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Mars2501 [29]
3 years ago
8

If you place a cup of 210 degree Fahrenheit coffee on a table in a room that is 68 degrees fareinheit, and ten minutes later, it

is 200 degrees fareinheit. How long will it be before the coffee is 180 degrees fareinheit? Use newtons law of cooling
Mathematics
1 answer:
Lana71 [14]3 years ago
8 0
Newton's Law of Cooling

Tf=Ts+(Ti-Ts)e^(-kt)   where Tf is temp at time t, Ts is temp of surroundings, Ti is temp of object/fluid.  So we need to find k first.

200=68+(210-68)e^(-10k)

132=142e^(-10k)

132/142=e^(-10k)

ln(132/142)=-10k

k=-ln(132/142)/10

k≈0.0073  so 

T(t)=68+142e^(-0.0073t)  so how long until it reaches 180°?

180=68+142e^(-0.0073t)

112=142e^(-0.0073t)

112/142=e^(-0.0073t)

ln(112/142)=-0.0073t

t= -ln(112/142)/(0.0073)

t≈32.51 minutes


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The large box is 45 pounds and the small is 20 pounds

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2 years ago
How many solutions does this linear system have? one solution: (0, 0) one solution: (1, –4) no solution infinite number of solut
Anna35 [415]

The system of equations has infinite solutions.

<h2>Given to us,</h2>
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<h3>Equation 2,</h3>

The value of y is already given in equation 1,

-12x-2y=-4

substituting the value of y in equation 2,

-12x-2(-6x+2)=-4\\-12x +12x-4=-4\\-12x+12x=-4+4\\0=0

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Further, the image also shows that the line of the two equations are coinciding.

Hence, the system of equations has infinite solutions.

Learn more about System of solutions:

brainly.com/question/14264175

3 0
2 years ago
F(x)=(x+4)(x-2)(x+4)(x+4)<br><br> What is the multiple zero? Multiplicity is?
kari74 [83]
f(x)=(x+4)(x-2)(x+4)(x+4)\\f(x)=(x+4)^3(x-2)=0\\(x+4)^3=0~|~(x-2)=0\\(x+4)(x+4)(x+4)=0~|~x=2\\x=-4,2

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8 0
2 years ago
If 18 is subtracted from twice the square of an integer, the
Sergeu [11.5K]

Answer:

-3/2

Step-by-step explanation:

Let x = the integer:

2x^2 - 18 = 9x

2x^2 - 9x - 18 = 0

Now either factor that or use the quadratic formula if you're lazy like me.

x = -3/2 and 6, so x must be 6 because it has to be an integer.

5 0
2 years ago
HELP PLZ PICK ONE OF THE ONES SHOWN:
defon

I am doing with Question Number 2

Let the two numbers be 'x' and 'y'.

According to the question, the product of two numbers is 14.

x \times y=14

So, xy=14 (Equation 1)

Now, one of the numbers is 3 ½ times the other.

So, x = 3\frac{1}{2}\times y

x=\frac{7}{2}y (Equation 2)

Substituting the value of 'x' from equation 2 in equation 1, we get

\frac{7}{2}y \times y = 14

\frac{7}{2}y^{2} = 14

y^{2} = 4

So, y= 2 and -2

So, x=\frac{14}{2} and x=\frac{14}{-2}

x=7 and -7

Numbers are 2,7 and -2,-7.

Sum of numbers 2 and 7 = 9

Sum of numbers -2 and -7 = -9.


6 0
3 years ago
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