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Klio2033 [76]
3 years ago
10

Solve the following 16,17,18,19,20.​

Mathematics
1 answer:
Shtirlitz [24]3 years ago
6 0

Answer:

show your work

Step-by-step explanation:

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Convert 0.5 liters to milliliters.​
Kipish [7]

Answer:

500 millilitres

Step-by-step explanation:

I hope it will help you

7 0
3 years ago
Read 2 more answers
Find the dimensions of the rectangle with largest area that can be inscribed in an equilateral triangle with sides of 1 unit, if
prohojiy [21]
<span>Maximum area = sqrt(3)/8 Let's first express the width of the triangle as a function of it's height. If you draw an equilateral triangle, then a rectangle using one of the triangles edges as the base, you'll see that there's 4 regions created. They are the rectangle, a smaller equilateral triangle above the rectangle, and 2 right triangles with one leg being the height of the rectangle and the other 2 angles being 30 and 60 degrees. Let's call the short leg of that triangle b. And that makes the width of the rectangle equal to 1 minus twice b. So we have w = 1 - 2b b = h/sqrt(3) So w = 1 - 2*h/sqrt(3) The area of the rectangle is A = hw A = h(1 - 2*h/sqrt(3)) A = h*1 - h*2*h/sqrt(3) A = h - 2h^2/sqrt(3) We now have a quadratic equation where A = -2/sqrt(3), b = 1, and c=0. We can solve the problem by using a bit of calculus and calculating the first derivative, then solving for 0. But since this is a simple quadratic, we could also take advantage that a parabola is symmetrical and that the maximum value will be the midpoint between it's roots. So let's use the quadratic formula and solve it that way. The 2 roots are 0, and 1.5/sqrt(3). The midpoint is (0 + 1.5/sqrt(3))/2 = 1.5/sqrt(3) / 2 = 0.75/sqrt(3) So the desired height is 0.75/sqrt(3). Now let's calculate the width: w = 1 - 2*h/sqrt(3) w = 1 - 2* 0.75/sqrt(3) /sqrt(3) w = 1 - 2* 0.75/3 w = 1 - 1.5/3 w = 1 - 0.5 w = 0.5 The area is A = hw A = 0.75/sqrt(3) * 0.5 A = 0.375/sqrt(3) Now as I said earlier, we could use the first derivative. Let's do that as well and see what happens. A = h - 2h^2/sqrt(3) A' = 1h^0 - 4h/sqrt(3) A' = 1 - 4h/sqrt(3) Now solve for 0. A' = 1 - 4h/sqrt(3) 0 = 1 - 4h/sqrt(3) 4h/sqrt(3) = 1 4h = sqrt(3) h = sqrt(3)/4 w = 1 - 2*(sqrt(3)/4)/sqrt(3) w = 1 - 2/4 w = 1 -1/2 w = 1/2 A = wh A = 1/2 * sqrt(3)/4 A = sqrt(3)/8 And the other method got us 0.375/sqrt(3). Are they the same? Let's see. 0.375/sqrt(3) Multiply top and bottom by sqrt(3) 0.375*sqrt(3)/3 Multiply top and bottom by 8 3*sqrt(3)/24 Divide top and bottom by 3 sqrt(3)/8 Yep, they're the same. And since sqrt(3)/8 looks so much nicer than 0.375/sqrt(3), let's use that as the answer.</span>
7 0
3 years ago
Read 2 more answers
Julio bought 4 pencils and 3 erasers for $0.37 and David paid $0.33 for 3 pencils and 4 erasers. What is the cost of one pencil?
nirvana33 [79]

Answer:

Each pencil costs $0.07 and each eraser costs $0.03

Step-by-step explanation:

System of linear equations

It refers to the study of systems when n variables are related in m linear equations, each one is not independent from the others. Solving such systems can be done following very diverse approaches.  

Let p=the price of each pencil while e is the price each eraser

Julio bought 4 pencils and 3 erasers, spending

4p+3e=0.37

David bought 3 pencils and 4 erasers, spending

3p+4e=0.33

The system of equations is written in the form

\left\{\begin{matrix}4p+3e=0.37\\ 3p+4e=0.33\end{matrix}\right

We'll solve it by reduction. Multiplying the first equation by -3 and the second by 4:

\left\{\begin{matrix}-12p-9e=-1.11\\ 12p+16e=1.32\end{matrix}\right.

Adding both equations:

7e=0.21  

e=0.03

Multiplying the first one by -4 and the second by 3

\left\{\begin{matrix}-16p-12e=-1.48\\ 9p+12e=0.99\end{matrix}\right.\end{matrix}\right.

Adding both equations:

-7p=-0.49

p=0.07  

Solution: Each pencil costs $0.07 and each eraser costs $0.03

7 0
3 years ago
At 6:00 AM the temperature was 2 degrees Celsius. At 11:00 AMthe temperature was -11 degrees Celsius. By how many degrees Celsiu
bonufazy [111]

Answer:

-9

Step-by-step explanation:

Its dropping down from 2 to 0 so that is negative then the -11 so it would be -9.

6 0
3 years ago
Is this correct? Look at pic attached
Georgia [21]

Answer:

Perfect!

Step-by-step explanation:

Complementary= 90 degrees

Supplementary= 180 degrees

Looks like you got both of those. Good job!

<1 + <2 = 90

<1 = 55

90-55=35

<2=35

<2+ <3= 180

180-35= 145

<3 = 145 degrees

You did awesome! Amazing job!

3 0
3 years ago
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