What is the blank for 3.441 <>= 3.409

A ball dropped from the top of a building can be modeled by the function f(t)=-16^2+36, where t represents time in seconds

Viefleur [7K]

Answer:

The ball is dropped from a height of 36 feet

The bee and the ball will collide after approximately 1.3 seconds

The bee and the ball will collide at approximately 8 feet above the ground

The ball hits the ground after 1.5 seconds

Step-by-step explanation:

The complete question is

A ball dropped from the top of the building can be modeled by the function f(t)=-16t^2 + 36 , where t represents time in seconds after the ball was dropped. A bee's flight can be modeled by the function, g(t)=3t+4, where t represents time in seconds after the bee starts the flight.

The graph represents the situation.

select all that apply

1) The bee launches into flight from the ground.

2) The ball is dropped from a height of 36 feet.

3) The bee and the ball will collide after approximately 1.3 seconds.

4) The bee and the ball will collide after approximately 8 seconds.

5) The bee and the ball will collide at approximately 8 feet above the ground.

6) The bee and the ball will not collide.

7) The ball hits the ground after 1.5 seconds

see the attached figure to better understand the problem

Verify all the options

case 1) The bee launches into flight from the ground.

The statement is false

Because

we have

$g(t)=3t+4$

For t=0

$g(t)=3(0)+4=4\ ft$

That means ----> The bee launches into flight from a height 4 feet above the ground

case 2) The ball is dropped from a height of 36 feet

The statement is true

Because

For t=0

$f(t)=-16(0)^2+36=36\ ft$

case 3) The bee and the ball will collide after approximately 1.3 seconds

The statement is true

Because

Equate f(t) and g(t)

$-16t^2+36=3t+4$

$-16t^2-3t+32=0$

solve the quadratic equation by graphing

The solution is t=1.324 sec

see the attached figure N 2

case 4) The bee and the ball will collide after approximately 8 seconds

The statement is false

Because, the bee and the ball will collide after approximately 1.3 seconds (see case 3)

case 5) The bee and the ball will collide at approximately 8 feet above the ground

The statement is true

Because

For t=1.324 sec

substitute the value of t in f(t) or g(t)

$g(t)=3(1.324)+4=7.97\ ft$

case 6) The bee and the ball will not collide

The statement is false

see case 3) and case 5)

case 7) The ball hits the ground after 1.5 seconds

The statement is true

Because

we know that

The ball hit the ground when the value of f(t) is equal to zero

so

For f(t)=0

$-16t^2+36=0$

$t^2=\frac{36}{16}$

$t=\frac{6}{4}=1.5\ sec$

4 0

3 years ago

Read 2 more answers

A number n is greater than 22

8_murik_8 [283]

23 keep the picture save it and shush

3 0

3 years ago

Read 2 more answers

A car dealership offers a special interest rate of 3.5%. What is 3.5% written as a decimal? A. 0.0035 B. 0.035 C. 0.35 D. 35.0

wel

Make 3.5% out of 100: $\frac{3.5}{100}$ 3.5÷100=0.035. So the Answer is B. 0.035.

7 0

3 years ago

Solve the equation to find a positive value of c: 62 + 82 = c2

Artist 52 [7]

$c^{2}$ = 144
c = ± $\sqrt{144}$
c = ±12

5 0

4 years ago

Read 2 more answers

Sarah is driving. Her distance in km from Tempe after t hours of driving is given by: x = D(t) = 13 + 57t

777dan777 [17]

Answer:

The solutions for your four question problem are:

a) t = D^-1(x) = (1/57)*x -(13/57)

b) t = D^-1(x) = 1 h

c) D^-1(x) represents time.

d) The number of hours of driving needed for Sarah to be x km from Tempe. (option (c))

Step-by-step explanation:

a) Determine a formula in terms of x for: t = D^-1(x)

The distance in km from Tempe after t hours of driving is given by

x = D(t) = 13 + 57t.

We just need to find the value t function of x

x = 13 + 57*t

x -13 = 57*t

57*t = x -13

t = (1/57)*x -(13/57)

We can see the plots of both equation in the picture below.

b) Compute D^-1(70)

Once we find the expression for D^-1(x)

We substitute for x = 70 km

t = D^-1(x) = (1/57)*x -(13/57)

t = D^-1(x) = (1/57)*(70) -(13/57)

t = D^-1(x) = (70/57) -(13/57)

t = D^-1(x) = (1.228) -(0.228)

t = D^-1(x) = 1 h

c) In the expression D^-1(x) : what quantity (distance or time) does the x represent? what quantity (distance or time) does the entire D^-1(x) represent?

x represents Distance in both equations (D(t), and D^-1(x))

t represents Time in both equations (D(t), and D^-1(x))

Since t = D^-1(x),

D^-1(x) represents time.

d) Which of the following statements best describes D^-1(x)?

The number of hours of driving needed for Sarah to be x km from Tempe.

Since, t = D^-1(x), and t represents the amount of time elapsed since Sarah, parted from Tempe, the correct answer is option (c)

The expression for D^-1(x) can be found in the previous answers

t = D^-1(x) = (1/57)*x -(13/57)

The input is x (distance) and the output is t (time)

6 0

4 years ago