Questions 5 and 6 please C X b/Si C My Chegg l Chegg.com HW2 ok Convert Select T

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Questions 5 and 6 please

C X b/Si C My Chegg l Chegg.com HW2 ok Convert Select The slope represents the distance traveled in miles. Need Help? Read It Chat About It 5. 3 points My Notes I ET2 1.2 Biologists have noticed that the chirping rate of crickets of a certain species is related to temperature, and the relationship appears to be very nearly linear. A cricket produces 113 chirps per minute at 70F and 173 chirps per minute at 800F. (a) Find a linear equation that models the temperature Tas a function of the number of chirps per minute N. (b) What is the slope of the graph? What does it represent? The slope means that the temperature in Fahrenheit degrees increases as rapidly as the number of cricket chirps per minute. (c) If the crickets are chirping at 160 chirps per minute, estimate the temperature. (Round your answer to the nearest whole number.) Need Help? Read It Watch It Chat About It 6. 3 points My Notes I ET2 1.2.015 physical quantities are connected by inverse square laws, that is, by power functions of the form f(x) kx e. In particular, the illumination of an object by a light source is inversely proportional to the square of the distance y from the source. Suppose that after dark you are in a room with just one lamp and you are trying to read a book. The light is too dim and so you move halfway to the lamp. How much brighter is the light? times as bright Need Help? Read it Chat About It Submit Answer Save Progress 7. 3 points My Notes I ET2 1.2 The graph of y-f(x) is given. Match each equation with its graph 7/11/2013

Explanation / Answer

5.) First find the slope of the line given by (y2 - y1) / (x2 - x1) where y is the temperature and x is the chirping rate.

(x1,y1) = (113,70) and (x2,y2) = (173,80)

So (y2 - y1) / (x2 - x1) = (80 - 70) / (173 - 113) = 10 / 60 = 1/6 = slope

The equation of a straight line is y = mx + b where m is the slope and b is the y-intercept.

So far we have y = 1/6 x + b. To find b, plug in one of the two points. I'll use (x1,y1).

y = 1/6 x + b
70 = 1/6 (113) + b
70 = 113/6 + b
70-113/6 = b

b = 307/6

So our final equation is
y = 1/6 x + 307/6

6y = x+307

Now, at 160 chirps per min,

6y = 160+307

6y = 467

y = 467/6 = 77.84 degrees F

6.) Let brightness be b, distance be r

So, b is directly proportional to 1/r^2

=> br^2 is constant

=> b1(r1)^2=b2(r2)^2

Here, r2=(r1)/2

=> b2/b1=(r1/r2)^2=(r1/r1/2)^2=(2*r1/r1)^2=2^2=4

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