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
Ostrovityanka [42]
3 years ago
12

A ball is dropped from a state of rest at time t=0.The distance traveled after t seconds is s(t)=16t^2 ft.

Mathematics
1 answer:
natka813 [3]3 years ago
7 0

Answer:

i) Δs  = 196 - 144 = 52 feet

ii) Δs / Δt = 104 feet/second

iii) Therefore the velocity at t = 3 is v(3) = 96 feet/second

Step-by-step explanation:

a.) i) s = 16t^{2}

   ii) at 3 seconds the distance traveled s(3) = 16\times (3)^2\hspace{0.2cm} =  16 \times 9 = 144 feet

   iii) at 3.5 seconds the distance traveled s(3.5) = 16\times (3.5)^2\hspace{0.2cm} =  16 \times 12.25 = 196 feet

  iv) Δs  = 196 - 144 = 52 feet

b) Average velocity over [3, 3.5] = Δs / Δt  = 52/(0.5) = 104 feet/second

c) the average velocity over the interval

  I) i) [3, 3.01]

     ii) s(3.01) = 16\times (3.01)^2\hspace{0.2cm} =  16 \times 9.0601 = 144.962 feet

     iii) Δs  = 144.962 - 144 = 0.962 feet

     iv) Average velocity over [3, 3.01] = Δs / Δt  = 0.962/(0.01) =

          96.2 feet/second

II) i) [3, 3.001]

     ii) s(3.001) = 16\times (3.001)^2\hspace{0.2cm} =  16 \times 9.006001 = 144.096 \hspace{0.1cm} feet

     iii) Δs  = 144.096 - 144 = 0.096 feet

     iv) Average velocity over [3, 3.001] = Δs / Δt  = 0.096/(0.001) =

         96 feet/second

III) i) [3, 3.0001]

     ii) s(3.0001) = 16\times (3.0001)^2\hspace{0.2cm} =  16 \times 9.00060001 = 144.0096 \hspace{0.1cm} feet

     iii) Δs  = 144.0096 - 144 = 0.0096 feet

     iv) Average velocity over [3, 3.0001] = Δs / Δt  = 0.0096/(0.0001) =

         96 feet/second

IV) i) [2.9999, 3]

     ii) s(2.9999) = 16\times (2.9999)^2\hspace{0.2cm} =  16 \times 8.9994 = 143.99\hspace{0.1cm} feet

     iii) Δs  = 144 - 143.99 = 0.0096 feet

     iv) Average velocity over [2.9999, 3] = Δs / Δt  = 0.0096/(0.0001) =

         96 feet/second

V) i) [2.999, 3]

     ii) s(2.999) = 16\times (2.999)^2\hspace{0.2cm} =  16 \times 8.994 = 143.904\hspace{0.1cm} feet

     iii) Δs  = 144 - 143.904 = 0.09598 feet

     iv) Average velocity over [2.999, 3] = Δs / Δt  = 0.09598/(0.001) =

         95.98 feet/second

VI) i) [2.99, 3]

     ii) s(2.99) = 16\times (2.99)^2\hspace{0.2cm} =  16 \times 8.94 = 143.0416\hspace{0.1cm} feet

     iii) Δs  = 144 - 143.042 = 0.098 feet

     iv) Average velocity over [2.99, 3] = Δs / Δt  = 0.098/(0.01) =

         98 feet/second

 Therefore the velocity at t = 3 is v(3) = 96 feet/second

You might be interested in
Anyone else in College Algebra?
ruslelena [56]

Answer: no

Step-by-step explanation:

6 0
3 years ago
find rodrigos percent increase or decrease in sales each week. week 1, is 17 wwek 2, is 25 week 3, is 18 and week 4, is 27. his
sveticcg [70]
<span>Answer: The multiplication factor of increase should be inverse of the multiplication factor of decrease.

    e.g. Say you have a number 100. You increase it by 25%. The multiplication factor is 5/4 i.e. when you multiply 100 by 5/4, you get 100*5/4 = 125. This is 25% more than 100. Now you want to decrease it by a certain % such that you get 100 back. Basically, 100*5/4 * x = 100 So x = 4/5 (inverse of 5/4) Hence, you decrease by 20% (the multiplication factor of 20% is 4/5) or Use this formula: cumulative % change = a + b + ab/100 You want the cumulative change to be 0. a + b + ab/100 = 0 If you know that you are increasing by 25% and want to find the % by which you should decrease to get the same number, 25 + b + 25b/100 = 0 5b/4 = -25 b = -20 So you need to decrease (hence you get the -ve sign) by 20%.</span>
3 0
3 years ago
If p(x)=2x^3+cx^2+16x+84 and x+2 is a factor of p(x),find the value of c.
Nuetrik [128]

Answer:

c = -9

Step-by-step explanation:

Knowing that -2 is a root, you can do the synthetic division with an unknown value for c. Then solve for the value of c that makes the remainder be zero. See the attachment for the work.

The second attachment shows that (x+2) is a factor of the resulting cubic.

4 0
3 years ago
Where to place the lines
vazorg [7]
Use photo math it works well
7 0
3 years ago
Simplify the algebraic expression.<br> 2v−8(3+2v)
ra1l [238]

Answer: -14v-24

Step-by-step explanation:

2v-8(3+2v)

2v-(24+16v)

2v-24-16v

-14v-24

3 0
2 years ago
Read 2 more answers
Other questions:
  • <img src="https://tex.z-dn.net/?f=5%3D%20x%5E%7B2%7D%20%2B2x" id="TexFormula1" title="5= x^{2} +2x" alt="5= x^{2} +2x" align="ab
    13·1 answer
  • A diagonal of a cube goes from one of rhe cube's top corners to the opposite corner of the base of the cube. Find the length of
    15·1 answer
  • A survey was conducted in a town regarding the construction of a new highway bypass. Of the 3,500 people surveyed, 65% agreed th
    8·1 answer
  • Five times the sum of a number and 4 is 9
    7·1 answer
  • True r false? A circle could be circumscribed about the quadrilateral below?
    15·2 answers
  • The volume of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a mean of 12.45 oun
    11·1 answer
  • X + x2 - 5x -5 = 0<br> state the possible rational zeros and find all the zeros of the polynomial
    8·1 answer
  • Light A flashes every 8 seconds.
    12·1 answer
  • Brainliest Question Of The Day:
    15·1 answer
  • Who knows all the answers
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!