Question

HELP: I need help on multiple questions for a quiz before tomorrow night. If all is answered, you will get 40+ points and marked as the Brainliest for whoever explains the process to these problems.
1. Evaluate the function to answer the question.

The value of a tractor decreases over time and is given by V(t)=55,000 - 5,500t, where V(t) is the value in dollars of the after t years. Find the value (in dollars) of the tractor after 4 years.

2. Evaluate the function to answer the question.

The value in dollars of a $5,000 investment after n years is given by f(n) = 5,000(1.05)^n. Find the value of the investment (in dollars) after 4 years. (Round your answer to the nearest cent.)

3. The time, T, in seconds, it takes a pendulum to make one swing depends on the length of the pendulum and is given by

T (L) = 2π√(L/32),

where L is the length of the pendulum in feet.

(a) Find the time (in seconds) it takes the pendulum to make one swing if the length of the pendulum is 6ft. Round to the nearest hundredth of a second.

(b) Find the time it takes (in seconds) the pendulum to make one swing if the length of the pendulum is 9in. Round to the nearest hundredth of a second.

4. Evaluate the function to answer the question.

Botanists have determined that some species of weed grow in a circular pattern. For one such species, the area A, in square meters, can be approximated by A(t) = 0.006πt^2 where t is the time in days after the growth of the weed first can be observed. Find the area (in square meters) this weed will cover 100 days after the growth is first observed. Round to the nearest square meter.

5. A weight loss program advertises a person can attain an average weight loss of 4 pounds per week.

(a) What is the average rate of change (in pounds per week) for this weight loss program?

(b) If a person who weighs 180 pounds follows the weight loss program, what is the person's weight (in pounds) after 5 weeks?

6. Evaluate the function to answer the question.
The Karvonen formula is one formula used to determine the target heart rate for a person training for fitness. The formula is given by T = p (220 – A) + H (1 – p), where T is the target heart rate (in beats per minute), A is the age of the person (in years), H is the resting heart rate (in beats per minute), and p is the percent intensity (expressed as a decimal) of the workout.

What are the independent variables? (Select all that apply.)
A
H
P
T

What are the dependent variables?
A
H
P
T

A trainer has determined that a client who is 35 years old and has a resting heart rate of 60 beats per minute should train at an intensity of 65%. What is the target heart rate (in beats per minute) for this person? Round to the nearest whole number.

Answer 1

Answer:

1.  $33,000

2.  $6077.53

3.

a)  2.72 seconds

b)  0.96 seconds

4.  189 square meters

5.

a)  Average Rate of Change = 4 pounds per week, or -4

b)  160 pounds (after 5 weeks)

6.  

Independent Variables = p, A, and H

Dependent Variable = T

141 beats per minute (rounded to nearest whole number)

Step-by-step explanation:

1.

The value of a tractor V(t) decreases over time, t. Its value is given by:

$V(t)=55000-5500t$

To find value of tractor after 4 years, we would need to substitute "4" into t and calculate. It is shown below:

$V(t)=55000-5500t\\V(4)=55000-5500(4)\\V(4) =33000$

The value of the tractor after 4 years is $33,000

2.

The value of investment that is growing each year, is given by:

$f(n)=5000(1.05)^{n}$

Where

5000 is the initial investment (deposit)

1.05 means a 5% growth rate per year

n is the time in years

We want the investment's value after 4 years, so n would be 4. Substituting we get our answer:

$f(n)=5000(1.05)^{n}\\f(4)=5000(1.05)^{4}\\f(4)=6077.53$

To the nearest cent, the value of the investment would be:

$6077.53

3,

The time it takes of pendulum to make one swing is given by the formula:

$T(L)=2\pi \sqrt{\frac{L}{32}}$

Where L is the length of the pendulum in feet

a)

If L = 6ft, the time it will take is:

$T(6)=2\pi \sqrt{\frac{6}{32}}\\T(6)=2.72$

About 2.72 seconds

b)

Now, the length is 9 inches, we convert it to feet first:

9/12 = 0.75 feet

So, the time it will take:

$T(0.75)=2\pi \sqrt{\frac{0.75}{32}}\\T(0.75)=0.96$

So, it will take about 0.96 seconds

4.

The area of weed after t days can be modeled by:

$A(t)=0.006 \pi t^2$

Where t is number of days

Now, we want to find area after 100 days, so let t = 100, we get:

$A(t)=0.006 \pi t^2\\A(100)=0.006 \pi (100)^2\\A(100)=188.5$

Rounded to nearest sq. m, we have the area to be:

189 square meters

5.

a)

The avg. rate of change is basically how much the program is advertising that someone can loose in a week. It says "4 pounds per week". Since decrease, we give the value of "4" and negative sign So:

Average Rate of Change = 4 pounds per week, or -4

b)

Initial weight is 180 pounds, we know 4 pounds is decreased every week when going through the program course. So, after 5 weeks,

5 * 4 = 20 pounds will be less

So, he will be:

180 - 20 = 160 pounds (after 5 weeks)

6.

The Karvonen formula is given as:

$T=p(220-A)+H(1-p)$

Where

T is target heart rate (in bpm)

p is the percent intensity (expressed as decimal)

A is the age (in yrs)

H is the resting heart rate (in bpm)

We need to identity the independent and dependent variables. Now, lets that a simple example:

y = 2x

Here,

x is the independent variable

y is dependent on x, so y in dependent

Similarly, if you look at the formula, you can see:

p, A, and H are all independent

T depends on them

So,

p, A, H are independent variables

T is the dependent variable

Independent Variables = p, A, and H

Dependent Variable = T

We are given

A = 35

H = 60

p = 65% = 65/100 = 0.65

Now, we want T, lets substitute and find:

$T=0.65(220-35)+60(1-0.65)\\T=141.25$

The target heart rate should be:  141 beats per minute (rounded to nearest whole number)