9/10( -2/3) ( symplify )

A heavy rope, 50 ft long, weighs 0.6 lb/ft and hangs over the edge of a building 120 ft high. Approximate the required work by a

Anastasy [175]

Answer:

Exercise (a)

The work done in pulling the rope to the top of the building is 750 lb·ft

Exercise (b)

The work done in pulling half the rope to the top of the building is 562.5 lb·ft

Step-by-step explanation:

Exercise (a)

The given parameters of the rope are;

The length of the rope = 50 ft.

The weight of the rope = 0.6 lb/ft.

The height of the building = 120 ft.

We have;

The work done in pulling a piece of the upper portion, ΔW₁ is given as follows;

ΔW₁ = 0.6Δx·x

The work done for the second half, ΔW₂, is given as follows;

ΔW₂ = 0.6Δx·x + 25×0.6 × 25 = 0.6Δx·x + 375

The total work done, W = W₁ + W₂ = 0.6Δx·x + 0.6Δx·x + 375

∴ We have;

W = $2 \times \int\limits^{25}_0 {0.6 \cdot x} \, dx + 375= 2 \times \left[0.6 \cdot \dfrac{x^2}{2} \right]^{25}_0 + 375 = 750$

The work done in pulling the rope to the top of the building, W = 750 lb·ft

Exercise (b)

The work done in pulling half the rope is given by W₂ as follows;

$W_2 = \int\limits^{25}_0 {0.6 \cdot x} \, dx + 375= \left[0.6 \cdot \dfrac{x^2}{2} \right]^{25}_0 + 375 = 562.5$

The work done in pulling half the rope, W₂ = 562.5 lb·ft

6 0

2 years ago

Round the number 76.4491 to 1 decimal place

solniwko [45]

Answer:

Step-by-step explanation:

76.4

4 0

3 years ago

i need help with this question aka all the little questions in it. Will give brainliest!! Worth 10 pts but EXTRA if needed as pa

polet [3.4K]

A: x= 2.5
b: y= 12.9
c: z= 12
d: w= 2.75
e: t= 4
(Lemme know if it’s wrong)

6 0

2 years ago

Read 2 more answers

Please help

user100 [1]

Answer:

Length of garden will be 30 metres.

Step-by-step explanation:

Let the Width of garden be x metres.

then,

Length of garden will be (x+6) metres.

Area = Length × Breadth

720 = x X (c+6)

720 = x²+6x

0 = x²+6x-720

As we can see above equation is a quadratic equation in the form of ax²+bx+C.

so,

$= \frac{ - b ± \sqrt{{b}^{2} - 4ac} }{2a} \\ = \frac{ - 6 ± \sqrt{{6}^{2} - 4 \times 1 \times - 720} }{2} \\ = \frac{ - 6 ± \sqrt{36 + 2880} }{2} \\ = \frac{ - 6 ± \sqrt{2916} }{2} \\ = \frac{ - 6 ± 54}{2}\\= \frac{-6+54}{2} ... \frac{ - 6 - 54}{2} \\ = \frac{48}{2} ... \frac{ - 60}{2} \\ = 24... - 30$

One of the Roots of the Quadratic equation is 24 and other is -30.

And as we know width of any garden cannot be negative so the width of garden will be 24 metres.

As we got the width,

adding 6 to it will give us the Length,

So,

24 metres + 6 = 30 metres.

Length of the garden is 30 metres.

Hope It Helped You ;)

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8 0

3 years ago

The 44 members of the glee club are trying to raise at least $6,000 so they can compete in the state championship. They already

Anna [14]

Answer:

x=44x(6,000)x1,210

Step-by-step explanation:

7 0

2 years ago