The depth of snow after n hours of a snowstorm is represented by the function f(n + 1) = f(n) + 0.8 where f(0) = 2.5. Which statement describes the sequence of numbers generated by the function?The depth of snow was 0.8 inches when the storm began, and 2.5 inches after the first hour of the storm.
The depth of snow was 1.7 inches when the storm began, and 0.8 inches of snow fell each hour.
The depth of snow was 2.5 inches when the storm began, and increased by 0.8 inches each hour.
The depth of snow was 3.3 inches when the storm began, and 2.5 inches of snow fell in 1 hour.
Answers
Answer:
C)The depth of snow was 2.5 inches when the storm began, and increased by 0.8 inches each hour.
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The depth of snow after n hours of a snowstorm is represented by the function f(n + 1) = f(n) + 0.8 where f(0) = 2.5. The statement that describes the sequence of numbers generated by the function is ‘The depth of snow was 2.5 inches when the storm began, and increased by 0.8 inches each hour.’
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The ratio is 2:1.
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distance between ponts (a,b) an (c,d) is
D=
do the rest yourself by intuistion
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Final answer:
Haddie is likely to pay one overdraft fee due to her account being overdrawn by the check she wrote to the grocery store.
Explanation:
Haddie has written a check for $156.00 but she only has $122.66 in her checking account. Because she has opted into the standard overdraft practices at her bank, she will likely have to pay a fee. The exact number of fees can depend on the individual bank's policies. Generally, when you overdraw on your checking account, banks will charge an overdraft fee - usually around $35. So, in this scenario, Haddie is likely to pay one overdraft fee. However, it should be noted that some banks may charge additional fees if the account remains overdrawn for a certain number of consecutive days.
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Answers
Answers
sY(s) - y(0) + 6Y(s) = 1/(s-4)
(s+6)Y(s) - 2 = 1/(s-4)
Y(s) = 2/(s+6) + 1/(s-4)(s+6), by partial fraction decomposition
Y(s) = 2/(s+6) + 1/10 * (1/(s-4) + 1/(s+6))
Y(s) = 0.1/(s-4) + 2.1/(s+6)
Performing inverse laplace transform,
y(t) = 0.1e^4t + 2.1e^(-6t)
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Final answer:
The Laplace transform method is applied to solve the differential equation y' + 6y = e^4t with the initial condition y(0)=2. After transforming, simplifying, and solving for Y(s), we use inverse Laplace transform to find the solution y(t) in the time domain.
Explanation:
Laplace transform is a powerful tool in the field of mathematics used for solving differential equations. To solve the given initial value problem y' + 6y = e^4t ; y(0)=2, we can start by taking the Laplace transform of both sides of the equation.
The Laplace transform of y' is sY(s) - y(0) and the Laplace transform of y is Y(s). Therefore, the Laplace transform of y' + 6y gives sY(s) - y(0) + 6Y(s). Given that y(0)=2, this simplifies to sY(s) + 6Y(s) - 2.
On the right-hand side, the Laplace transform of e^4t is 1/(s-4). Thus, we have the equation sY(s) + 6Y(s) - 2 = 1/(s-4).
By solving for Y(s), we can find the inverse Laplace transform to get the solution y(t) in the time domain.
Learn more about Laplace Transform here:
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A.
–2z – 14
B.
–25 + 4z
C.
–2z + 15
D.
30 – 3z
Answers
A) –2z – 14 = -2(8)-14 = -16-14 = -30
-2x-14 is negative when z = 8. So A is one possible answer :)
B) –25 + 4z = -25 + 4(8) = -25 + 32 = 7
7 is positive when z = 8, so B is not a correct answer.
C) –2z + 15 = -2(8) + 15 = -16 + 15 = -1
-1 is negative when z 8, So C is another correct answer choice.
D) 30 – 3z = 30 - 3(8) = 30 - 24 = 6
6 is positive when z=8, So D is not a correct answer.
To summarize, your answer would be A and C.