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Lana71 [14]
3 years ago
11

A steel pipe is being carried down a hallway 9 ft wide. At the end of the hall there is a right-angled turn into a narrower hall

way 6 ft wide. What is the length of the longest pipe that can be carried horizontally around the corner

Mathematics
1 answer:
Rudiy273 years ago
8 0

Answer:

21.62m

Step-by-step explanation:

first draw the the pipe

second you need know wich is the angle between the pipe and the corner

β=Tan^-1(6/9)=33.7

find the components using tow triangles

a=9/cos(33.7)=10.81m

b=6/sen(33.7)=10.81m

finally sum the leghts

L=10.81+10.81=21.62mm

attached procedure

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Twice the sum of two numbers is 24. if one number is 2 times larger than the other, what is the smaller of the two numbers?
Vikki [24]
2(x+y)=24
2x=y

Use substitution. If y=2x, than we can substitute 2x for it in the other equation, because x and y equal the same things in both equations. 

So using that we get 2(x+2x)=24

SIMPLIFY
2(3x)=24

DISTRIBUTE
6x=24. 

DIVIDE: x=4.

If we substitute x into the original equations we get x=4 and y=8. Those are your two numbers. 

Have a nice day! :)


4 0
2 years ago
3 out of five picks are orange . If 12 picks are orange , how many picks are there in all?
tekilochka [14]

20 picks in total .

8 0
3 years ago
A 10-foot ladder is leaning against a wall. The base of the ladder is 2 feet from the base of the building. How far up the build
Svetlanka [38]
We can see on this graph that the triangle has legs of x and 6 with a hypotenuse of 10 and we can use Pythagoreans theorem to find the unknown side.
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x^2+6^2=10^2 Plugin a=x, b=6, and c=10. Now let us solve for x 

x^2+36=100 Square each individual term 

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sqrt(2)=sqrt(64) Take the square root of both sides 

x = 8 Simplify the square root 

So our answer is x = 8 
The ladder touches the 8 feet mark on the wall.
5 0
3 years ago
What is the value of n?<br> <img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B2n-7%7D%7B3%7D%20%3D15" id="TexFormula1" title=" \fra
kirill [66]
\frac{2n-7}{3} = 15

2n - 7 × 1 = 15 × 3

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Have a nice days.........
5 0
3 years ago
At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 10 cubic feet per minute. The di
lawyer [7]

Answer:

0.0063 ft / min

Step-by-step explanation:

From the problem statement we have that the variation in volume with respect to time is equal 10, like this:

dV / dt = 10 ft ^ 3 / min

We know that the volume of the cone is given by the equation:

V = (1/3) * Pi * r ^ 2 * h

Now, we are mentioned that the diameter of the base of the cone is approximately three times the altitude, therefore:

2r = 3h, solving for r we have:

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V = (1/3) * Pi * [(3h / 2) ^ 2] * h, solving we have:

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They ask us to calculate the change in height with respect to time, that is dh / dt

Therefore we derive both sides with respect to time, we have to:

dV / dt = (3/4) * Pi [3 * (h ^ 2) dh / dt] = (9/4) * pi * (h ^ 2) * dh / dt

reorganizing for dh / dt, we have:

dh / dt = [4/9 * pi * (h ^ 2)] * dV / dt

Knowing that h is 15 and dV / dt is 10, we replace these values:

dh / dt = [4/9 * 3.14 * (15 ^ 2)] * 10 = 0.0063 ft / min

0.0063 ft / min would be the change in height with respect to time.

4 0
3 years ago
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