MATHEMATICS COLLEGE

To make the cone, melted chocolate is pumped onto a huge cold plate at a rate of 2 ft3/sec. Due to the low temperature, the chocolate forms the shape of a cone as it solidifies quickly. If the height is always equal to the diameter as the cone is formed, how fast is the height of the cone changing when it is 5 ft high?

Answers

Answer 1
Answer:

Answer:

The height of cone is increasing at a rate 0.102 feet per second.

Step-by-step explanation:

We are given the following in the question:

(dV)/(dt) = 2\text{ cubic feet per second}

Instant height = 5 feet

The height of the cone is always equal to the diameter.

Volume of cone =

V = (1)/(3)\pi (d^2)/(4)h\n\n\text{where d is the diameter and h is the height of cone}\n\nV = (1)/(12)\pi h^3

Rate of change of volume =

(dV)/(dt) = (d)/(dt)((1)/(12)\pi h^3)\n\n(dV)/(dt) =(\pi)/(4)h^2(dh)/(dt)

Putting all the values, we get,

2=(\pi)/(4)(5)^2(dh)/(dt)\n\n\Rightarrow (dh)/(dt) = (8)/(25\pi) =0.102

Thus, the height of cone is increasing at a rate 0.102 feet per second.

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Answers

Answer:

a) According to probability theory, the following are possible:

(1) The probability that a customer will buy 5 items in a single purchase is 30%.  This represents a 0.30 chance of the customer buying 5 items.

(3) The probability that a customer will buy 3 items in a single purchase is 99%  This means that there a 0.99 chance that the customer will buy 3 items.

b) According to probability theory, the following are not possible:

2) The probability that a customer will buy 3 items in a single purchase is 101%.  Probability is always equal to 1 or 100%.  It cannot exceed 100%.

(4) The probability that a customer will buy 8 item.  This part lacks the necessary information to solve the problem.

Step-by-step explanation:

Probability describes the likelihood or chance of an event happening out of the many possible events that can take place.  The sum of all probabilities for a particular event is always equal to 1.  This shows that probability does not exceed 100%.

Earlier we analyzed the revenue earned by the junior class at East High School from their discount card fundraiser. They hada goal to earn a profit of more than $10,000 from the fundraiser.
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Answers

Approximately 520 cards actually sold this year in the class, more than 505, have fulfilled their objective.

According to the question,

If the students sell c cards the,

The total revenue,

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The total production costs,

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`

The inequality of profit, or income, which is less than 10 thousand dollars represents their objective, such as:

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→               c > (10,000)/(19.8c)

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Sample Answer for Edmentum

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Answers

Answer:

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Step-by-step explanation:

Put 2 where x is and do the arithmetic.

  f(x) = 5x +12

  f(2) = 5(2) +12 = 10 +12

  f(2) = 22

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Answers

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Answers

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Answers

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