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:
To find value of tractor after 4 years, we would need to substitute "4" into t and calculate. It is shown below:
The value of the tractor after 4 years is $33,000
2.
The value of investment that is growing each year, is given by:
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
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:
Where L is the length of the pendulum in feet
a)
If L = 6ft, the time it will take is:
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:
So, it will take about 0.96 seconds
4.
The area of weed after t days can be modeled by:
Where t is number of days
Now, we want to find area after 100 days, so let t = 100, we get:
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:
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:
The target heart rate should be: 141 beats per minute (rounded to nearest whole number)
4
Get Answer
29
is shifted 2 units down with respect to the graph of 
. We can prove this by taking, for instance, x=0, and calculating the value of y in the two cases. In the first function:
and 
. The second solution is negative, so it has no physical meaning, therefore the correct answer is 160.56 m.
and 
. In this case, we have to choose the second solution (27.43 m), since the rock was thrown backward from the initial height of 37 m, so the negative solution corresponds to the backward direction.
(1)
(2)
(1)
(2)
, we see this is equivalent to the perfect square:
