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8_murik_8 [283]
3 years ago
14

Find the first and second derivative of the function defined by the parametric equation.

Mathematics
1 answer:
Sergeu [11.5K]3 years ago
6 0

Answer:

Step-by-step explanation:

Given two parametric equations x(t) and y(t), the first derivative can be found using the following equation:

\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}

In this problem, x(t) = 3e and y(t) = 3^{3t} - 1. Finding the derivative of each of these functions with respect to t gives us the following:

\frac{dx}{dt} = 0

\frac{dy}{dt} = 3^{3t + 1}\log{3}

Because \frac{dx}{dt} = 0, that means the function is a vertical line and has an infinite first derivative.

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Help me pwees no links<br><br> what is 159 rounded to the nearest tenth minus 10
r-ruslan [8.4K]

Answer:

150

Step-by-step explanation:

159 rounded to the nearest tenth is 160

160-10=150

8 0
3 years ago
EMERGENCY QUESTION! No Decimal answers plz!
telo118 [61]

Answer:

1,145,375 cm³

Step-by-step explanation:

Like with an earlier question you had, there is a chunk missing. If that chunk was filled in, this would be a 205 * 70 * 85 rectangular prism.

205 * 70 * 85

17,425 * 70

1,219,750

The cut out chunk is a 25 * 70 * 85 triangular prism.

1/2 (25 * 70 * 85)

1/2(2,125 * 70)

1/2(148,750)

74,375

Now that we know what the cut-out chunk is, subtract that from the first value we got.

1,219,750 -74,375

1,145,375 cm³

The volume of the Canadian Post mailbox is 1,145,375 cm³.

8 0
3 years ago
Read 2 more answers
-3(7w-3)+8w=-5(w+1) what is the value of w
bogdanovich [222]

Answer:

2

Step-by-step explanation:

Step 1:

- 21w + 9 + 8w = - 5w - 5

Step 2:

- 13w + 9 = - 5w - 5

Step 3:

- 7w + 9 = - 5

Step 4:

- 7w = - 14

Step 5:

14 = 7w

Answer:

w = 2

Hope This Helps :)

6 0
3 years ago
Write a function modeling this debt situation if the initial debt in 2009 was
Karolina [17]

Answer:

To solve this, we are going to use the standard decay function where

is the final amount remaining after  years of decay is the initial amount is the decay rate in decimal form

is the decay factor

is the time in years

I will tell Greece to decrease their expending by 25%

To find our decay factor , we are going to convert the rate from percentage to decimal; to do it, we are going to divide the rate by 100%

Decay factor =

Decay factor =

Decay factor = (0.75)

We can conclude that our decay factor is (0.75)

c. To solve this, we are going to use the standard decay function  from our previous point.

where

is the final amount remaining after  years of decay is the initial amount is the decay rate in decimal form

is the decay factor

is the time in years

We know from our problem that the initial debt in 2009 was $500 billion, so ; we also know from our previous calculation that our decay factor is (0.75), so lets replace those values in our function:

We can conclude that the function that model this debt situation is: .

Greece will be debt-free when heir debt is zero. Translating this into our model, Greece will be debt-free when . Since we will need logarithms to find the time , and the logarithm of zero is not defined, we are going to use a small value for , so we can use logarithms to find .

Let . After all, a $1 debt for a country is practically the same as being debt-free.

Now, we can solve for  using logarithms:

We can conclude that, with me in charge, Greece will be debt free after 93.6 years. I won't reconsider my answer b. Even tough 93.6 years is a lot of time, decreasing the public expense more than 25% will have worse consequences for the economy of the country than the debt itself.

6 0
2 years ago
Hotel managers wish to learn the average length of stay of all visitors that are senior citizens. A statistician determines that
LiRa [457]

The answer & explanation for this question is given in the attachment below.

8 0
3 years ago
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