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
vekshin1
3 years ago
9

Zadanie optymalizacyjne z matematyki. Proszę o rozwiązanie i wyjaśnienie

Mathematics
1 answer:
Yakvenalex [24]3 years ago
5 0

Volume of the pyramid:

V=\dfrac{s^2h}3

Perimeter of the cross-section:

40=\sqrt2\,s+2\sqrt{\dfrac{s^2}2+h^2}=\sqrt2\left(s+\sqrt{s^2+2h^2}\right)

\implies h=\sqrt{\dfrac{(20\sqrt2-s)^2-s^2}2}=\sqrt{400-20\sqrt2\,s}

Area of the cross-section:

P=\dfrac12(\sqrt2\,s)h=\dfrac{sh}{\sqrt2}

\implies P=\dfrac{s\sqrt{400-20\sqrt2\,s}}{\sqrt2}=s\sqrt{200-10\sqrt2\,s}

First derivative test:

\dfrac{\mathrm dP}{\mathrm ds}=\dfrac{20\sqrt2-3s}{\sqrt{4-\dfrac{\sqrt2}5s}}=0\implies s=\dfrac{20\sqrt2}3

Then the height of the cross-section/pyramid is

h=\sqrt{400-20\sqrt2\,s}=\dfrac{20}{\sqrt3}

The volume of the pyramid that maximizes the cross-sectional area P is

V=\dfrac{\left(\frac{20\sqrt2}3\right)^2\frac{20}{\sqrt3}}3=\dfrac{16000}{27\sqrt3}

You might be interested in
Stealth Bank has deposits of $700 million. It holds reserves of $70 million and has purchased government bonds worth $215 millio
zhannawk [14.2K]

Answer:

$75 million

Step-by-step explanation:

Given that:

Reserve value = $70 million

Purchased government bond = 215 million

Market value of loan = $490 million

Net worth :

Assets - liability

Assets = (Market value of loan + purchased government bond + reserve value)

(490 million + 215 million + 70 million)

275 million + 70 million

= $775 million

Liability = Deposits = $700 million

Net worth = ($775 - $700) million

Net worth = $75 million

4 0
2 years ago
The fastest time for completing an obstacle course is 218 seconds. Artest completed the first half of the course in 95 seconds.
Anon25 [30]

Answer:

219 Seconds ; He was 1 second faster

Step-by-step explanation:

Two halfs equal one whole, meaning both of the times added will equal the full time he took:

95+124=219

219 Seconds

He was 1 second faster because:

219-218=1

8 0
3 years ago
What is the multiplicative property of 0
shtirl [24]

Answer:

0

Step-by-step explanation:

What ever times 0 always is 0, take 100 × 0 it will make it Into 0. If you need help use a calculator, hope this helps

4 0
3 years ago
Natalie paid $20.7 for 3 small pizzas and a salad which was $3.
Svet_ta [14]

Answer: x=5.9

Equation: 20.7= 3x+3

Step-by-step explanation:

20.7=3x+3

-3 -3

——————

17.7= 3x

————-

3

5.9= X

Was that ok? :) ur a smart kid so I’m sure you’ll figure this out but if u do have questions just put it in the comments :)

5 0
3 years ago
What is the slope of the line represented by the equation y=-1/2 x+ 1/4
sukhopar [10]
The correct answer is D
3 0
3 years ago
Other questions:
  • Heather is riding her bicycle. she takes 3 hours to ride 37.5 kilometers. what is her speed?
    14·1 answer
  • Sydney invested $440 in an account paying an interest rate of 5.6% compounded daily. Assuming no deposits or withdrawals are mad
    11·1 answer
  • Help Me! Fake Answers will be reported.<br><br> How many triangles are there in this picture?
    12·1 answer
  • Just look at the picture
    15·1 answer
  • PLEASE EXPLAIN: ASAP <br> Express your answer in scientific notation<br> 2.8*10^-3-0.00065=
    7·1 answer
  • A cylindrical water tower has a volume of
    6·2 answers
  • Can anyone help me with these 3 problom there due today pls :D
    9·2 answers
  • 40% Of Francine's t shirts are red. If she has 20 shirts. How many are red
    6·1 answer
  • PLEASE I NEED HELP QUICKLY
    13·2 answers
  • Two of the angles in a triangle measure 57º and 25°. What must be the measure of the
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!