Round the answer to the nearest hundredth

Step-by-step explanation:

Initial amount deposited into the account is $10000 This means that the principal, P = 10000

The rate at which the principal was compounded is 7%. So

r = 7/100 = 0.07

It was compounded for 7 years. So

t = 7

The formula for compound interest is

A = P(1+r/n)^nt

A = total amount in the account at the end of t years.

a) compounded semi annually

It means that it was compounded twice in a year, so n = 2

Therefore

A = 10000 (1+0.07/2)^2×7

A = 10000(1.035)^14 = $16186.9

b) compounded quarterly

It means that it was compounded four times in a year, so n = 4

Therefore

A = 10000 (1+0.07/4)^4×7

A = 10000(1.0175)^28 = $16254.1

c) compounded monthly

It means that it was compounded 12 times in a year, so n = 12

Therefore

A = 10000 (1+0.07/12)^12×7

A = 10000(1.0058)^84 = $16254.6

d) compounded continuously

A = Pe^Rt

A = 10000e^7×0.07 = 10000×e^0.49

A = $16323.2

Step-by-step explanation:

Initial amount deposited into the account is $10000 This means that the principal, P = 10000

The rate at which the principal was compounded is 7%. So

r = 7/100 = 0.07

It was compounded for 7 years. So

t = 7

The formula for compound interest is

A = P(1+r/n)^nt

A = total amount in the account at the end of t years.

a) compounded semi annually

It means that it was compounded twice in a year, so n = 2

Therefore

A = 10000 (1+0.07/2)^2×7

A = 10000(1.035)^14 = $16186.9

b) compounded quarterly

It means that it was compounded four times in a year, so n = 4

Therefore

A = 10000 (1+0.07/4)^4×7

A = 10000(1.0175)^28 = $16254.1

c) compounded monthly

It means that it was compounded 12 times in a year, so n = 12

Therefore

A = 10000 (1+0.07/12)^12×7

A = 10000(1.0058)^84 = $16254.6

d) compounded continuously

A = Pe^Rt

A = 10000e^7×0.07 = 10000×e^0.49

A = $16323.2

#1

put t=0 in function

#2

It's already located

#3

#4

Count on t axis on graph

#5

Just the initial velocity and height becomes zero

New function

#6

Sam e initial velocity but height becomes zero

New function

1. It is shifted 2 units down.

The graph of 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:

In the second function:

So, the first graph is shifted 2 units down.

2. 160.56 m

The path of the rocket is given by:

The problem asks us to find how far horizontally the rocket lands - this corresponds to find the value of x at which the height is zero: y=0. This means we have to solve the following equation

Using the formula,

which has two solutions: and . The second solution is negative, so it has no physical meaning, therefore the correct answer is 160.56 m.

3. 27.43 m

The path of the rock is given by:

The problem asks us to find how far horizontally the rock lands - this corresponds to find the value of x at which the height is zero: y=0. This means we have to solve the following equation

Using the formula,

which has two solutions: 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.

4. (-2, 16) and (1, -2)

The system is:

(1)

(2)

We can equalize the two equations:

which becomes:

Solving it with the formula, we find two solutions: x=-2 and x=1. Substituting both into eq.(2):

x=-2 -->

x=1 -->

So, the solutions are (-2, 16) and (1, -2).

5. (-1, 1) and (7, 33)

The system is:

(1)

(2)

We can equalize the two equations:

which becomes:

Solving it with the formula, we find two solutions: x=7 and x=-1. Substituting both into eq.(2):

x=7 -->

x=-1 -->

So, the solutions are (-1, 1) and (7, 33).

