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
Brilliant_brown [7]
3 years ago
12

If a tank holds 4500 gallons of water, which drains from the bottom of the tank in 50 minutes, then Toricelli's Law gives the vo

lume V of water remaining in the tank after t minutes as
V = 4500(1 - 1/50t)2 0 < or = t < or = 50
1) Find the rate at which water is draining from the tank after the following amounts of time.
(a) 5 min gal/min
(b) 10 min gal/min
(c) 20 min gal/min
(d) 50 min gal/min
2) At what time is the water flowing out the fastest?
3) At what time is the water flowing out the slowest?
Mathematics
1 answer:
disa [49]3 years ago
4 0

Answer:

The response to this question can be defined as follows:

Step-by-step explanation:

v =4500 (1-\frac{t}{50})^2\\\\\to \frac{dV}{dt}= 9000 (1- \frac{t}{50})(\frac{1}{50})\\\\

          = 180 (\frac{50-t}{50})\\\\= 3.6(50-t)\\\\

For point a:

t=5\\\\V'=3.6\times 45 = 162\\\\ans= - 162\ \frac{gal}{min}\\\\

For point b:

t=10\\\\V'=3.6\times 40 = 144\\\\ans= - 144 \ \frac{gal}{min}\\\\

For point c:

t=20\\\\V'=3.6\times 30 = 108\\\\ans= - 108 \ \frac{gal}{min}\\\\

For point d:

t=50\\\\V'=3.6\times 0 = 0\\\\ans= 0 \ \frac{gal}{min}\\\\

You might be interested in
Find the equation of the line through the point (2, 5) that cuts off the least area from the first quadrant. Give your answer us
Amanda [17]

The equation of the line would be

y = mx+b 

where m is the slope, b is the y intercept. 

<span>The line will form a triangular region in the first quadrant. Its area would be 1/2 base times height. The height is the y intercept and the base is y intercept divided by slope. Therefore,</span>

A = b^2/2m

At point (2,5)

5 = 2m+b

Substitute that in the area

A = b^2/5-b to find the least area, differentiate the area with respect to the height and equate it to 0 

dA/db = 0

<span>find b and use that to find m. Then, you can have the equation of the line.</span>


4 0
3 years ago
Read 2 more answers
Carl has quarters and dimes that is worth at most $15. There are twice as many dimes as quarters. What is the greatest number of
skelet666 [1.2K]

I think it's 30 because 2 times 15 is 30. Hope it helped!

6 0
3 years ago
Read 2 more answers
(SAT Prep) Find the value of x.<br> X<br> 125°<br> 115°
Ymorist [56]
<h3>Answer : 60°</h3>

<h3>Way to do </h3>

#look pic for detailed info

180° - 125° = 55°

180° - 115° = 65°

180° - 55° - 65° = 60°

180° - 60° = 120°

180° - 120° = 60°

3 0
2 years ago
Read 2 more answers
In matrix multiplication, such as AB=C, the columns of B form the rows of C. why is this?
Gnesinka [82]
Let's work with 2-by-2 matrices so we're on the same page. The ideas will work for any appropriate matrices.

From the rule of matrix multiplication, we see:
\left[\begin{array}{cc}a_{11} & a_{12} \\a_{21} & a_{22} \end{array}\right] \left[\begin{array}{cc}b_{11} & b_{12} \\b_{21} & b_{22} \end{array}\right] = \left[\begin{array}{cc} a_{11}b_{11} + a_{12}b_{21} & a_{11}b_{12} + a_{12}b_{22} \\ a_{21}b_{11} + a_{22}b_{21} & a_{21}b_{12} + a_{22} b_{22} \end{array}\right]
As you noted, we see the columns of B contributing to the rows of C. The question is, why would we ever have defined matrix multiplication this way?

Here's a nontraditional way of feeling this connection. We can define matrix multiplication as "adding multiplication tables." A multiplication table is made by starting with a column and a row. For example,
\begin{array}{ccc} {} & 1 & 2 \\ 1 & {} & {} \\ 2 & {} & {} \end{array}
We then fill this table in by multiplying the row and column entries:
\begin{array}{ccc} {} & [1] & [2] \\ 1| &1 & 2 \\ 2| & 2 &4 \end{array}
It's then reasonable to say that given two matrices A and B, we can construct multiplication tables by taking the columns of A and pairing them with the rows of B:
\left[\begin{array}{cc}a_{11} & a_{12} \\a_{21} & a_{22} \end{array}\right] \left[\begin{array}{cc}b_{11} & b_{12} \\b_{21} & b_{22} \end{array}\right]

= \begin{array}{cc} {} & \left[\begin{array}{cc} b_{11} & b_{12}\end{array} \right]\\ \left[\begin{array}{c} a_{11} \\ a_{21} \end{array} \right] \end{array} +\begin{array}{cc} {} & \left[\begin{array}{cc} b_{21} & b_{22}\end{array} \right]\\ \left[\begin{array}{c} a_{12} \\ a_{22} \end{array} \right] \end{array}

= \left[\begin{array}{cc} a_{11} b_{11} & a_{11} b_{12} \\ a_{21} b_{11} & a_{21} b_{12} \end{array} \right] + \left[\begin{array}{cc} a_{12} b_{21} & a_{12} b_{22} \\ a_{22} b_{21} & a_{22} b_{22} \end{array} \right]

Adding these matrices together, we get the exact same expression as the traditional definition. 




5 0
3 years ago
Luis's car used 4/5
antoniya [11.8K]

Answer:

36.25 miles per gallon

Step-by-step explanation:

4/5 = .8

29/.8 = x/1

cross-multiply:

.8x = 29

x = 36.25

7 0
3 years ago
Other questions:
  • SOMEONE PLEASE ANSWER ASAP FOR BRAINLIEST!!!!!
    6·1 answer
  • Multiply 1/3 1/5<br><br>-1/10<br><br>-1/15<br><br>1/15<br><br>1/10​
    12·1 answer
  • Alegebra liner equations.
    14·1 answer
  • What percent of 287.5 is 46
    8·2 answers
  • I need help on #4 ASAP!!!!
    13·1 answer
  • Solve and graph -4&lt;-1-4x&lt;-1
    6·1 answer
  • 6x+1/2xy=3 please help im confused
    9·2 answers
  • Suppose the polynomial function below represents the power generated by a wind turbine, where x represents the wind speed in met
    12·2 answers
  • 2, 4, 3, 6, 5, 10, 9, 16, does anyone know the next 3 numbers and the pattern ??????????????
    9·1 answer
  • Order the rational numbers from least to greatest
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!