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3 years ago

Explain how to multiply 28 and 36 using the set of steps you learned.

Mathematics

2 answers:

shutvik [7]3 years ago

5 0

Answer:

1008

Step-by-step explanation:

Georgia [21]3 years ago

3 0

Answer:

Sample Response:

Start by multiplying the ones: 6 times 28 is 168. Next, multiply the tens: 30 times 28 is 840. Add the products to get 1,008.

Your welcome!

Step-by-step explanation:

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Simplify the product. 8x^2(4x^2 + 4y^6)

dsp73

Answer:

32x2y6+32x4

Step-by-step explanation:

8 0

3 years ago

A trough is 5 meters long, 2 meters wide, and 3 meters deep. The vertical cross-section of the trough parallel to an end is shap

SSSSS [86.1K]

We need a work of 294210 watts to pump the water over the top. $\blacksquare$

<h3>Work needed to pump all the water over the top</h3>

Since the cross section area of the trough ( $A$ ), in square meters, varies with the height of the water ( $h$ ), in meters, and considering that pumping system extracts water at constant rate, then the work needed to pump all the water ( $W$ ), in joules, is:

$W = \int\limits^{V_{max}}_0 {p} \, dV$ (1)

Where:

$p$ - Pressure of the infinitesimal volume, in pascals.
$V$ - Volume, in cubic meters.
$V_{max}$ - Maximum volume allowed by the trough, in cubic meters.

The infinitesimal volume is equivalent to the following expression:

$dV = A\, dh$ (2)

Since the area is directly proportional to the height of the water, we have the following expression:

$A = \frac{A_{max}}{H_{max}}\cdot h$ (3)

Where:

$A_{max}$ - Area of the base of the trough, in square meters.
$H_{max}$ - Maximum height of the water, in meters.

In addition, we know that pressure of the water is entirely hydrostatic:

$p = \rho \cdot g \cdot h$ (4)

Where:

$\rho$ - Density of water, in kilograms per cubic meters.
$g$ - Gravitational acceleration, in meters per square second.

By (2), (3) and (4) in (1):

$W = \frac{\rho\cdot g\cdot W_{max}\cdot L_{max}}{H_{max}} \int\limits^{H_{max}}_{0} {h^{2}} \, dh$ (5)

Where:

$W_{max}$ - Width of the base of the triangle, in meters.
$L_{max}$ - Length of the base of the triangle, in meters.
$H_{max}$ - Maximum height of the triangle, in meters.

The resulting expression is:

$W = \frac{\rho\cdot g\cdot W_{max}\cdot L_{max}\cdot H_{max}^{2}}{3}$ (5b)

If we know that $\rho = 1000\,\frac{kg}{m^{3}}$ , $g = 9.807\,\frac{m}{s^{2}}$ , $W_{max} = 2\,m$ , $L_{max} = 5\,m$ and $H_{max} = 3\,m$ , then the work needed to pump the water is: