-by-step explanation:

Volume of the spherical balloon V= 4/3πr³

Rate of change of volume dV/dt = dV/dr * dr/dt

dV/dr = 3(4/3πr²)

dV/dr = 4πr²

dV/dr = 4π(2)²

dV/dr = 16π

If V = 72cm²/s

72 = 16π*dr/dt

dr/dt = 72/16π

dr/dt = 9/2π cm/s

Hence the radius is changing at 9/2π cm/s

You might be interested in

One summer, an ice cream truck driver sold 381 Popsicles and 76 ice creams. How many treats did the driver sell in all?

vazorg [7]

The answer is 457 because when you add 381 and 76 together you get 457

8 0

3 years ago

Find dy/dx given that y = sin x / 1 + cos x

kobusy [5.1K]

Answer:

$\frac{1}{1 + \cos(x) }$

Step-by-step explanation:

$y = \frac{ \sin(x) }{1 + \cos(x) }$

<u>differentiating numerator wrt x :-</u>

(sinx)' = cos x

<u>differentiating denominator wrt x :- </u>

(1 + cos x)' = (cosx)' = - sinx

Let's say the denominator was "v" and the numerator was "u"

$(\frac{u}{v} )' = \frac{v. \: (u)' - u.(v)' }{ {v}^{2} }$

here,

since u is the numerator u= sinx and u = cos x
v(denominator) = 1 + cos x; v' = - sinx

$= \frac{((1 + \cos \: x) \cos \: x )- (\sin \: x. ( - \sin \: x) ) }{( {1 + \cos(x)) }^{2} }$

$= \frac{ \cos(x) + \cos {}^{2} (x) + \sin {}^{2} (x) }{(1 + \cos \: x) {}^{2} }$

since cos²x + sin²x = 1

$= \frac{ \cos \: x + 1}{(1 + \cos \: x) {}^{2} }$

diving numerator and denominator by 1 + cos x

$= \frac{1}{1 + \cos(x) }$

6 0

3 years ago

The minimum and maximum temperature on a cold day in Lollypop Town can be modeled by the equation below: 2|x − 6| + 14 = 38 What

enyata [817]

$2|x-6|+14=38$
$\rightarrow2|x-6|=24$
$\rightarrow|x-6|=12$

There are two cases:
1. $x-6=12\rightarrow x=18$
2. $x-6=-12\rightarrow x=-6$

So the minimum temperature is -6, and the maximum is 18.

5 0

3 years ago

Read 2 more answers

Annual rent $ 7,380

jeyben [28]

Answer:

Part A:

Rent = $7380

Mortgage payments = $9800

Insurance = $145

Taxes, insurance, maintenance = $1780+1050$ = $2830

Loss of Interest on security deposit = (650*6%) = $39

Interest lost on down payment and closing cost = (4,500*6%) = $270

Growth in equity = $225

Annual appreciation = $1700

Tax savings for mortgage interest = (9,575*28%) = $2,681

Tax savings for property taxes = (1,780*28%) = $498

Total rental cost = $7,380+145+39=7,564$ dollars

Total buying costs = $9,800+2,830+270-225-1,700-2,681-498=7,796$ dollars

Part B:

You should consider rent because the cost of renting is less than the cost of buying.

7 0

3 years ago

What simple machine is similar to a pulley?

jek_recluse [69]

A lever in like a pully becasue it can pull just as so. Hope that helped. It is what my teacher taught me.

5 0

3 years ago