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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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In the graph below, Point A represents Owen's house, Point B represents David's house and Point C represents the school. Who liv
ycow [4]

Answer:

• David

,

• 4 miles

Explanation:

In the graph:

The given locations are:

• Owen's House, A(11,3)

,

• David's House, B(15,13)

,

• School, C(3,18)

We determine both Owen's and David's distance from the school using the distance formula.

Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Owen's distance from school (AC)

\begin{gathered} AC=\sqrt[]{(3-11)^2+(18-3)^2} \\ =\sqrt[]{(-8)^2+(15)^2} \\ =\sqrt[]{64+225} \\ =\sqrt[]{289} \\ AC=17\text{ miles} \end{gathered}

David's distance from school (BC)

\begin{gathered} BC=\sqrt[]{(3-15)^2+(18-13)^2} \\ =\sqrt[]{(-12)^2+(5)^2} \\ =\sqrt[]{144+25} \\ =\sqrt[]{169} \\ BC=13\text{ miles} \end{gathered}

We see from the calculations that David lives closer to the school, and by 4 miles.

The graph below is attached for further understanding:

5 0
11 months ago
Solve the system of equations.<br> -10x+3y=5 <br> x=y-4
blsea [12.9K]

Answer:

x=y-4                                          -10x+3y=5

y=x+4                                     y=10/3x+5/3

        x+4  =10/3x+5/3              

x=1

y=1+4                                      y=10/3(1)+5/3

y=5                                                    y=5

so

x=1

y=5

(1,5)

5 0
3 years ago
Jade has $451.89 in her checking account. After 3 checks, each for the same amount, are deducted from her account, she has $358.
Lana71 [14]

and the second one 2 will work!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

6 0
3 years ago
Read 2 more answers
Solve these equations. Thanks.
Nutka1998 [239]

Answer:

1. 3.572 x 10^(-1)

2. 3.108 x 10^(6)

3. 5.31881533 x 10^(-6)

4. 4.18676122 x 10^(-1)

Hope this helps

8 0
3 years ago
Find the distance between the two points rounding to the nearest tenth
mixas84 [53]

Answer:

8.54

Step-by-step explanation:

formula:

d=\sqrt{(x2-x1)^2 + (y2-y1)^2}

d=\sqrt{(-4 - (-7))^2 + (0-(-8))^2}

d=\sqrt{3^2 + 8^2}

d=\sqrt{9 + 64}

d=\sqrt{73}

d= 8.54

6 0
3 years ago
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