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
Pls help me plssss help asap
Anestetic [448]

Answer:

1) 15

2) 18

3) 72

8 0
3 years ago
The scale drawing of a rectangular oty park measures 10.0 cm by 50 cm
satela [25.4K]
The answer is 2... I think idrk 2 second ago was I thinking abt Damon Salvatore bunt GOOD LUCK!!!
6 0
2 years ago
Paula purchase 3 dvd and 7 cds and spent between 90 and 100. Each dvd costs the same amount the price of cd is 10 select all amo
sveticcg [70]

The options aren't given, however, the range of amount spent could be calculated

Answer:

Kindly check explanation

Step-by-step explanation:

Paula purchase 3 dvd and 7 cds and spent between 90 and 100. Each dvd costs the same amount the price of cd is 10 select all amounts that could be the price of the dvd

Given that :

DVD costs the same amount

Number of DVD's = 3

Cost of cds = 10

Number of cds = 7

Total cost of cd's = 10 * 7 = 70

Let the price of DVD = x

Total amount spent = 90 - 100

Lowest price of DVD :

(amount spent - price of cd) / number of dvd

(90 - 70) / 3 = 20 /3 = 6.667

Highest price :

(100 - 70) / 3 = 30 / 3 = 10

Hence the pice of each DVD will range between /

6.6666 and 10.

Hence, prices listed within the range above are possible.

3 0
2 years ago
James reads that 1 out of 6 eggs contains salmonella bacteria. So he never uses more than 5 eggs in cooking. If eggs do or don't
Dmitrij [34]

Answer:

B. binomial with n = 5 and p = 1/6

Step-by-step explanation:

Given that James reads that 1 out of 6 eggs contains salmonella bacteria.

So he never uses more than 5 eggs in cooking.

If eggs do or don't contain salmonella independently of each other, then

probability for any one egg to contain salmonella bacteria is the constant 1/6.

Also there are only two outcomes, either bacteria present or not.

Hence the  number of contaminated eggs when James uses 5 chosen at random has the distribution is Binomial

Here n = no of trials = no of eggs he uses = 5

Probability = 1/6

So option B is right.

3 0
3 years ago
can someone answer these 2 questions asap and thank you its also double the points because it 2 questions ;)
Juli2301 [7.4K]

9:

r\leq15.5 (not the one with the line under it i just couldnt find the one that didnt have the line under it)

for the graph, put 16 on the right side and label the lines right to left 16 15.5 14 14.5 etc. Put an open circle on the 15.5 line. then make an arrow pointing to the left.

10:

80\leqp+64

This is because she needs 80 points OR MORE and (p represents the points) she already has 64. She needs 80 to be less than or equal to the amount of points earned.

The solution is 16\leqp because 80-64=16 and p is needs to be greater than or equal to 16

7 0
2 years ago
Other questions:
  • Emily recorded the test scores of the students in her class in the dot plot below. Which measure of center would be best to use
    5·2 answers
  • Help....it it easy.
    11·2 answers
  • A pair of jeans was in a 15% off sale but, when Bill came to buy them a month later, the sale was over and he had to pay the reg
    8·2 answers
  • A square pyramid has base edge length 10 cm. The slant height of the pyramid is 13 cm. What is the volume of the​ pyramid?
    10·1 answer
  • John has a rectangular-shaped field whose length is 62.5 yards and width is 45.3 yards. The area of the field is ________ square
    14·1 answer
  • A machine uses pieces of tape to seal packages. it cuts the tape into pieces exactly 2.375 inches long. if it uses 4 pieces of t
    7·2 answers
  • Slope= -1/2, y-intercept = 4​
    11·1 answer
  • Mohamed decided to track the number of leaves on the tree in his back yard each year. This year there were 500 leaves. Each year
    6·1 answer
  • PLEASE THIS IS URGENT​
    12·2 answers
  • If you and answer any of these 7-9 that would really help!!<br> (pic below)
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!