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Gelneren [198K]

3 years ago

6

a psychologist contends that the number of facts of a certain type that are remembered after t hours is given by the following f

unction. f(t)equals startfraction 85 t over 99 t minus 85 endfraction find the rate of change at which the number of facts remembered is changing after 1 hour and after 10 hours.

1 answer:

laiz [17]3 years ago

4 0

Answer:

At t=1, Rate of Change=-36.86

At t=10 hours, Rate of Change =-0.0088

Step-by-step explanation:

The function which describes the number of facts of a certain type which are remembered after t hours is given as:

$f(t)=\frac{85t}{99t-85}$

To determine the Rate of Change at the given time, we first look for the derivative of f(t).

Applying quotient rule:

$f^{'}(t)=\frac{-7225}{{\left( 85 - 99\,t\right) }^{2}}$

At t=1

$f^{'}(1)=\frac{-7225}{(85-99)^{2}}$

=-36.86

At t=10 hours

$f^{'}(10)=\frac{-7225}{(85-99(10))^{2}}$

=-0.0088

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If 30,000 cm2 of material is available to make a box with a square base and an open top, what is the largest possible volume (in

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Answer:

The largest possible volume of the box is 2000000 cubic meters.

Step-by-step explanation:

The volume ( $V$ ), in cubic centimeters, and surface area ( $A_{s}$ ), in square centimeters, of the box with a square base are described below:

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$V' = A_{s}-3\cdot l^{2}$ (4)

$V'' = -6\cdot l$ (5)

If $V' = 0$ and $A_{s} = 30000\,cm^{2}$ , then we find the critical value of the side length of the base is:

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4 0

2 years ago

14/2 three equivalent ratios

Anna71 [15]

Answer:

Three equivalent ratios of $\frac{14}{2}$ are $\frac{7}{1}$ , $\frac{21}{3}$ and $\frac{28}{8}$ .

Step-by-step explanation:

We are given a fraction $\frac{14}{2}$ .

We need to find the three equivalent ratios/fractions of $\frac{14}{2}$ .

The common factor of 14 and 2 is 2.

So, dividing top and bottom by 2, we get

14÷2 = 7 and 2÷2 that is $\frac{7}{1}$ .

Multiplying $\frac{7}{1}$ fraction by a common number 3 in top and bottom, we get

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So, we get another equivalent fraction $\frac{21}{6}$ .

Multiplying $\frac{7}{1}$ fraction by a common number 3 in top and bottom, we get

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So, we get another equivalent fraction $\frac{28}{4}$ .

Therefore, three equivalent ratios of $\frac{14}{2}$ are $\frac{7}{1}$ , $\frac{21}{3}$ and $\frac{28}{4}$ .

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