6. 2.30 seconds

The height of the object is given by:

The time at which the object hits the ground is the time t at which the height becomes zero: h(t)=0, therefore

By solving it,

7. Reaches a maximum height of 19.25 feet after 0.88 seconds.

The height of the ball is given by

The vertical velocity of the ball is equal to the derivative of the height:

The maximum height is reached when the vertical velocity becomes zero: v=0, therefore when

from which we find

And by substituting these value into h(t), we find the maximum height:

8. Reaches a maximum height of 372.25 feet after 4.63 seconds.

The height of the boulder is given by

The vertical velocity of the boulder is equal to the derivative of the height:

The maximum height is reached when the vertical velocity becomes zero: v=0, therefore when

from which we find

And by substituting these value into h(t), we find the maximum height:

9. 12 m

Let's call x the length of the side of the original garden. The side of the new garden has length (x+3), so its area is

Solvign this equation, we find

10. 225/4

In fact, if we write , we see this is equivalent to the perfect square:

11. -11.56, 1.56

The equation is:

By using the formula:

which has two solutions: x=-11.56 and 1.56.

12. -10.35, 1.35

The equation is:

By using the formula:

which has two solutions: x=-10.35 and 1.35.

1. It is shifted 2 units down.

The graph of 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:

In the second function:

So, the first graph is shifted 2 units down.

2. 160.56 m

The path of the rocket is given by:

The problem asks us to find how far horizontally the rocket lands - this corresponds to find the value of x at which the height is zero: y=0. This means we have to solve the following equation

Using the formula,

which has two solutions: and . The second solution is negative, so it has no physical meaning, therefore the correct answer is 160.56 m.

3. 27.43 m

The path of the rock is given by:

The problem asks us to find how far horizontally the rock lands - this corresponds to find the value of x at which the height is zero: y=0. This means we have to solve the following equation

Using the formula,

which has two solutions: 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.

4. (-2, 16) and (1, -2)

The system is:

(1)

(2)

We can equalize the two equations:

which becomes:

Solving it with the formula, we find two solutions: x=-2 and x=1. Substituting both into eq.(2):

x=-2 -->

x=1 -->

So, the solutions are (-2, 16) and (1, -2).

5. (-1, 1) and (7, 33)

The system is:

(1)

(2)

We can equalize the two equations:

which becomes:

Solving it with the formula, we find two solutions: x=7 and x=-1. Substituting both into eq.(2):

x=7 -->

x=-1 -->

So, the solutions are (-1, 1) and (7, 33).

6. 2.30 seconds

The height of the object is given by:

The time at which the object hits the ground is the time t at which the height becomes zero: h(t)=0, therefore

By solving it,

7. Reaches a maximum height of 19.25 feet after 0.88 seconds.

The height of the ball is given by

The vertical velocity of the ball is equal to the derivative of the height:

The maximum height is reached when the vertical velocity becomes zero: v=0, therefore when

from which we find

And by substituting these value into h(t), we find the maximum height:

8. Reaches a maximum height of 372.25 feet after 4.63 seconds.

The height of the boulder is given by

The vertical velocity of the boulder is equal to the derivative of the height:

The maximum height is reached when the vertical velocity becomes zero: v=0, therefore when

from which we find

And by substituting these value into h(t), we find the maximum height:

9. 12 m

Let's call x the length of the side of the original garden. The side of the new garden has length (x+3), so its area is

Solvign this equation, we find

10. 225/4

In fact, if we write , we see this is equivalent to the perfect square:

11. -11.56, 1.56

The equation is:

By using the formula:

which has two solutions: x=-11.56 and 1.56.

12. -10.35, 1.35

The equation is:

By using the formula:

which has two solutions: x=-10.35 and 1.35.

Note: It seems you have asked the exact same type of questions again and again. So, I will solve the first question. The rest of the questions is the carbon copy of the same concept and solution method. Hopefully, it would get your concept clear.

The distance between the points (3, 6) and (8, -1)

Step-by-step explanation:

Given the points

Finding the distance between the points (3, 6) and (8, -1)

(x₁, y₁) = (3, 6)

(x₂, y₂) = (8, -1)

Thus, the distance between the points (3, 6) and (8, -1)

NOTE: All the remaning questions have the same method of solution.

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)

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)