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Sholpan [36]
3 years ago
11

A model rocket is launched with an initial velocity of 200 ft per second. The height h, in feet, of the rocket t seconds after t

he launch is given by h = −16t2 + 200t. How many seconds after the launch will the rocket be 350 ft above the ground? Round to the nearest hundredth of a second. (Enter your answers as a comma-separated list.)
Mathematics
1 answer:
Solnce55 [7]3 years ago
4 0

Answer:

2.10 s, 10.40 s.

Step-by-step explanation:

We know that the height of the rocket is given by the function:

h=-16t^2+200t

We are asked to find the time for which the height of the rocket will be 350 ft. So, for that moment, we know the height but we don't know the time; however, we know that the equation can help us to find the time, doing h=350:

350=-16t^2+200t

The last is a quadratic equation, which can be put in the form at^2+bt+c=0 and solved applying the formula:

t=\frac{-b+-\sqrt{b^2-4ac} }{2a}

So, let's put the equation on the form at^2+bt+c=0 adding 16t^2 and subtracting 200t to each side of the equation; the result is:

16t^2-200t+350=0

So, we note that a=16, b=-200, and c=350.

Then,

t_1=\frac{200-\sqrt{200^2-4*16*350} }{2*16}=2.10

t_2=\frac{200+\sqrt{200^2-4*16*350} }{2*16}=10.40

According to the equation, that are the times for which the height will be 350 ft; that is because the rocket is going to ascend and then to fail again to the ground.

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Answer:

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Step-by-step explanation:

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Amount of pool emptied in one hour if both pumpkins work together=

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Total 25.45 hours will be taken to empty the pool.

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Let the no be x

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3 0
3 years ago
I need help with this ASAP and can you explain so i can understand?!
Elanso [62]

Answer:

Adult tickets sold =  225

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Step-by-step explanation:

Let:

Adult tickets sold = x

Student Tickets sold = y

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Cost of one Student ticket = $4.50

So, we can write: 6x+4.5y=3037.50

Now, we get a system of equations, that if solved we can find values of x and y

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x+y = 600--eq(1)\\6x+4.5y=3037.50--eq(2)

We can solve using substitution method.

Finding value of x from eq(1) and putting it in eq(2)

We\:have\\x+y=600\\x=600-y

Put in eq(2)

6x+4.5y=3037.50\\6(600-y)+4.5y=3037.50\\3600-6y+4.5y=3037.50\\-1.5y=3037.50-3600\\-1.5y=-562.5\\y=\frac{-562.5}{-1.5}\\y=375

So, we get value of y = 375

Now put value of y in eq(1) to find value of x

x+y=600\\Put\:y=375\\x+375=600\\x=600-375\\x=225

So, we get value of x = 225

The Tickets sold will be:

Adult tickets sold = x = 225

Student Tickets sold = y = 375

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