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Nitella [24]
3 years ago
5

The point (x,y) is first rotated 180 degrees clockwise about the origin, translated 6 units to the left, and then reflected acro

ss the line y=x.
Write a function S to represent the sequence of transformations applied to the point(x,y)

Mathematics
2 answers:
dangina [55]3 years ago
6 0

Answer:

Karen needs to take her pet kitten, Scooter, to the vet for a checkup. It's hard to get Scooter into his carrying case for the trip to the vet. He never wants to go! Scooter's carrying case has a rectangular front that is 11 inches wide and 9 inches tall. The case is 16 inches long. What is the volume of Scooter's carrying case?

Step-by-step explanation:

Assoli18 [71]3 years ago
4 0

Answer:

answer below

Step-by-step explanation:

S (x , y) -> S (-x , -y)     rotated 180 degrees clockwise about the origin

(-x , -y) -> (-x - 6 , -y)    translated 6 units to the left

(-x - 6 , -y) -> (-y , -x-6) reflected across the line y=x

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Answer:

The equation is A=6000e^{-0.23t}  at a rate of -23%.

Step-by-step explanation:

Decay can be represented by the equation A=A_0e^{rt}. We can find the rate at which it decays by using t=3 hours and A=3000. This means A_0=6000 in this context.

A=A_0e^{rt}\\3000=6000e^{r(3)}

0.5=e^{(24.5)r}

After substituting, we divided by 6000 to each side to get 0.5 on the left. Now to solve for r, we will take the natural log of both sides and use log rules to isolate r.

ln 0.5=ln e^{(3)r}\\ln 0.5=3r (ln e)\\\frac{ln0.5}{3} =r

We know lne=1 so we were able to cancel it out and divide both sides by 3.

We solve with a calculator \frac{ln0.5}{3} =r\\-0.23=r

We change -0.23 into a percent by multiplying by 100 to get -23% as the rate.

The equation is A=6000e^{-0.23t}


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