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3 years ago

The length of a field in feet is a function f(n) of the length nin yards. Write a function rule for this situation.

Mathematics

1 answer:

qwelly [4]3 years ago

5 0

Given:

The length of field is n yards.

The length of a field in feet is a function f(n).

To find:

The function rule for this situation.

Solution:

We know that,

1 yard = 3 feet

Using this conversion, we get

n yard = 3n feet

The length of field is n yards. So, the length of the field is 3n feets.

The length of a field in feet is a function f(n). So,

$f(n)=3n$

Therefore, the required function rule for this situation is $f(n)=3n$ .

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A tank contains 250 liters of fluid in which 40 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pu

VashaNatasha [74]

Answer:

$A(t)=250-210e^{-\frac{t}{50}}$

Step-by-step explanation:

We are given that

Volume,V=250 L

Mass of salt=m=40 g

Brine containing 1 g per liter

Pumped into the tank at the rate=5 L/min

We have to find the number A(t) of grams of salt in the tank at time t.

Rate of change of salt in the tank

$\frac{dA}{dt}=$ Rate in-Rate out

Rate in=5 L/min

Rate out= $\frac{A}{250}\times 5=\frac{A}{50}$ L/min

$\frac{dA}{dt}=5-\frac{A}{50}=\frac{250-A}{50}$

$\int \frac{50dA}{250-A}=\int dt$

$-50ln(250-A)=t+C$

Using the formula

$\int \frac{dx}{x}=ln x$

A=40 and t=0

$-50ln(250-40)=0+C$

$-50ln(210)=C$

Substitute the value

$-50ln(250-A)=t-50ln(210)$

$-50ln(250-A)+50ln(210)=t$

$50ln\frac{210}{250-A}=t$

$t=50ln\frac{210}{250-A}$

$\frac{t}{50}=ln\frac{210}{250-A}$

$\frac{210}{250-A}=e^{\frac{t}{50}$

$\frac{250-A}{210}=e^{-\frac{t}{50}}$

$250-A=210e^{-\frac{t}{50}}$

$A(t)=250-210e^{-\frac{t}{50}}$

8 0

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Factor the expression. <br><br> 9x^2 + 48x + 64

Savatey [412]

(3x+8)(3x+8) is the answer :))

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3 years ago

Keisha makes a large sandwich for her family picnic she takes one half of the sandwich to the picnic at the picnic her family ea

Ivanshal [37]

Answer:

Keisha has 1/8th of the sandwich that she brings back.

Step-by-step explanation:

To start, take a whole sandwich and subtract the 1/2 she left at home and the 3/8 that her family ate.

1 - 1/2 - 3/8 = Leftover

We also need to give them common denominators to complete the action.

8/8 - 4/8 - 3/8 = Leftover

1/8 = Leftover

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3 years ago

Double the sum of 36 and 5

vesna_86 [32]

36 + 5 = 41

41 x 2 = 82

The answer is 82

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3 years ago

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Please see attached. <br> Please explain.

Gemiola [76]

Your mom can explain ok stop asking

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