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Answer:

t = 40

Step-by-step explanation:

Given the logarithmic expression:

Use the Logarithmic Property (Quotient Rule):

Next, using the Logarithmic Property:  

We must determine the possible value oft that can be divided by 5 to produce a quotient of 8 that will make the logarithmic property, , true.  In that case, t = 40 divided by 5 results in a quotient of 8.

Therefore, the value oft = 40.

Answer:

x = pi/2 + 2 pi n                            x = pi + 2 pi n   where n is an integer

x = 5pi /3 + 2 pi n                      

Step-by-step explanation:

8 cos^2 x + 4 cos x-4 = 0

Divide by 4

2 cos^2 x +  cos x-1 = 0

Let u = cos x

2 u^2 +u -1 =0

Factor

(2u -1) ( u+1) = 0

Using the zero product property

2u-1 =0    u+1 =0

u = 1/2      u = -1

Substitute cosx for u

cos x = 1/2    cos x = -1

Take the inverse cos on each side

cos ^-1(cos x) = cos ^-1(1/2)   cos ^-1( cos x) =cos ^-1( -1)

x = pi/2 + 2 pi n                            x = pi + 2 pi n   where n is an integer

x = 5pi /3 + 2 pi n                      

Based on the table, the values relating t and e with their viability is given by:

1. e = 330 (not viable).
2. e = 265 (viable).
3. e = 0 (viable).

What is a linear function?

A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.

What is an average rate of change?

An average rate of change is also referred to as slope and it can be defined as a type of function that describes the average rate at which a quantity changes (decreases or increases) with respect to another quantity, over a period of time.

From the table, we would determine which values are viable points as follows:

At a = -2, we have:

e = 300 - 10t

e = 300 - 10(-2)

e = 300 + 30

e = 330 (not viable).

At b = 3.5, we have:

e = 300 - 10t

e = 300 - 10(3.5)

e = 300 - 35

e = 265 (viable).

At c = 10, we have:

e = 300 - 10t

e = 300 - 10(30)

e = 300 - 300

e = 0 (viable).

Read more on linear function here: brainly.com/question/6978079

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Answer:

A 2-column table with 3 rows. The first column is labeled time (t) with entries negative 2, 3.5, 30. The second column is labeled Elevation(e) with entries a, b, c.

Rory is staying in a cabin on a hill 300 feet above sea level. She walks down the hill to the water’s edge. The equation of her average change in elevation over time is e = 300 – 10t, where t is the time in minutes since she left the cabin, and e is her elevation with regard to sea level. Which values are viable points, and what are their values in the table relating t and e?

a =

✔ not viable

b =

✔ 265

c =

✔ 0

Step-by-step explanation:

Answer:

It's the first answer.

Step-by-step explanation:

As demonstrated through the image, the slope increases. Thus making it a positive slope.