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kumpel [21]
2 years ago
8

A quantity with an initial value of 3700 decays exponentially at a rate of 6% every 5

Mathematics
1 answer:
SSSSS [86.1K]2 years ago
4 0

Answer:

2369.86

Step-by-step explanation:

f(36)=3700(1−0.06) ^36/5

2369.857704098921

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A roller coaster at XTRA Fun Rides goes into an underground tunnel during the first descent of the
gregori [183]

Answer:

y-intercept:  (0, 75) ⇒ y = 75

x-intercepts:  (3, 0) and (5, 0) ⇒ x = 3 and x = 5

vertex: (4, -5)

Step-by-step explanation:

Let the x-axis be the ground (when y = 0).  Therefore underground when y < 0 and overground when y > 0

The function is a quadratic:  f(x) = ax² + bx + c

If the coaster enters the tunnel three seconds after the first descent starts and stays in the tunnel for a total of 2 seconds, then y = 0 when x = 3 and x = 5

Also, when x = 1, y = 40

  • f(3) = 0
    ⇒ 9a + 3b + c = 0
  • f(5) = 0
    ⇒ 25a + 5b + c = 0
  • f(1) = 40
    ⇒ a + b + c = 40

Solve 2 equations simultaneously:

  • 9a + 3b + c = 0
  • 25a + 5b + c = 0
  • a + b + c = 40

⇒ a = 5  b = -40  c = 75

⇒ f(x) = 5x² - 40x + 75

<u>y-intercept</u>

when x = 0

⇒ f(0) = 5(0²) - 40(0) + 75 = 75

⇒ y-intercept = (0, 75)

<u>x-intercepts</u>

x = 3 and x = 5

<u>Vertex</u>

If the x-intercepts are when x = 3 and x = 5, then vertex is when x = 4

⇒ f(4) = 5(4²) - 40(4) + 75 = -5

⇒ vertex = (4, -5)

5 0
2 years ago
HELP THIS IS DUE AT 1:30
love history [14]

Answer: The Ming Dynasty contributed significantly to the fields of culture, science, and technology. Moreover, textiles and mining industries also flourished during this time. Towards the end of the Ming Dynasty, a capitalist production system was gradually developing. The Ming Dynasty achievements resulted in many entrepreneurs readily seizing economic development opportunities building the great wall. One of the most significant Ming Dynasty achievements in engineering is the completion and repair of the Great Wall. Ming, The restoration of the Grand Canal was also an important achievement of this era. A wide range of machinery and equipment from which silk and cotton looms were made were invented during this era.  Dynasty achievements also included significant contributions in the fields of philosophy, art, and literature. The Forbidden City, Beijing, was an essential architectural achievement that was also constructed during this era.

The famous white and blue porcelain of China originated in the era of the Ming Dynasty.

Step-by-step explanation: hoped this helped :)

3 0
3 years ago
Simplify Sinx + cosx/ cos²x - sin²x​
bonufazy [111]

\dfrac{\sin x + \cos x}{\cos^2 x - \sin^2 x}\\ \\\\=\dfrac{\sin x + \cos x}{(\cos x + \sin x )\\\\(\cos x - \sin  x)}\\\\\\=\dfrac{1}{\cos x - \sin x}

3 0
2 years ago
What is .333 written in its simplest fraction from
gayaneshka [121]
Hi.
your answer is 1/3, or 2/6, or 3/9, or 4/12, etc.
hope this helps!!!


6 0
3 years ago
A digital clock displays military time in hh:mm format. Find the probability that the number made up of the first two digits on
egoroff_w [7]

Answer: The probability that the number made up of the first two digits on the clock is less than 25 is 1.

Step-by-step explanation:

The probability of an event is a number which describe the chances of the event will happen.

We know that on digital clock, the first two digits always show as number less that 25.

Therefore, the event that the number made up of the first two digits on the clock is less than 25 is certain.  [Since An event that is certain to happen has a probability of 1.]

Hence, the probability that the number made up of the first two digits on the clock is less than 25 is 1.

4 0
3 years ago
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