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2 years ago

Steven earns extra money babysitting. He charges $31.25 for 5 hours and $50 for 8 hours..

Mathematics

1 answer:

Maru [420]2 years ago

3 0

$6.25 × h = c
h = hours, c = total cost

$31.25 for 5 hours. $6.25 per hour

$50 for 8 hours. $6.25 per hour

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A certain flagpole that is 298 feet tall casts a shadow 139 feet long. Find the angle of elevation on the sun.

Svetllana [295]

Answer:

57.6159 round if needed

Step-by-step explanation:

We know the length of the triangle which is 298. We know the base of the triangle which is 189.

We need to find angle of elevation so we must use tangent function.

$\tan(x) = \frac{298}{189}$

Use inverse tan function

$\tan {}^{ - 1} ( \frac{298}{189} ) = 57.6159$

Round if needed.

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Subtracting a number is the same as adding its opposite.

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in first question, answer is 12

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Factor 4x 2 + 12x + 5 . (2x + 5)(2x + 1)

swat32

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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

Vedmedyk [2.9K]

(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

$\ln|T - 75| = kt + \ln 110 \Rightarrow |T - 75| = e^{kt + \ln110} \Rightarrow \\ \\
|T - 75| = 110e^{kt} \Rightarrow T - 75 = \pm110e^{(1/30)\ln(15/22)t} \Rightarrow \\
T = 75 \pm110e^{(1/30)\ln(15/22)t}$

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

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

(b)

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

Dogs of the AMS.

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2 years ago