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malfutka [58]
3 years ago
6

a bird is in a tree 30 feet off the ground and drops at Twigs at lands on a rose bush 25 ft below. the function h(t)=-16t^2+30,

where T represents the time in seconds gifts the height H and feet of The Twig above the ground as it falls when will The Twig land on the bush
Mathematics
2 answers:
yulyashka [42]3 years ago
8 0

Answer:

After 1.25 seconds the twig land on the bush.

Step-by-step explanation:

Given function that shows the height of twig from the ground after t seconds,

h(t)=-16t^2+30

When twig is on the bush,

h(t) = 5 feet   ( ∵ the distance from bush to ground = 30 - 25 = 5 feet )

\implies -16t^2+30=5

-16t^2=-25

t^2=\frac{25}{16}

\implies t=\pm \frac{5}{4}  

Since, time can not be negative,

Hence, t = \frac{5}{4} ≈ 1.25

Therefore, after 1.25 seconds the twig land on the bush.

Serggg [28]3 years ago
5 0
Answer: It will land on the bush after 1.25 seconds.

First, we will start with what we are given the equation: h(t) = -16t^2 + 30

Now, we should input a 5 for the h(t) because we want the seconds that will give us a height of 5 seconds.

5 = -16t^2 + 30

Solve the equation:
0 = -16t^2 + 25

To solve this, you could use the quadratic formula or factor out a -1 and you will have the difference of two squares.

Either way the answer is 1.25 seconds.
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10 months ago
1. The mechanics at Lincoln Automotive are reborning a 6 in deep cylinder to fit a new piston. The machine they are using increa
Firdavs [7]

Answer:

0.0239\frac{in^{3}}{min}

Step-by-step explanation:

In order to solve this problem, we must start by drawing a diagram of the cylinder. (See attached picture)

This diagram will help us visualize the problem better.

So we start by determining what data we already know:

Height=6in

Diameter=3.8in

Radius = 1.9 in (because the radius is half the length of the diameter)

The problem also states that the radius will increase on thousandth of an inch every 3 minutes. We can find the velocity at which the radius is increasing with this data:

r'=\frac{1/1000in}{3min}

which yields:

r'=\frac{1}{3000}\frac{in}{min}

with this information we can start solving the problem.

First, the problem wants us to know how fast the volume is increasing, so in order to find that we need to start with the volume formula for a cylinder, which is:

V=\pi r^{2}h

where V is the volumen, r is the radius, h is the height and π is a mathematical constant equal approximately to 3.1416.

Now, the height of the cylinder will not change at any time during the reborning, so we can directly substitute the provided height, so we get:

V=\pi r^{2}(6)

or

V=6 \pi r^{2}

We can now take the derivative to this formula so we get:

\frac{dV}{dt}=2(6)\pi r \frac{dr}{dt}

Which simplifies to:

\frac{dV}{dt}=12\pi r \frac{dr}{dt}

We can now substitute the data provided by the problem to get:

\frac{dV}{dt}=12\pi (1.9) (\frac{1}{3000})

which yields:

\frac{dV}{dt}=0.0239\frac{in^{3}}{min}

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3 years ago
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