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3 years ago

15

A ball is thrown directly up in the air from a height of 5 feet with an initial velocity of 60 ft/s. Ignoring air resistance, ho

w long until the ball hits the ground? Use the formula where h is the height of the ball in feet and t is the time in seconds since it is thrown. Round your answer to the nearest tenth.

1 answer:

Mice21 [21]3 years ago

4 0

Answer:

3.8 seconds

Step-by-step explanation:

Given equation

$h= -16t^2 + 60t + 5$

When the ball hits the ground then height is 0

So we replace h with 0 and solve for t

$0= -16t^2 + 60t + 5$

a= -16 , b= 60 and c= 5

Apply quadratic formula to solve for t

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

= $\frac{-60+\sqrt{60^2-4\left(-16\right)\cdot \:5}}{2\left(-16\right)}[/tex[tex]=\frac{-60+-\sqrt{3920}}{-32}$

$=\frac{-60+-28\sqrt{5}}{-32}$

$=\frac{4(-15+-7\sqrt{5})}{-32}$

$=\frac{(-15+-7\sqrt{5})}{-8}$

Now make two fractions and solve for x

t= $-\frac{7\sqrt{5}-15}{8}$ =-0.0815

t= $\frac{7\sqrt{5}+15}{8}$ =3.83

So answer is 3.8 seconds

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Answer:

$\frac{4}{21}$

Step-by-step explanation:

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Salut!

b=baiat

f=fata

In clasa sunt 35 elevi.

75/100 x b=f

3b/4=f

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A hot-air balloon is traveling at an altitude of 3,000 feet. It begins to descend at a rate of 80 feet per minute. Which equatio

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Equation can be used to represent the altitude of the balloon, b, based on time, t be 3000-80x

<h3>What is equation?</h3>

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Given:

A hot-air balloon is traveling at an altitude of 3,000 feet.

It begins to descend at a rate of 80 feet per minute.

let x be the time in minutes.

let y be the altitude in feet.

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Carlota wrote the equation y + 1 = 2 (x - 3) for the line passing through the points (-1, 3) and (2, 9). Explain and correct her

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For this case we have the following equation:

$y + 1 = 2 (x - 3)$

That can be rewritten in the form $y = mx + b$

Where:

m is the slope of the line

b is the cut point

So, we have:

$y + 1 = 2 (x - 3)\\y + 1 = 2x-6\\y = 2x-6-1\\y = 2x-7$

Where:

$m = 2$ is the slope

$b = -7$ is the cut point

Carlota has the following points:

(-1, 3) and (2, 9)

To know if the line $y = 2x-7$ passes through these points, we must replace them in the equation and the equality must be fulfilled. So:

Point (-1, 3):

Substituting:

$3 = 2 (-1) -7\\3 = -2-7$

$3 = -9$ It's false, equality is not met. The point (-1, 3) does not go through the line.

The equation written by Carlota is erroneous, the procedure to follow is:

Given $(x1, y1) = (- 1, 3)$ and $(x2, y2) = (2, 9)$ , we find the slope:

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$m=\frac{(9-3)}{(2-(-1))}$

$m=\frac{6}{3}$

$m=2$

We observe that the slope found by Carlota is the same. Let's see cut point "b". For this we substitute any of the points given in the equation:

$y = 2x + b$

Substituting (2,9) we have:

$9 = 2 (2) + b\\9 = 4 + b\\b = 9-4\\b = 5$

Thus, Carlota's error was at the cut-off point. The correct equation of the line that passes through the given points is $y = 2x + 5$

Answer:

The correct equation of the line that passes through the given points is $y = 2x + 5$

Carlota's mistake was at the cutoff point

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