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
lana [24]
3 years ago
10

An inverted pyramid is being filled with water at a constant rate of 25 cubic centimeters per second. The pyramid, at the top, h

as the shape of a square with sides of length 4 cm, and the height is 12 cm. Find the rate at which the water level is rising when the water level is 4 cm.
Mathematics
1 answer:
UNO [17]3 years ago
5 0

Answer:

\frac{225}{16} cm/s

Step-by-step explanation:

We are given that

\frac{dV}{dt}=25cm^3/s

Side of base=4 cm

l=w=4 cm

Height,h=12 cm

We have to find the rate at which the water level rising when the water level is 4 cm.

Volume of pyramid=\frac{1}{3}lwh=\frac{1}{3}l^2h

\frac{l}{h}=\frac{4}{12}=\frac{1}{3}

l=\frac{1}{3}h

Substitute the value

V=\frac{1}{27}h^3

Differentiate w.r.t t

\frac{dV}{dt}=\frac{3}{27}h^2\frac{dh}{dt}

Substitute the values

25=\frac{1}{9}(4^2)\frac{dh}{dt}

\frac{dh}{dt}=\frac{25\times 9}{16}=\frac{225}{16} cm/s

You might be interested in
Please view the attachment.
quester [9]
-1 * (-4) = 4; 3 * (-4) = -12; 6 * (-4) = -24; -3 * (-4) = 12
7 0
3 years ago
Problemas de razonamiento división de números decimales. Ayer Susana se fue de viaje a visitar a unos familiares. Recorrió 135,7
schepotkina [342]

Usando las relaciones entre velocidad, distancia y tiempo, se encuentra que ella condujo a una velocidad media de 90,5 km/h.

--------------------------

La <u>velocidad </u><u>es la distancia dividida por el tiempo</u>, por lo que:

v = \frac{d}{t}

  • Total de 135,75 km, o sea, d = 135,75
  • Llego en 1,5 horas, o sea, t = 1,5

La velocidad es:

v = \frac{d}{t} = \frac{135,75}{1,5}

División de decimales, o sea, seguimos multiplicando los números por 10 hasta que ninguno sea decimal:

v = \frac{135,75}{1,5} = \frac{1357,5}{15} = \frac{13575}{150} = 90,5

Ella condujo a una velocidad media de 90,5 km/h.

Un problema similar es dado en brainly.com/question/24558377

4 0
1 year ago
The table represents the function (x) = 2x+1<br> Which value goes in the empty cell?
frozen [14]

Answer:

8 maybe

Step-by-step explanation:

My guess but if it is not Sorry

7 0
3 years ago
Find all the zeros of the equation. -3x^4+27x^2+1200=0 PLEASE HELP and show work
asambeis [7]

Answer: x=−5 or x=5


Step-by-step explanation:

−3x4+27x2+1200=0

Step 1: Factor left side of equation.

−3(x2+16)(x+5)(x−5)=0

Step 2: Set factors equal to 0.

x2+16=0 or x+5=0 or x−5=0

x=−5 or x=5


8 0
3 years ago
Newborn babies: A study conducted by the Center for Population Economics at the University of Chicago studied the birth weights
Fed [463]

Answer:

a) 615

b) 715

c) 344

Step-by-step explanation:

According to the Question,

  • Given that,  A study conducted by the Center for Population Economics at the University of Chicago studied the birth weights of 732 babies born in New York. The mean weight was 3311 grams with a standard deviation of 860 grams

  • Since the distribution is approximately bell-shaped, we can use the normal distribution and calculate the Z scores for each scenario.

Z = (x - mean)/standard deviation

Now,

For x = 4171,  Z = (4171 - 3311)/860 = 1  

  • P(Z < 1) using Z table for areas for the standard normal distribution, you will get 0.8413.

Next, multiply that by the sample size of 732.

  • Therefore 732(0.8413) = 615.8316, so approximately 615 will weigh less than 4171  

 

  • For part b, use the same method except x is now 1591.    

Z = (1581 - 3311)/860 = -2    

  • P(Z > -2) , using the Z table is 1 - 0.0228 = 0.9772 . Now 732(0.9772) = 715.3104, so approximately 715 will weigh more than 1591.

 

  • For part c, we now need to get two Z scores, one for 3311 and another for 5031.

Z1 = (3311 - 3311)/860 = 0

Z2 = (5031 - 3311)/860= 2  

P(0 ≤ Z ≤ 2) = 0.9772 - 0.5000 = 0.4772

  approximately 47% fall between 0 and 1 standard deviation, so take 0.47 times 732 ⇒ 732×0.47 = 344.

5 0
2 years ago
Other questions:
  • What is the product
    5·1 answer
  • NEED HELP ASAP | 25 POINTS!!!!
    7·1 answer
  • How do you write 1.25 into a fraction
    15·2 answers
  • An lpn earned a gross pay of 650.04 last week. if 21 1/2% of her gross paycheck is taken out in taxes, what is her bring home pa
    9·2 answers
  • Solve each if the given equalities<br>2x + 5&lt;-3​
    13·1 answer
  • Find the probability of having 2,3, or 4 successes in five trials of a binomial experiment in which the probability of success i
    8·1 answer
  • I WILL GIVE BRAINLIEST AND POINTS
    5·1 answer
  • Help me solve this problem please
    6·1 answer
  • The volume of a cube is calculated by multiplying the length, width, and height. What is the volume of this cube?
    6·1 answer
  • Surface area of a cube length: 10ft width: 7.5ft height: 12ft
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!