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2 years ago

How much money does the dessert store make from selling three muffins and four cakes?

Mathematics

1 answer:

Lapatulllka [165]2 years ago

8 0

Answer:

If everything is a dollar then the store will make $7 from selling all of those treats.

Step-by-step explanation:

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Zadanie optymalizacyjne z matematyki. Proszę o rozwiązanie i wyjaśnienie

Yakvenalex [24]

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

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

5 0

2 years ago

2x < 2<br> What is the value of x?

TEA [102]

X can be a value of any number less than 0.9.
Solved, this is x<1 as an inequality.

6 0

2 years ago

Which two sentences indicate a first-person point of view? 1 Shelley, our cat, always gets excited when Mrs. Peters visits us. 2

irga5000 [103]

The two sentences are 1 and 5.

3 0

3 years ago

PLEASE HELP ASAP! Will give BRAINLIEST! Please answer correctly!<br> No guessing!

jeka94

Answer:

A) 9

Step-by-step explanation:

f(2) is basically asking what the y-coordinate is at x = 2

If you trace x = 2, you see it intersects f(x) at (2, 9).

4 0

2 years ago

Font

balu736 [363]

Answer:

A. 4.2 times

Step-by-step explanation:

Chlorine level of the pool as adjusted by Paula = 6.3 parts per million

Ideal Chlorine level as suggested by the magazine = 1.5 parts per million.

Thus, the number of times the ideal level of Chlorine that the current level is = current level ÷ ideal level

= $\frac{6.3}{1.5} = 4.2$

The current Chlorine level is 4.2 times the ideal Chlorine level.

7 0

3 years ago