answer.
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
mina [271]
1 year ago
12

There are many square prisms with volume 125 in. Let w represent the side length of the square base and h represent the height i

n
inches. Then the formula for the volume V, in cubic inches of these prisms is V = w2h and the equation for the surface area S, in
square inches, is S = 2w2 + 4wh.
Mathematics
1 answer:
iogann1982 [59]1 year ago
5 0

Answer:

5in by 5in by 5in

Step-by-step explanation:

We are not told wat to find but we can as well find the dimension of the prism that will minimize its surface area.

Given

Volume = 125in³

Formula

V = w²h ..... 1

S = 2w²+4wh ..... 2

w is the side length of the square base

h is the height of the prism

125 = w²h

h = 125/w² ..... 3

Substitute eqn 3 into 2 as shown

S = 2w²+4wh

S = 2w²+4w(125/w²)

S = 2w²+500/w

To minimize the surface area, dS/dw = 0

dS/dw =4w-500/w²

0= 4w-500/w²

Multiply through by w²

0 = 4w³-500

-4w³ = -500

w³ = 500/4

w³ =125

w = cuberoot(125)

w = 5in

Get the height

125 =w²h

125 = 25h

h = 125/25

h = 5in

Hence the dimension of the prism is 5in by 5in by 5in

You might be interested in
The half life of a certain tranquilizer in the bloodstream is 37 hours. How long will it take for the drug to decay to 86% of th
nata0808 [166]

Answer:

  8.1 hours

Step-by-step explanation:

A model of the fraction remaining can be ...

  f = (1/2)^(t/37) . . . . t in hours

So, for the fraction remaining being 86%, we can solve for t using ...

  0.86 = 0.5^(t/37)

  log(0.86) = (t/37)log(0.5)

  t = 37·log(0.86)/log(0.5) ≈ 8.0509 ≈ 8.1 . . . hours

It takes about 8.1 hours to decay to 86% of the original concentration.

5 0
1 year ago
Statements and reasonings 2(4x+2)=20
Katarina [22]

distribute-   8x+4=20

subtract-    8x=20

divide-      20/8=x

answer-   x=2.5


6 0
2 years ago
Basing the Results on Probability
kodGreya [7K]
Basing the results on Probability is calculation. The correct option among all the options that are given in the question is the third option or option "c". Probability is basically calculating the chance of an event happening based on an experiment that is performed. I hope the answer comes to your help.
5 0
1 year ago
Read 2 more answers
The lengths of the sides of a rectangular window have the ratio 1.2 to 1. The area of the window is 1920 square inches. What are
PilotLPTM [1.2K]
The answer is 40 by 48 inches

40 * 48 = 1920
5 0
2 years ago
What is the midpoint of the segment shown below?<br> (-12,-3) (3,-8)
shepuryov [24]

Answer:

D

Step-by-step explanation:

In order to find the midpoint of a line segment on a graph, you must add both "x" coordinates, then divide by 2.

Then, add both "y" coordinates, and divide by 2.

5 0
1 year ago
Other questions:
  • A plane cuts a pyramid as shown in the diagram. What is the shape of the cross section?
    5·2 answers
  • Name the corresponding part if RST WXY.<br><br> ST =<br><br> A) WY<br> B) WX<br> C) XY
    15·2 answers
  • Of the following people in the concentration camp , who behaves kindly to wiesel and his father
    12·1 answer
  • Three pounds of squid can be purchased at the market for $18. Determine the equation and represent the function that defines the
    9·1 answer
  • Which equation could be used to find the length of the hypotenuse ?
    10·2 answers
  • Write the following as algebraic expressions:
    10·1 answer
  • The positions of two divers from the water's surface after a dive are shown: Justine: −10 feet Mina: −13 feet Which inequality e
    14·2 answers
  • Which expression is a sum of cubes?
    6·2 answers
  • If one row in an echelon form of an augmented matrix is left bracket Start 1 By 5 Matrix 1st Row 1st Column 0 2nd Column 0 3rd C
    10·1 answer
  • A certain type of plywood consists of six layers. The thickness of the layers are independent and normally distributed with mean
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!