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
NISA [10]
3 years ago
10

A pyramid-shaped vat has square cross-section and stands on its tip. The dimensions at the top are 2 m × 2 m, and the depth is 5

m. If water is flowing into the vat at 3 m3 /min, how fast is the water level rising when the depth of water (at the deepest point) is 4 m? Note: the volume of any "conical" shape (including pyramids) is (1/3)(height)(area of base).
Mathematics
1 answer:
Strike441 [17]3 years ago
8 0

Answer:

the water level increases at a rate of 1.718 m/min when the depth is 4 m

Step-by-step explanation:

the volume of the pyramid is

V = (1/3)(height)(area of base) = 1/3 H*L²

For the diagonal in the pyramid

tg Ф = Side Length/ Height = L / H = x / h

where h= depth of water , x= side of the corresponding cross section

therefore x= L *h/H

the volume of the water is

v= 1/3 h*x² = 1/3 (L/H)² h³

in terms of time

v = Q*t

then

Q*t = 1/3 (L/H)² h³

h³ = 3*(H/L)² *Q *t

h = ∛(3*(H/L)² *Q *t) = ∛(3*(H/L)² *Q) *∛t = k* ∛t , where k=∛(3*(H/L)² *Q)

h = k* ∛t

then the rate of increase in depth is dh/dt

dh/dt = 1/3*k* t^(-2/3)

since

t = (h/k)³

dh/dt = 1/3*k* t^(-2/3) = 1/3*k* (h/k)³ ^(-2/3)  = 1/3*k* (h/k)^(-2) = 1/3 k³ / h²

=  1/3 (3*(H/L)²*Q) / h²  = (H/L)²*Q /h²

dh/dt= [H/(h*L)]²*Q

replacing values, when h=4m

dh/dt= [H/(h*L)]²*Q  = [5m/(4m*2m)]² * (3m³/min)= 1.718 m/min

You might be interested in
Kat is painting the edge of a triangular stage prop with reflective orange paint. The lengths of the edges of the triangle are (
vfiekz [6]
We are given with three lengths of a triangle expressed in terms and variables: (3x – 4) feet, (x^2 – 1) feet,  and (2x^2 – 15) feet. The perimeter of the triangle is equal to the sum of the three sides of the triangle. In this case, the sum is 3x^2 + 3x -20. When x is equal to 4, we substitute  <span>3*16 + 3*4 -20 equal to 40 feet.</span>
4 0
3 years ago
What's slope Line<br> pass through( 14, 4)( 21, 6
Svet_ta [14]
What's slope Line
pass through( 14, 4)( 21, 6 Answer :m=2/7
5 0
3 years ago
HELP NOW I NEED IT AND IS DUE TODAY
Mnenie [13.5K]
D and E because they are both colder than -10
3 0
2 years ago
7 x 2/3 in simplest form
kozerog [31]

Answer:

4.67

Step-by-step explanation:

calculator says so

8 0
3 years ago
Read 2 more answers
A soda bottling company’s manufacturing process is calibrated so that 99% of bottles are filled to within specifications, while
bija089 [108]

Answer:

The probability that the assembly line will be shut down is 0.00617.

Step-by-step explanation:

We are given that a soda bottling company’s manufacturing process is calibrated so that 99% of bottles are filled to within specifications, while 1% is not within specification.

Every hour, 12 random bottles are taken from the assembly line and tested. If 2 or more bottles in the sample are not within specification, the assembly line is shut down for recalibration.

Let X = <u><em>Number of bottles in the sample that are not within specification</em></u>.

The above situation can be represented through binomial distribution;

P(X=r)=\binom{n}{r} \times p^{r}\times (1-p)^{n-r};x=0,1,2,3,.....

where, n = number of trials (samples) taken = 12 bottles

             x = number of success  = 2 or more bottles

            p = probabilitiy of success which in our question is probability that  

                 bottles are not within specification, i.e. p = 0.01

So, X ~ Binom (n = 12, p = 0.01)

Now, the probability that the assembly line will be shut down is given by = P(X \geq 2)

  P(X \geq 2) = 1 - P(X = 0) - P(X = 1)

                 = 1-\binom{12}{0} \times 0.01^{0}\times (1-0.01)^{12-0}-\binom{12}{1} \times 0.01^{1}\times (1-0.01)^{12-1}

                 = 1-(1 \times 1\times 0.99^{12})-(12 \times 0.01^{1}\times 0.99^{11})

                 = <u>0.00617</u>

8 0
3 years ago
Other questions:
  • I have a set of numbers 125, 200, 150, 75, 275, &amp; 300 what is the most reasonable interval answer choices 5,10,25 &amp; 100
    5·1 answer
  • Claudia's skis are 150 centimeters long. how many millimeters is this?
    7·2 answers
  • What’s the slope of y=-7x+5
    6·1 answer
  • What is 15% of "x"<br><br> PLEASE HELP
    12·1 answer
  • 7-3 and 7-4 pls.<br> Thank you so much.
    9·1 answer
  • I need help on number 15
    9·1 answer
  • 24 divided by 111 in a decimal number
    13·1 answer
  • Write context for 0.60x = 450
    11·1 answer
  • Can someone PLEASE answer 5 and 6 for me?this assignment is due in a few minutes
    13·1 answer
  • Give the domain and range of the relation.
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!