The area of a circle is 98. 74cm2. Find the length of the radius rounded to 2 DP

Where did the Industrial Revolution begin?

garri49 [273]

Answer:

england

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

A gas is said to be compressed adiabatically if there is no gain or loss of heat. When such a gas is diatomic (has two atoms per

Tems11 [23]

Answer:

The pressure is changing at $\frac{dP}{dt}=3.68$

Step-by-step explanation:

Suppose we have two quantities, which are connected to each other and both changing with time. A related rate problem is a problem in which we know the rate of change of one of the quantities and want to find the rate of change of the other quantity.

We know that the volume is decreasing at the rate of $\frac{dV}{dt}=-4 \:{\frac{cm^3}{min}}$ and we want to find at what rate is the pressure changing.

The equation that model this situation is

$PV^{1.4}=k$

Differentiate both sides with respect to time t.

$\frac{d}{dt}(PV^{1.4})= \frac{d}{dt}k\\$

The Product rule tells us how to differentiate expressions that are the product of two other, more basic, expressions:

$\frac{d}{{dx}}\left( {f\left( x \right)g\left( x \right)} \right) = f\left( x \right)\frac{d}{{dx}}g\left( x \right) + \frac{d}{{dx}}f\left( x \right)g\left( x \right)$

Apply this rule to our expression we get

$V^{1.4}\cdot \frac{dP}{dt}+1.4\cdot P \cdot V^{0.4} \cdot \frac{dV}{dt}=0$

Solve for $\frac{dP}{dt}$

$V^{1.4}\cdot \frac{dP}{dt}=-1.4\cdot P \cdot V^{0.4} \cdot \frac{dV}{dt}\\\\\frac{dP}{dt}=\frac{-1.4\cdot P \cdot V^{0.4} \cdot \frac{dV}{dt}}{V^{1.4}} \\\\\frac{dP}{dt}=\frac{-1.4\cdot P \cdot \frac{dV}{dt}}{V}}$

when P = 23 kg/cm2, V = 35 cm3, and $\frac{dV}{dt}=-4 \:{\frac{cm^3}{min}}$ this becomes

$\frac{dP}{dt}=\frac{-1.4\cdot P \cdot \frac{dV}{dt}}{V}}\\\\\frac{dP}{dt}=\frac{-1.4\cdot 23 \cdot -4}{35}}\\\\\frac{dP}{dt}=3.68$

The pressure is changing at $\frac{dP}{dt}=3.68$ .

7 0

3 years ago

What’s in a equation or Leniar function y axis 1 and negative 7 and x axis negative 3 and 1

Elodia [21]

A linear function is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable. For example, a common equation,

y

=

m

x

+

b

, (namely the slope-intercept form, which we will learn more about later) is a linear function because it meets both criteria with

x

and

y

as variables and

m

and

b

as constants. It is linear: the exponent of the

x

term is a one (first power), and it follows the definition of a function: for each input (

x

) there is exactly one output (

y

). Also, its graph is a straight line.

5 0

2 years ago

You invest $5,000 in a savings account paying 4% interest compounded quarterly. How much is in the account after 5 years if ther

Hitman42 [59]

1 years is $5200
2 years is $5408
3 years is $5624.32
4 years is $5849.29
5 years is $6083.26

3 0

2 years ago

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Find the total weekly earnings for a waitress with a weekly salary of $257 plus a 4% commission on dinners, if the total worth o

ss7ja [257]

The waitress earns $425 weekly.

Work:
Use proportions.
x 4
------- = ------
4,200 100

4,200 x 4 = 16800
100 multiply x = 100x
16800 divided by 100 = 168
Commission = $168
Base salary = $257
$168 + $257 = $425

8 0

2 years ago