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Paul [167]
3 years ago
10

A circle has a diameter of 26 units. What is the area of the circle to the nearest hundred of a square unit?

Mathematics
2 answers:
Nady [450]3 years ago
5 0

Answer: The area is 530 square units

Step-by-step explanation: The diameter of the circle has been given as 26. That makes the radius 13, that is;

Radius = diameter/2

Radius = 26/2

Radius = 13

The area of a circle is derived by the formula;

Area = pi x r^2

Where pi is 3.14 and r is 13,

Area = (3.14) x 13^2

Area = 3.14 x 169

Area = 530.66

Approximately to the nearest hundred of a square unit,

The area of the circle is 530 square units

iVinArrow [24]3 years ago
4 0

Answer:

531 square units

Step-by-step explanation:

Area of a circle = pi r2

Given

Diameter = 26 units

Radius r = diameter/2 = 26/2

= 13units

Pi = 3.14

Therefore

Area = 3.14 x (13)^2

= 3.14 x 13 x 13

= 530.66

= 531 square units

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(a) Using Newton's Law of Cooling, \dfrac{dT}{dt} = k(T - T_s), we have \dfrac{dT}{dt} = k(T - 75) where T is temperature after T minutes.
Separate by dividing both sides by T - 75 to get \dfrac{dT}{T - 75} = k dt. Integrate both sides to get \ln|T - 75| = kt + C.

Since T(0) = 185, we solve for C:
|185 - 75| = k(0) + C\ \Rightarrow\ C = \ln 110
So we get \ln|T - 75| = kt + \ln 110. Use T(30) = 150 to solve for k:
\ln| 150 - 75 | = 30k + \ln 110\ \Rightarrow\ \ln 75 - \ln 110= 30k \Rightarrow \\ k= \frac{1}{30}\ln (75/110) = \frac{1}{30}\ln(15/22)

So

\ln|T - 75| = kt + \ln 110 \Rightarrow |T - 75| = e^{kt + \ln110} \Rightarrow \\ \\
|T - 75| = 110e^{kt} \Rightarrow T - 75 = \pm110e^{(1/30)\ln(15/22)t}  \Rightarrow \\
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But choose Positive because T > 75. Temp of turkey can't go under.

T(t) = 75 + 110e^{(1/30)\ln(15/22)t} \\
T(45) = 75 + 110e^{(1/30)\ln(15/22)(45)}  = 136.929 \approx 137{}^{\circ}F

(b)

T(t) = 75 + 110e^{(1/30)\ln(15/22)t} = 75 + 110(15/22)^{t/30}  \\
100 = 75 + 110(15/22)^{t/30}   \\
25 = 110(15/22)^{t/30}  
\frac{25}{110} = (15/22)^{t/30}   \\
\ln(25/110) / ln(15/22) = t/30 \\
t = 30\ln(25/110) / ln(15/22)  \approx 116\ \mathrm{min}

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