The population P of a small island was 6380 , correct to the nearest 10.

a ball is thrown with a slingshot at a velocity of 110ft/sec at an angle of 20 degrees above the ground from a height of 4.5 ft.

satela [25.4K]

Answer:

$t=2.47\ s$

Step-by-step explanation:

The equation that models the height of the ball in feet as a function of time is

$h(t) = h_0 + s_0t -16t ^ 2$

Where $h_0$ is the initial height, $s_0$ is the initial velocity and t is the time in seconds.

We know that the initial height is:

$h_0 = 4.5\ ft$

The initial speed is:

$s_0 = 110sin(20\°)\\\\s_0 = 37.62\ ft/s$

So the equation is:

$h (t) = 4.5 + 37.62t -16t ^ 2$

The ball hits the ground when when $h(t) = 0$

So

$4.5 + 37.62t -16t ^ 2 = 0$

We use the quadratic formula to solve the equation for t

For a quadratic equation of the form

$at^2 +bt + c$

The quadratic formula is:

$t=\frac{-b\±\sqrt{b^2 -4ac}}{2a}$

In this case

$a= -16\\\\b=37.62\\\\c=4.5$

Therefore

$t=\frac{-37.62\±\sqrt{(37.62)^2 -4(-16)(4.5)}}{2(-16)}$

$t_1=-0.114\ s\\\\t_2=2.47\ s$

We take the positive solution.

Finally the ball takes 2.47 seconds to touch the ground

4 0

2 years ago

You receive an email asking you to forward it to four other people to ensure prosperity. Assuming the chain isn't broken, how ma

dolphi86 [110]

well if it asks you to send to 4 people and there are 8 generations which includes yours that mean

1 sent to 4 - 4 recived

4 send to 4 each = 16 recived + the 4 before = 20 (generation 2)

16 send to 4 = 64 + 20 = 84 (generation 3)

64 send to 4 = 256 + 84= 320 (g4)

256 send to 4 = 1024 + 320 = 1344 (g5)

1344 s t 4 = 5376 + 1344= 6730 (g6)

so on and so forth till generation 8

4 0

1 year ago

Read 2 more answers

The formula that relates the length of a ladder, L, that leans against a wall with distance d from the base of the wall and the

Ulleksa [173]

Answer:

Step-by-step explanation:

The formula that relates the length of a ladder, L, that leans against a wall with distance d from the base of the wall and the height h that the ladder reaches up the wall is L = StartRoot d squared + h squared EndRoot. What height on the wall will a 15-foot ladder reach if it is placed 3.5 feet from the base of a wall?

L = √d² + h²

4 0

1 year ago

Read 2 more answers

What is the length of the hypotenuse of the triangle below?

liberstina [14]

Answer:

$\boxed{B. Hypotenuse = 10}$

Step-by-step explanation:

By applying <em>Pythagoras theorem</em> we can find hypotenuse of a right angle triangle.

Side of right angle triangle (a) = 5√2 cm

Side of right angle triangle (b) = 5√2 cm

Hypotenuse² = a² × b²

${Hypotenuse}^{2} = {(5 \sqrt{2} )}^{2} \times {(5 \sqrt{2} )}^{2} \\ \\ {Hypotenuse}^{2} = (25 \times 2) + (25 \times 2)\\ \\ {Hypotenuse}^{2} = 50 + 50\\ \\ {Hypotenuse}^{2} = 100\\ \\ {Hypotenuse}^{ \cancel{2}} = {10}^{ \cancel{2}} \\ \\ Hypotenuse = 10$