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
Serggg [28]
3 years ago
8

a ball is shot straight upward. with it's height, in feet, after t seconds given by the function f(t)=-16t^2+192t. Find the aver

age velocity of the ball from t=1 to t=6
Mathematics
1 answer:
jekas [21]3 years ago
7 0

ANSWER

80  {ms}^{ - 1}

EXPLANATION

The average velocity of the ball is the rateof displacement over the total time.

The height of the ball, in feet, after t seconds is given by the function:

f(t)=-16t^2+192t

At time t=1, the height of the ball is

f(1)=-16(1)^2+192(1)

f(1)=-16+192 = 176ft

At time t=6, the height of the ball is

f(6)=-16(6)^2+192(6)

f(6)=-16(36)+192(6)

f(6)=-576+1152 = 576

The average velocity

=  \frac{f(6) - f(1)}{6 - 1}

=  \frac{576- 176}{6 - 1}

=  \frac{400}{5}

= 80  {ms}^{ - 1}

You might be interested in
A typical cup of coffee contains about 100 mg of caffeine and every hour approximately 16% ofthe amount of caffeine inthe body i
Over [174]

Answer:

a) \frac{dC}{dt} = rC

And for this case we can rewrite the model like this:

\frac{dC}{C} = r dt

If we integrate both sides we got:

ln C = rt + k

If we use exponentials for both sides we got:

C = e^{rt} e^k = C_o e^{rt}

For this case C_o = 100 mg and r = -0.16

So then our model would be given by:

C(t) = 100 e^{-0.16 t}

Where t represent the number of hours

b) C(5) = 100 e^{-0.16*5}= 44.9329

Step-by-step explanation:

Part a

For this case we can assume the proportional model given by:

\frac{dC}{dt} = rC

And for this case we can rewrite the model like this:

\frac{dC}{C} = r dt

If we integrate both sides we got:

ln C = rt + k

If we use exponentials for both sides we got:

C = e^{rt} e^k = C_o e^{rt}

For this case C_o = 100 mg and r = -0.16

So then our model would be given by:

C(t) = 100 e^{-0.16 t}

Where t represent the number of hours

Part b

For this case we can replace the value t=5 into the model and we got:

C(5) = 100 e^{-0.16*5}= 44.9329

7 0
3 years ago
lex has 84 quarters and nickels worth a total of $17.80. Which equation can be used to find q, the number of quarters Alex has?
emmasim [6.3K]
There are 68 quarters and 16 nickels
3 0
3 years ago
Read 2 more answers
Use spherical coordinates. evaluate (9 − x2 − y2) dv, where h is the solid hemisphere x2 + y2 + z2 ≤ 4, z ≥ 0.
avanturin [10]
In spherical coordinates, we have

\begin{cases}x=\rho\cos\theta\sin\varphi\\y=\rho\sin\theta\sin\varphi\\z=\rho\cos\varphi\end{cases}

which gives volume element

\mathrm dV=\mathrm dx\,\mathrm dy\,\mathrm dz=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\varphi\,\mathrm d\theta

and so the triple integral is given by

\displaystyle\iiint_H(9-x^2-y^2)\,\mathrm dV
=\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{\varphi=0}^{\varphi=\pi/2}\int_{\rho=0}^{\rho=2}(9-\rho^2\sin^2\varphi)\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\varphi\,\mathrm d\theta
=\displaystyle2\pi\int_{\varphi=0}^{\varphi=\pi/2}\int_{\rho=0}^{\rho=2}(9\rho^2\sin\varphi-\rho^4\sin^3\varphi)\,\mathrm d\rho\,\mathrm d\varphi
=\dfrac{592\pi}{15}
4 0
3 years ago
Which of the scatter plots below shows the most accurate line of best fit?
Marina86 [1]
I think its letter b
3 0
2 years ago
I need help one all of these questions please help please it due today please​
GrogVix [38]

Answer:

jsut do it by your self

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • If x is the probability of an event happening, then which of the following represents x?
    8·1 answer
  • the discriminant in an equation derived directly from the quadratic formula is positive the variable value represented by the qu
    11·1 answer
  • Determine whether each table represents a linear, quadratic, exponential function.
    7·1 answer
  • What is the answer to this math problem 9/11 = /22
    6·1 answer
  • 2×10 to the six power times 0.00009
    15·1 answer
  • there are 3 blue balls, 5 red balls, and 2 white balls in a bag of balls. If a person selects two of the balls, what is the prob
    13·1 answer
  • Does the graph represent a function?<br> Yes or No
    13·2 answers
  • Please help worth 25 points
    10·2 answers
  • Graph the function in the image.
    13·1 answer
  • Write a numerical expression to represent the phrase.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!