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Semmy [17]
3 years ago
15

Calculate his speed in miles per hour

Mathematics
1 answer:
BartSMP [9]3 years ago
8 0

Answer:

22

Step-by-step explanation:


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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
If rain is falling at a rate of 1/4 inch per hour, how much rain would you expect after 6 hours?
serg [7]
I think its 1.5 but im not sure 100%

5 0
3 years ago
Read 2 more answers
se vendieron 144 boletos. 2 pesos por adulto y un peso por niño, si se gastaron 207 pesos cuantos boletos de adulto se vendieron
natulia [17]

Answer:

Se vendieron 81 boletos de niños y 63 boletos de adultos.

Step-by-step explanation:

La cantidad de boletos vendidos es igual a:

144 = a + n   (1)

En donde <em>a </em>es por adultos y <em>n</em> por niños

A su vez, el dinero gastado equivale:

207 = 2*a + 1*n   (2)

Resolviendo la ecuación (1) para <em>a:</em>

a = 144 - n   (3)

Introduciendo (3) en la ecuación (2) tenemos:

207 = 2*(144 - n) + n

n = 81

Ahora podemos calcular el numero de boletos de adultos vendidos introduciendo <em>n</em> en la ecuación (3):

a = 144 - n = 144 - 81 = 63

Entonces, se vendieron 81 boletos de niños y 63 boletos de adultos.  

Espero que te sea de utilidad!      

5 0
2 years ago
A and B are partners sharing profit and loss in the ratio of 3:2. A new partner C is admitted and 1/4 share off profit is given.
Gre4nikov [31]

Answer:

Correct option is: 9:6:5

Step-by-step explanation:

I'm not sure but hope it helps.

6 0
3 years ago
If point A is located at (-7,5) and is rotated around 270 clockwise about the origin, then point A' is located at...
jonny [76]

Answer:

B.(-5,-7)

Step-by-step explanation:

According to the rule of rotation if you were to have a 270* clockwise you would first switch the x and y values. Ex: (-7,5) -> (5,-7). next you would make the original y coordinate a negative. (5,-7) -> (-5,-7).

6 0
3 years ago
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