The highest point in a particular section of a graph is called

A bucket that weighs 4 lb and a rope of negligible weight are used to draw water from a well that is 60 ft deep. The bucket is f

jonny [76]

Answer:

2580 ft-lb

Step-by-step explanation:

Water leaks out of the bucket at a rate of $\frac{0.15 \mathrm{lb} / \mathrm{s}}{1.5 \mathrm{ft} / \mathrm{s}}=0.1 \mathrm{lb} / \mathrm{ft}$

Work done required to pull the bucket to the top of the well is given by integral

$W=\int_{a}^{b} F(x) dx$

Here, function $F(x)$ is the total weight of the bucket and water $x$ feet above the bottom of the well. That is,

$F(x)=4+(42-0.1 x)$

$=46-0.1x$

$a$ is the initial height and $b$ is the maximum height of well. That is,

$a=0 \text { and } b=60$

Find the work done as,

$W=\int_{a}^{b} F(x) d x$

$=\int_{0}^{60}(46-0.1 x) dx$

$&\left.=46x-0.05 x^{2}\right]_{0}^{60}$

$=(2760-180)-0[$

$=2580 \mathrm{ft}-\mathrm{lb}
$

Hence, the work done required to pull the bucket to the top of the well is $2580 \mathrm{ft}- \mathrm{lb}$

4 0

3 years ago

Can you help me with this.

Ugo [173]

Answer:

1. x = 2

y = 1

2. x = 3 or 6 (Mistake or typo in problem)

3. y = 13

4. x = 7

y = 15

5. x = 4

Step-by-step explanation:

1. 6x - 3 = x + 7, 5x = 10, x = 2

3y + 2 = y + 4, 2y = 2, y = 1

2. There is most likely a typo. Either 8x = 24 and x = 3 or 2x + 10 = 3x + 4 and x = 6

3. 5y -3 = 2y + 36, 3y = 39, y = 13

4. 8y + 11 + 3y + 4 = 180, 11y + 15 = 180, 11y = 165, y = 15

7x = 3y + 4 = 49, x = 7

5. 7x - 10 = 4x + 2, 3x = 12, x = 4

5 0

3 years ago

Read 2 more answers

A certain shade of pink is created by adding 3 cups of red paint to 7 cups of white paint.

vazorg [7]

Answer:

7/3 is constant of proportionality and, 3/7 of a cup of red paint should be added to 1 cup of white paint.

Step-by-step explanation:

Constant of proportionality is the constant value of the ratio of two proportional quantities x and y; usually written y = kx, where k is the factor of proportionality.

To make color pink,

for every 3 cups of red , we need 7 cups of white.

Let 'r' be the cups of red required

let 'w' be the cups of white required

so , as per the question

for 3 r we need = 7 w

r = 7/3 w

so, 7/3 is constant of proportionality and, 3/7 of a cup of red paint should be added to 1 cup of white paint.

You already have the answer! ;)

4 0

3 years ago

What is a tangent line

Mashutka [201]

In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve

8 0

3 years ago

Can someone walk me through these? I need a better understanding. Or maybe just one of them so I can understand and do the rest

Olin [163]

Step-by-step explanation:

I'll do the first one as an example.

"What are the coordinates of the point on the directed line segment from K(-5,-4) to L(5,1) that partitions the segment into a ratio of 3 to 2?"

Let's call the point we're trying to find P. Ratio of 3 to 2 means that the distance from K to P divided by the distance from P to L is 3/2.

KP / PL = 3 / 2

Which also means the horizontal distances and vertical distances between the points have a ratio of 3:2.

KxPx / PxLx = 3 / 2

KyPy / PyLy = 3 / 2

First, let's use the x coordinates:

(x − (-5)) / (5 − x) = 3 / 2

(x + 5) / (5 − x) = 3 / 2

2 (x + 5) = 3 (5 − x)

2x + 10 = 15 − 3x

5x = 5

x = 1

And now with the y coordinates:

(y − (-4)) / (1 − y) = 3 / 2

(y + 4) / (1 − y) = 3 / 2

2 (y + 4) = 3 (1 − y)

2y + 8 = 3 − 3y

5y = -5

y = -1

So the point P is at (1,-1).

4 0

3 years ago