Answer:
a)
, b) ![\frac{dB}{dt}\approx 5.595](https://tex.z-dn.net/?f=%5Cfrac%7BdB%7D%7Bdt%7D%5Capprox%205.595)
Step-by-step explanation:
a) The rate of change of the brightness of the Cepheid can be determined by deriving the function in time:
![\frac{dB}{dt} = \left(\frac{2\pi}{4.2} \right)\cdot 0.25\cdot \cos (2\pi\cdot \frac{t}{4.2})](https://tex.z-dn.net/?f=%5Cfrac%7BdB%7D%7Bdt%7D%20%3D%20%5Cleft%28%5Cfrac%7B2%5Cpi%7D%7B4.2%7D%20%5Cright%29%5Ccdot%200.25%5Ccdot%20%5Ccos%20%282%5Cpi%5Ccdot%20%5Cfrac%7Bt%7D%7B4.2%7D%29)
![\frac{dB}{dt} = \frac{5\pi}{4.2} \cdot \cos \left(2\pi\cdot \frac{t}{4.2} \right)](https://tex.z-dn.net/?f=%5Cfrac%7BdB%7D%7Bdt%7D%20%3D%20%5Cfrac%7B5%5Cpi%7D%7B4.2%7D%20%5Ccdot%20%5Ccos%20%5Cleft%282%5Cpi%5Ccdot%20%5Cfrac%7Bt%7D%7B4.2%7D%20%5Cright%29)
b) The rate of increase after one day is:
![\frac{dB}{dt} = \frac{5\pi}{4.2} \cdot \left(2\pi \cdot \frac{1}{4.2} \right)](https://tex.z-dn.net/?f=%5Cfrac%7BdB%7D%7Bdt%7D%20%3D%20%5Cfrac%7B5%5Cpi%7D%7B4.2%7D%20%5Ccdot%20%5Cleft%282%5Cpi%20%5Ccdot%20%5Cfrac%7B1%7D%7B4.2%7D%20%5Cright%29)
![\frac{dB}{dt}\approx 5.595](https://tex.z-dn.net/?f=%5Cfrac%7BdB%7D%7Bdt%7D%5Capprox%205.595)
30% , as:
Let the percentage of people preferring wooden skateboards be 'x'.
Therefore, x/100*643=209
x/100=209/643
x=209*100/643
x=20900/643
x=32.50.......
By rounding it off to 30, we get 30% as answer.
Answer:
ABQ = 139
BCR is the same as QBC since they are alternate interior angles
BCR = 41
Step-by-step explanation:
CBQ and SCB are same side interior angles so they add to 180
2a-9 + 5a +14 = 180
Combine like terms
7a +5 = 180
Subtract 5 from each side
7a = 175
Divide by 7
7a/7 = 175/7
a = 25
ABQ is the same as SCB since they are corresponding angles so
ABQ = SCB = 5a+14 = 5*25+14 = 125+14 = 139
BCR is the same as QBC since they are alternate interior angles
BCR = QBC = 2a-9 = 2*25 -9 = 50-9 = 41
F(x) = 1/x and g(x) = -10/x
Domain: same: all real numbers other than x=0.
Range: strictly speaking, these 2 functions have the same range: all real numbers other than y=0. But the graph of g(x) = -10/x looks stretched vertically when compared with that of f(x) = 1/x.