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aev [14]
2 years ago
12

The Sears Tower, at 1,451 feet, is one of the tallest structures in the United States. A penny is thrown from the top of the tow

er. The height, h, of the penny is recorded after each second, t, in the table. Write an equation for the curve of best fit, then find the approximate height of the penny after 7 seconds.
Mathematics
1 answer:
padilas [110]2 years ago
6 0

Answer:

The equation for the height of the penny in function of time is:

h(t)=1451-16t^2

After 7 seconds, the penny will be at a height of 667 feet.

Step-by-step explanation:

The penny will have a free fall.

The initial velocity is zero, and the initial height is h(0)=1,451.

The acceleration will be the gravity, that has a value g=32 ft/s^2.

Then, we can model this starting by the speed:

dv/dt=-g\\\\v(t)=v_0-gt=-gt

Then, the height becomes:

dh/dt=v(t)=-gt\\\\h(t)=h_0-\dfrac{gt^2}{2}=1451-\dfrac{32}{2}t^2\\\\\\h(t)=1451-16t^2

The approximate height of the penny after 7 seconds can be calculated as:

h(7)=1451-16(7^2)=1451-16*49=1451-784=667

After 7 seconds, the penny will be at a height of 667 feet.

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Answer:

4 часа

Step-by-step explanation:

Формула для расстояния = скорость × время

Шаг 1

Первый поезд

Ехал со скоростью 75 км / час 2 часа.

Следовательно, пройденное расстояние = 75 км / час × 2 часа = 150 км.

Шаг 2

Из вопроса мы знаем, что расстояние между городами A и B = 710 км.

Следовательно, оставшееся расстояние = 710 км - 150 км.

= 560 км

Шаг 3

Суммарная скорость обоих поездов =

75 км / ч + 65 км / ч

= 140 км / час

Шаг B

Количество часов, в течение которых оба поезда встретятся после отправления второго поезда, рассчитывается следующим образом:

Время = Расстояние / Скорость

Время = 560 км / 140 км

Время = 4 часа.

Поэтому оба поезда встретятся через 4 часа.

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2 years ago
A teacher gives each of five students a box that contains 25 red balls, 25 blue balls, 25 green balls, and 25 purple balls. The
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1 year ago
Malachy and Paul win some money and share it in the ratio 4:5. Malachy gets £44. How much did Paul get?
Gelneren [198K]

if Malachy gets £44 then Paul get $55.

Step-by-step explanation:

Malachy and Paul win some money and share it in the ratio = 4:5

if Malachy gets £44 we need to find how much did Paul get?

let Paul get x so, we will have

4:5=44:x

\frac{4}{5}=\frac{44}{x}

Cross multiply and solve:

4x=44*5\\x=\frac{44*5}{4}\\x=55

So, Paul get $55

Keywords: Ratio

Learn more about Ratio at:

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Michael has 4 red shirts, 3 green shirts, and 5 blue shirts in his closet. If he randomly selects a shirt what is the probabilit
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2 years ago
A boat is heading towards a lighthouse, where Mason is watching from a vertical
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The distance between point A and point B is 371 ft if the Mason measures an angle of depression to the boat at point A to be 16°.

<h3>What is trigonometry?</h3>

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have:

A boat is heading towards a lighthouse, where Mason is watching from a vertical distance of 122 feet above the water. Mason measures an angle of depression to the boat at point A to be 16°.

We can draw the above situation as a form of a right-angle triangle.

From the figure, the distance between AB is x ft

From the right angle triangle DBC:

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From the right angle triangle DAC

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AC = 425.46 ft

x = AC - CB

x = 425.46 - 54.31

x = 371.15 ft ≈ 371 ft

Thus, the distance between point A and point B is 371 ft if the Mason measures an angle of depression to the boat at point A to be 16°.

Learn more about trigonometry here:

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