F(7)=2x-3 ?<br><br> please ?

A toy rocket is launched from a platform that is 48 ft high. The rocket height above the ground is modeled by h=-16t^2+32t+48. a

Komok [63]

Answer:

a) 64 feet

b) 3 seconds

Step-by-step explanation:

a)

The maximum height of $h=h(t)$ can be bound by finding the y-coordinate of the vertex of $y=-16x^2+32x+48$ .

Compare this equation to $y=ax^2+bx+c$ to find the values of $a,b,\text{ and } c$ .

$a=-16$

$b=32$

$c=48$ .

The x-coordinate of the vertex can be found by evaluating:

$\frac{-b}{2a}=\frac{-32}{2(-16)$

$\frac{-b}{2a}=\frac{-32}{-32}$

$\frac{-b}{2a}=1$

So the x-coordinate of the vertex is 1.

The y-coordinate can be found be evaluating $y=-16x^2+32x+48$ at $x=1$ :

$y=-16(1)^2+32(1)+48$

$y=-16+32+48$

$y=16+48$

$y=64$

So the maximum height of the rocket is 64 ft high.

b)

When the rocket hit's the ground the height that the rocket will be from the ground is 0 ft.

So we are trying to find the second t such that:

$0=-16t^2+32t+48$

I'm going to divide both sides by -16:

$0=t^2-2t-3$

Now we need to find two numbers that multiply to be -3 and add to be -2.

Those numbers are -3 and 1 since (-3)(1)=-3 and (-3)+(1)=-2.

$0=(t-3)(t+1)$

This implies we have either $t-3=0$ or $t+1=0$

The first equation can be solved by adding 3 on both sides: $t=3$ .

The second equation can be solved by subtracting 1 on both sides: $t=-1$ .

So when $t=3$ seconds, is when the rocket has hit the ground.

5 0

3 years ago

5. A 12 sided diɛ is rolled. The set of equally

professor190 [17]

Answer:

Step-by-step explanation:

5 0

3 years ago

A car covered a certain distance at a speed of 24 mph. While returning, the car covered the same distance at a speed of 16 mph.

igomit [66]

Since the distances were the same you can find the average speed directly by adding the speeds then dividing by 2. No need to weight anything.

If we’re considering speed regardless of direction, the average speed is:

(24 + 16) / 2 = 40 / 2 = 20mph

However if direction matters, then one number has to be negative since the directions are opposite:

(24 - 16) / 2 = 8 / 2 = 4mph (in the positive direction)

Depending on the context, either of these could be your answer.

7 0

3 years ago

Read 2 more answers

If you worked for 6 days for a total of 67.8 hours. If I worked the same number of hours each day, how many hours did I work in

Hunter-Best [27]

Hi there!

To solve this problem, we need to divide 67.8 by 6 to find the amount of hours each day.

67.8 / 6 = 11.3

You worked 11.3 hours each day.

Hope this helps!

8 0

3 years ago

Molly, a purchasing agent for a high-tech firm, is ordering computers for a new branch office. Laptops cost $540 apiece and desk

NISA [10]

Answer:

540x+680y<=20000

Step-by-step explanation:

x will be the number of laptops. Since they are $540 each, 540x is the amount spent on laptops, depending on how many (x) are purchased.

y will be the number if desktops. Since they are $680 each, 680y is the amount spent on desktops, depending on how many (y) are purchased.

Adding all the money spent on laptops and desktops, we get

540x + 680y. This amount must be less than the $20000. It can be exactly $20000 also. But it cannot be more than $20000.

540x+680y<=20000

3 0

2 years ago

F(7)=2x-3 ? please ?