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Romashka [77]
3 years ago
6

The picture below shows a box sliding down a ramp:

Mathematics
1 answer:
Gennadij [26K]3 years ago
4 0

Answer:

AC=15.1\ ft

Step-by-step explanation:

we know that

In the right triangle ABC

The function sine of angle 68 degrees is equal to divide the opposite side SB by the hypotenuse AC

so

sin(68\°)=\frac{AB}{AC}

substitute the values and solve for AC

sin(68\°)=\frac{14}{AC}

AC=\frac{14}{sin(68\°)}

AC=15.1\ ft

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A piece of wire of length L will be cut into two pieces, one piece to form a square and the other piece to form an equilateral t
inn [45]

Answer:

  (a)  square: L; triangle: 0.

  (b)  square: L·(-16+12√3)/11; triangle: L·(27-12√3)/11

Step-by-step explanation:

<u>Strategy</u>: First we will write each area in terms of its perimeter. Then we will find the total area in terms of the amount devoted to the square. Differentiating will give a way to find the minimum total area.

__

In terms of its perimeter p, the area of a square is ...

  A_square = p^2/16

In terms of its perimeter p, the area of an equilateral triangle is ...

  A_triangle = p^2/(12√3)

Then the total area of the two figures whose total perimeter is L with "x" devoted to the square is ...

  A_total = x^2/16 + (L-x)^2/(12√3)

__

(a) We know when polygons are regular, the one with the most area for the least perimeter is the one with the most sides. Hence, the total area is maximized when all of the wire is devoted to the square.

__

(b) The derivative of A_total with respect to x is ...

  dA/dx = x/8 -(L-x)/(6√3)

This will be zero when ...

  x/8 = (L-x)/(6√3)

  x(6√3) = 8L -8x

  x(8 +6√3) = 8L

  x = L·8/(6√3 +8) = 8L(6√3 -8)/(64-108)

  x = L·(12√3 -16)/11

The total area is minimized when L·(12√3 -16)/11 is devoted to the square, and the balance is devoted to the triangle.

5 0
3 years ago
A plane leaves at 11:22 AM and arrives at 3:13 PM how long was the flight
Fantom [35]

Answer:

3 hours and 51 minutes

Step-by-step explanation:

Hope this helps!!

7 0
3 years ago
Answer this please due in a hour
horrorfan [7]

Answer: 1. b=-3/2 or -1 1/2

2. B=17/3 or 5 2/3

3. K=-14

Step-by-step explanation:

3 0
3 years ago
The local park has 4 bike racks. Each bike rack can hold 15 bikes. There are 16 bikes in the bike racks. What expression shows t
Step2247 [10]
44 that's a tricky question at first i thought it was -1 lol
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3 years ago
Uche pumps gasoline at a rate of 18 L/min <br> what is uche pumping rate in ML/sec?
soldi70 [24.7K]
18L = 18,000 ML
18,000 (ML) ÷ 60 (seconds)
18,000 ÷ 60 = 300ML/sec
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3 years ago
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