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marshall27 [118]
2 years ago
9

A watermelon is launched from a 25-foot tall platform at a carnival. The watermelon's height h (in feet) at time t seconds can b

e modeled by the equation h = -16t^2 + 56t + 25. Find the maximum height of the watermelon
Mathematics
1 answer:
Nataly [62]2 years ago
5 0

Answer:

The maximum height of the watermelon is 74 feet.

Step-by-step explanation:

The watermelon reaches its maximum height when its velocity is zero. Mathematically speaking, velocity is the first derivative of the function height, that is:

v(t) = \frac{d}{dt} h(t) (1)

Where v(t) is the velocity, in feet per second.

If we know that h(t) = -16\cdot t^{2}+56\cdot t +25 and v(t) = 0\,\frac{ft}{s}, then the time associated with maximum height is:

v(t) = -32\cdot t +56 (2)

-32\cdot t + 56 = 0

t = 1.75\,s

Now we evaluate the function height at time found in the previous step: (t = 1.75\,s)

h(t) = -16\cdot t^{2}+56\cdot t +25

h(1.75) = 74\,ft

The maximum height of the watermelon is 74 feet.

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A certain semiconductor device requires a tunneling probability of T = 10-5 for an electron tunneling through a rectangular barr
Goryan [66]

Answer:

Generally the barrier width is a = 1.9322 *10^{-9} \ m

Step-by-step explanation:

From the question we are told that

     The tunneling probability required is  T  = 1 * 10^{-5}

      The barrier height is  V_o  = 0.4 eV

       The electron energy is  E = 0.08eV

Generally the wave number is mathematically represented as

      k  =  \sqrt{ \frac{2 * m [V_o - E]}{\= h^2} }

Here m is the mass of the electron with the value  m  =  9.11 *10^{-31} \  kg

         h  is is know as h-bar and the value is  \= h = 1.054*10^{-34} \  J \cdot s

So

          k  =  \sqrt{ \frac{2 * 9.11 *10^{-31 } [0.4 - 0.04] * 1.6*10^{-19}}{[1.054*10^{-34}^2]} }

=>      k = 3.073582 *10^{9}  \ m^{-1}

Generally the tunneling probability is mathematically represented as

          T  = 16 * \frac{E}{V_o }  * [1 - \frac{E}{V_o} ] * e^{-2 * k * a}

So

        1.0 *10^{-5} = 16 * \frac{0.04}{0.4 }  * [1 - \frac{0.04}{0.4} ] * e^{-2 * 3.0736 *10^{9} * a}

=>    6.944*10^{-6}= e^{-2 * 3.0736 *10^{9} * a}

Taking natural log of both sides

          ln[6.944*10^{-6}] = -2 * 3.0736 *10^{9} * a}

=>        -11.8776  = -2 * 3.0736 *10^{9} * a}

=>        a = 1.9322 *10^{-9} \ m

       

4 0
3 years ago
What is the product of 48.65(6.2)?<br> A 30.163<br> B296.77<br> C301.63<br> D306.49
love history [14]

The required solution is 301.63.

Option (C) is correct.

It is required to find the product of the given expression.

<h3>What is arithmetic?</h3>

The branch of mathematics dealing with the properties and manipulation of numbers. a science that deals with the addition, subtraction, multiplication, and division of numbers. Fractions, decimals, percentages, fractions, square root, exponents, and other arithmetic operations are used to achieve mathematical simplifications.

Given that:

The given expression is

48.65(6.2)

It is to find the product of the given expression we get

48.65*6.2

=301.63

Hence, the required solution is 301.63.

Learn more about arithmetic here:

brainly.com/question/28280038

#SPJ2

6 0
2 years ago
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