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Maksim231197 [3]
3 years ago
8

Renee is sewing a quilt whose pattern contains right triangles.

Mathematics
1 answer:
Mashutka [201]3 years ago
7 0

Answer:

  8 inches

Step-by-step explanation:

The area of a triangle is ...

  A = 1/2bh

Filling in the given values, we have ...

  24 = 1/2b(6)

  24/3 = b = 8 . . . . . divide by the coefficient of b

The base of each triangular quilt piece is 8 inches long.

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In the given figure poq is a line. if x=30 then find qor and ros​
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Answer:

2y + 3y + x = 180 \\ 5y + 30 = 180  \\ 5y = 180 - 30 \\ 5y = 150 \\ y = 30

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2 years ago
A roast turkey is taken from an oven when its temperature has reached 185 degrees F and is placed on a table in a room where the
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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 \\ \\&#10;|T - 75| = 110e^{kt} \Rightarrow T - 75 = \pm110e^{(1/30)\ln(15/22)t}  \Rightarrow \\&#10;T = 75 \pm110e^{(1/30)\ln(15/22)t}

But choose Positive because T > 75. Temp of turkey can't go under.

T(t) = 75 + 110e^{(1/30)\ln(15/22)t} \\&#10;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}  \\&#10;100 = 75 + 110(15/22)^{t/30}   \\&#10;25 = 110(15/22)^{t/30}  &#10;\frac{25}{110} = (15/22)^{t/30}   \\&#10;\ln(25/110) / ln(15/22) = t/30 \\&#10;t = 30\ln(25/110) / ln(15/22)  \approx 116\ \mathrm{min}

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