Which polynomial is written in standard form?

Circumfrance of a circle, (Show working)

Ronch [10]

Answer:

25.1cm

Step-by-step explanation:

C=2πr

here radius, r=4 cm and π=3.142

Put values in formula.

C=2(3.142)(4)

C=25.1 cm (Rounded to 1 decimal place)

3 0

3 years ago

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5. A tank initially contains 20 lb of salt dissolved in 200-gallon of water. Starting at time t = 0, a solution containing 0.5 l

sladkih [1.3K]

Answer:

(a) Amount of salt as a function of time

$A(t)=100-80e^{-0.02t}$

(b) The time at which the amount of salt in the tank reaches 50 lb is 23.5 minutes.

(c) The amount of salt when t approaches to +inf is 100 lb.

Step-by-step explanation:

The rate of change of the amount of salt can be written as

$\frac{dA}{dt} =rate\,in\,-\,rate\,out\\\\\frac{dA}{dt}=C_i*q_i-C_o*q_o=C_i*q_i-\frac{A(t)}{V}*q_o\\\\\frac{dA}{dt}=0.5*4-\frac{A(t)}{200}*4\\\\\frac{dA}{dt} =\frac{100-A(t)}{50}=-(\frac{A(t)-100}{50})$

Then we can rearrange and integrate

$\frac{dA}{dt}= -(\frac{A(t)-100}{50})\\\\\int \frac{dA}{A-100}=-\frac{1}{50} \int dt\\\\ln(A-100)=-\frac{t}{50}+C_0\\\\ A-100=Ce^{-0.02*t}\\\\\\A(0)=20 \rightarrow 20-100=Ce^0=C\\C=-80\\\\A=100-80e^{-0.02t}$

Then we have the model of A(t) like

$A(t)=100-80e^{-0.02t}$

(b) The time at which the amount of salt reaches 50 lb is

$A(t)=100-80e^{-0.02t}=50\\\\e^{-0.02t}=(50-100)/(-80)=0.625\\\\-0.02*t=ln(0.625)=-0.47\\\\t=(-0.47)/(-0.02)=23.5$

(c) When t approaches to +infinit, the term e^(-0.02t) approaches to zero, so the amount of salt in the solution approaches to 100 lb.

7 0

3 years ago

732,178+167-542,137=

madreJ [45]

( 732,178 + 167 ) = 899,178
899,178 - 542,137 = *357,041 that's the last result.

3 0

3 years ago

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Plzzzz help me on this

Grace [21]

Answer: 228 feet squared

How: To get the area of the entire field, multiply 25•36 to get 900. To find length of the area inside the path, you have to subtract 2 feet from both sides of 25, which is also 4 feet, to get 25-4=21. To find the width of the area inside the path, you have to subtract 2 feet from both sides of 36, which is also 4 feet, to get 36-4=32. You multiply 21•32 to get 672, which is the area of the field inside of the path. To find the area of the path, you subtract the total area of the field and the path together, which is 900, by 672 to get 228 feet squared.

7 0

3 years ago

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Rename the number 24 tenthousands =

KATRIN_1 [288]

24 ten thousands means 24 x 10, 000 which is equivalent to 240, 000. see attached file for the illustration.

3 0

4 years ago