A cube has six sides so you divide 3750 by 6 to find the area of a single face. This would be 625. Area is length times width and since it is a cube you know that both are the same. This gives you an answer of 25.

4 0

3 years ago

Solve for x: −2(x + 3) = −2x − 6 0 3 All real numbers No solution

Alik [6]

Answer:

x ∈ All real numbers

Step-by-step explanation:

When the distributive property is applied to the left side, the parentheses can be eliminated and the equation becomes ...

-2x -6 = -2x -6

This is true for all possible values of x, "all real numbers".

8 0

2 years ago

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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

2 years ago