1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Paha777 [63]
3 years ago
13

We are standing on the top of a 320 foot tall building and launch a small object upward. The object's vertical altitude, measure

d in feet, after t seconds is h ( t ) = − 16 t 2 + 128 t + 320 . What is the highest altitude that the object reaches?
Mathematics
1 answer:
STALIN [3.7K]3 years ago
6 0

Answer:

The highest altitude that the object reaches is 576 feet.

Step-by-step explanation:

The maximum altitude reached by the object can be found by using the first and second derivatives of the given function. (First and Second Derivative Tests). Let be h(t) = -16\cdot t^{2} + 128\cdot t + 320, the first and second derivatives are, respectively:

First Derivative

h'(t) = -32\cdot t +128

Second Derivative

h''(t) = -32

Then, the First and Second Derivative Test can be performed as follows. Let equalize the first derivative to zero and solve the resultant expression:

-32\cdot t +128 = 0

t = \frac{128}{32}\,s

t = 4\,s (Critical value)

The second derivative of the second-order polynomial presented above is a constant function and a negative number, which means that critical values leads to an absolute maximum, that is, the highest altitude reached by the object. Then, let is evaluate the function at the critical value:

h(4\,s) = -16\cdot (4\,s)^{2}+128\cdot (4\,s) +320

h(4\,s) = 576\,ft

The highest altitude that the object reaches is 576 feet.

You might be interested in
How do you factor something
Zepler [3.9K]
Finding what a number is diviseble by or finding multiples of a number
3 0
3 years ago
A company wants to determine the level of interest among its employees for an annual summer picnic. The company wants to survey
Alja [10]

Answer: Use employee identification numbers to randomly select 200 employees

Step-by-step explanation:

Random sampling refers to a sampling technique whereby each sample has an equal chance of being selected. It is an unbiased representation of the entire population and this is vital in drawing conclusion.

From the options given, the best way to randomly choose these 200 employees will be to use employee identification numbers to randomly select 200 employees.

7 0
3 years ago
Consider the function and its inverse.
Ber [7]

Answer:

The domain of f(x) is restricted to x\leq 0, and the domain of f^{-1}(x) is restricted to x\geq 4.

Step-by-step explanation:

From Function Theory we know that domain of a function is the set of values such that an image exist. Let f(x) = x^{2}+4 and f^{-1}(x) = \sqrt{x-4} the function and its inverse, respectively.

At first glance we notice that function is a second order polynomial and every polinomial is a continuous function and therefore, there exists an image for every element of domain.

But domain of its inverse is restricted to every value of x so that x-4 \geq 0, which means that x\geq 4.

Finally, we concluded that following answer offers the best approximation to our result:

The domain of f(x) is restricted to x\leq 0, and the domain of f^{-1}(x) is restricted to x\geq 4.

6 0
3 years ago
. <br><img src="https://tex.z-dn.net/?f=lim%20%5Cfrac%7B%20%5Ctan%28ax%20-%20a%29%20%2B%20b%20-%202%20%7D%7Bx%20-%201%7D%20" id=
navik [9.2K]

Answer:

i dont know

Step-by-step explanation:

6 0
3 years ago
Which graph represents the system 2X minus 5Y minus -5 or Y -2/5 X +1
Natali5045456 [20]
Hi, where are the graphs?
8 0
3 years ago
Other questions:
  • Which statement is best represented by the inequality c &gt; 3 1/2?
    12·2 answers
  • Which angle is an adjacent interior angle?<br> CO3<br> Save and Exit<br> Submit
    9·1 answer
  • 2/3 cup of cat food equally between 2 cats how much food do you give each cat
    8·2 answers
  • Which quadrilaterals have diagonals that are not lines of symmetry?
    6·1 answer
  • Micah deposited $4000 between two savings account. One account earns 4% simple interest each year. The other account earns 2% si
    5·1 answer
  • HELP ASAP WILL GIVE 20 POINTSSSSS
    8·1 answer
  • A typical marathon is 26.2 miles. Allan averages 12 kilometers per hour when running in marathons. Determine how long it would t
    11·1 answer
  • I need help .Can you do Questions 1,2,3,4,5,6 and 7 Please?
    12·1 answer
  • The quotient of x^2+x-6/x^2-6x+5*x^2+2x-3/x^2-7x+10 has ___ in the numerator and ______ in the denominator.
    14·1 answer
  • Which of the following is the simplest form of this expression?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!