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Nookie1986 [14]
4 years ago
15

The length of a rectangle is 2 less than two times the width. Perimeter is 42. Find the length and the width.

Mathematics
1 answer:
Nuetrik [128]4 years ago
6 0

Answer:

Hi there

Your answer is

width= 5.75

length= 9.5

Step-by-step explanation:

L=2w-2

P=42

Perimeter formula

L+L+W+W=P

(2w-2)+(2w-2)+w+w=42

8w-4=42

+4

8w=46

/8

w= 5.75

Plug in width in length formula!

L=2w-2

L=2(5.75)-2

L=9.5

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The total bill for the Cunningham family was $29.26.

Step-by-step explanation:

Step 1; First we total up the cost of the food alone. Mr. Cunningham spent $7.50, Mrs. Cunningham spent $6.25, the 2 children spent $4.99 each which equals $9.98 for both. So the total of the food alone was $23.73.

Step 2; The sales tax rate was 7.25% of the $23.73. So we multiply 0.0725 (7.25%) with the $23.73 which equals $1.72. So the total bill was for $23.73 + $1.72 which equals $25.45.

Step 3; The Cunningham family left a 15% tip. This was 15% of the toal bill which was $25.45. So we multiply 0.15 (15%) with $25.45 which equals $3.81. So the total bill was food cost + service tax + tips which is $23.73 + $1.72 + $3.81 = $29.26

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A 75-gallon tank is filled with brine (water nearly saturated with salt; used as a preservative) holding 11 pounds of salt in so
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Let A(t) = amount of salt (in pounds) in the tank at time t (in minutes). Then A(0) = 11.

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\left(0.6\dfrac{\rm lb}{\rm gal}\right) \left(3\dfrac{\rm gal}{\rm min}\right) = \dfrac95 \dfrac{\rm lb}{\rm min}

and flows out at a rate

\left(\dfrac{A(t)\,\rm lb}{75\,\rm gal + \left(3\frac{\rm gal}{\rm min} - 3.25\frac{\rm gal}{\rm min}\right)t}\right) \left(3.25\dfrac{\rm gal}{\rm min}\right) = \dfrac{13A(t)}{300-t} \dfrac{\rm lb}{\rm min}

where 4 quarts = 1 gallon so 13 quarts = 3.25 gallon.

Then the net rate of salt flow is given by the differential equation

\dfrac{dA}{dt} = \dfrac95 - \dfrac{13A}{300-t}

which I'll solve with the integrating factor method.

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\dfrac d{dt} \left(-\dfrac1{(300-t)^{13}} A\right) = -\dfrac9{5(300-t)^{13}}

Integrate both sides. By the fundamental theorem of calculus,

\displaystyle -\dfrac1{(300-t)^{13}} A = -\dfrac1{(300-t)^{13}} A\bigg|_{t=0} - \frac95 \int_0^t \frac{du}{(300-u)^{13}}

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\displaystyle -\dfrac1{(300-t)^{13}} A = \dfrac{34}{300^{13}} - \frac3{20}\frac1{(300-t)^{12}}

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\displaystyle A = 45 \left(1 - \frac t{300}\right) - 34 \left(1 - \frac t{300}\right)^{13}

After 1 hour = 60 minutes, the tank will contain

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pounds of salt.

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