28.12.2021

# Use a calculator to find the value of each expression rounded to two decimal places. Make sure you are in Radian Mode. cos-(0.75)

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09.07.2023, solved by verified expert

If you meant to write , then using a calculator in radian mode would show

Rounding to the nearest hundredth gets us

### Faq

Mathematics

If you meant to write , then using a calculator in radian mode would show

Rounding to the nearest hundredth gets us

Mathematics

Step-by-step explanation: is given value in dollars of a stock in t months after it is purchased.

a) Substitute 1 for t

V(12) =

b) Find derivative for V

c) When V(t) = 75

d) As t tends to infinity, exponent being in negative t tends to 0

So V tends to 42(1-0)+36 = 78

Mathematics

Step-by-step explanation: is given value in dollars of a stock in t months after it is purchased.

a) Substitute 1 for t

V(12) =

b) Find derivative for V

c) When V(t) = 75

d) As t tends to infinity, exponent being in negative t tends to 0

So V tends to 42(1-0)+36 = 78

Mathematics

It will take 26.34 minutes for the population to reach 5 times its initial value

Step-by-step explanation:

Exponential Growing

The population of bacteria grows at a rate expressed by the equation:

Where t is in minutes.

We need to know when the population will reach 5 times its initial value. The initial value can be determined by setting t=0:

Now we find the time when the population is 5*256=1,280. The equation to solve is:

Dividing by 256:

Taking natural logarithms:

Applying the logarithm properties:

Solving for t:

It will take 26.34 minutes for the population to reach 5 times its initial value

Mathematics

It will take 26.34 minutes for the population to reach 5 times its initial value

Step-by-step explanation:

Exponential Growing

The population of bacteria grows at a rate expressed by the equation:

Where t is in minutes.

We need to know when the population will reach 5 times its initial value. The initial value can be determined by setting t=0:

Now we find the time when the population is 5*256=1,280. The equation to solve is:

Dividing by 256:

Taking natural logarithms:

Applying the logarithm properties:

Solving for t:

It will take 26.34 minutes for the population to reach 5 times its initial value

Mathematics

The bacteria has an exponential growth rate and the population of the

bacteria increases rapidly with time.

(a) The relative rate of growth is .

(b) The initial size of the culture is 75 bacteria.

(c) The function that models the number of bacteria n(t) is;

(d) The number of bacteria after 4.5 hours is approximately 8,100 bacteria.

(e) The number of hours after which the bacteria will reach 75,000 is approximately 6.64 hours.

Reasons:

The count in the culture of bacteria after 2 hours = 600

The count after 6 hours = 38,400

(a) The relative rate of growth, k is given by the formula;

Therefore, we get;

Which gives;

4·k = ㏑(64)

(b) The initial size of the culture, C, is given by the relation;

Therefore, we get;

The initial size of the culture, C = 75

(c) The function is

Where:

y = n(t)

C = n₀

k = r

We get;

n₀ = C = 75

Which gives the function as follows;

(d) The number of bacteria after 4.5 hours is ≈ 8,100 bacteria

(e) At n(t) = 75,000, we have;

The time at which the bacteria population will reach 75,000, t ≈ 6.64 hours.

Mathematics

Cost of 7 gallons=$24.50 Cost of 1 gallon=24.50/7=3.5 Cost of 15 gallons=15*3.5=52.5 Cost of 15 gallons will be$52.5

Mathematics

The answer is in the image

Mathematics

The answer is in the image

Mathematics