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nadya68 [22]
3 years ago
10

A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by th

e given equation. Using this equation, find the time that the rocket will hit the ground, to the nearest 100th of second. y=-16x^2+224x+121 y=−16x 2 +224x+121
Mathematics
2 answers:
telo118 [61]3 years ago
8 0

Answer:

14.52 seconds

Step-by-step explanation:

equation of the distance of rocket traveled in time x is given by

y = -16x^{2}+224 x +121

The displacement of the rocket is zero when it hits the ground, so equate the equation equals to zero, we get

0= -16x^{2}+224 x +121

16x^{2}-224 x-121=0

x = \frac{224\pm \sqrt{224^{2}+4\times 16\times 121}}{2\times 16}

x = \frac{224\pm 240.67}{32}

x = - 0.52 second, 14.52 seconds

Time cannot have a negative value so the time taken by the rocket to hit the ground is 14.52 seconds.

olchik [2.2K]3 years ago
6 0

Answer:

14.52 seconds.

Step-by-step explanation:

We have been given that the height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation y=-16x^2+224x+121. We are asked to find the time, when the rocket will hit the ground.

We know that the rocket will hit the ground, when height will be 0. So to find the time when rocket will hit the ground, we will substitute y=0 in our given equation as:

0=-16x^2+224x+121

Let us solve for x using quadratic formula.

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

x=\frac{-224\pm\sqrt{224^2-4(-16)(121)}}{2(-16)}

x=\frac{-224\pm\sqrt{50176+7744}}{-32}

x=\frac{-224\pm\sqrt{57920}}{-32}

x=\frac{-224\pm240.66574}{-32}

x=\frac{-224+240.66574}{-32}, x=\frac{-224-240.66574}{-32}

x=\frac{16.66574}{-32}, x=\frac{-464.66574}{-32}

x=-0.520804375, x=14.520804375

Upon rounding to nearest 100th of second, we will get:

x\approx -0.52, x\approx 14.52

Since time cannot be negative, therefore, the rocket will hit the ground after 14.52 seconds.

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there are nickels, dimes, and quarters in a piggy bank. altogether, the coins are worth $3.65. the number of dimes is three time
hoa [83]

This question is solved using a system of equations, and doing this, we get that: There are 9 quarters, 4 nickels and 12 dimes.

I am going to say that:

x is the number of nickels.

y is the number of dimes.

z is the number of quarters.

In all, they are worth $3.65.

A nickel is worth $0.05, a dime is worth $0.1 and a quarter is worth $0.25, so:

0.05x + 0.1y + 0.25z = 3.65

Dimes: 3 times greater than nickels:

This means that:

y = 3x

Quarters: One greater than double the number of nickels:

This means that:

z = 2x + 1

Value of x:

We have y and z as function of x, so we can replace into the equation and find the value of x, so:

0.05x + 0.1y + 0.25z = 3.65

0.05x + 0.1(3x) + 0.25(2x+1) = 3.65

0.05x + 0.3x + 0.5x + 0.25 = 3.65

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x = \frac{3.4}{0.85}

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y and z:

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There are 9 quarters, 4 nickels and 12 dimes.

A similar question is found at brainly.com/question/17096268

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3 years ago
What is a good strategy for finding the distance between two numbers on a number line?
Gnom [1K]
The strategy is following
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For example you have 3 and 8
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Answer:

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Step-by-step explanation:

Well, I can't see a photo, so I'll have to assume that the description provides enough info.

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This means we have to multiply 5 by 15 to find x.

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Let's plug the new value back in...

10cm/2km = x/15km

10cm/2km = (75cm)/15km

<em>(Simplify each side to its simplest form)</em>

10cm/2km = 75cm/15km

5/1 = 5/1

It works! So x = 75cm.

Hope this helps! :)

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