Mathematics, 14.04.2020 19:55 sammimoose6490

A horizontal trough is 16 m long, and its end are isosceles trapezoids with an altitude of 4 m, a lower base of 4 m, and an upper base of 6 m. If the water level is decreasing at a rate of 25 cm/min when the water is 3 m deep, at what rate is the water being drawn from the trough?

Answers: 3

Show answers

Answers

Answer from: jackchelly

The rate at which the water level (the depth) is decreasing, increases as

more water is drawn from the trough.

The rate at which water is being drawn from the through is 22 m³/min.

Reasons:

The given parameter are;

Length of the through, L = 16 m

Height of the through = 4 m

Lower base of the trapezoidal cross section, a = 4 m

Upper base of the trapezoidal cross section, b = 6 m

Rate at which the water is decreasing at the depth of 3 m, $\dfrac{dh}{dt}$ = 25 cm/min

Required:

Rate at which water is being drawn from the through

Solution:

Let the length of the upper base at height h = 4 + 2·x

Volume of the through = Trapezoidal cross sectional area × Length

$Area \ of \ trapezoid = \dfrac{a + b}{2} \times h$

$Trapezoidal \ cross \ sectional \ area, \ A = \dfrac{4 + (4 + 2 \cdot x)}{2} \times h$ -

$Volume \ of \ water \ in \ the \ through, \ V = \dfrac{4 + (4 + 2 \cdot x)}{2} \times h \times L$

Therefore;

$V = \dfrac{4 + (4 + 2 \cdot x)}{2} \times h \times 16$

By similar triangles, we have;

$\dfrac{1}{x} = \dfrac{4}{h}$

h = 4·x

Which gives;

$V = \dfrac{4 + (4 + 2 \cdot \dfrac{h}{4} )}{2} \times 4 \cdot \dfrac{h}{4} \times 16 = 64\cdot h + 4 \cdot h^2$

$\dfrac{dV}{dh} = \dfrac{dV}{dt} \times \dfrac{dt}{dh}$

$\dfrac{dV}{dh} =64 + 8 \cdot h$

$\dfrac{dh}{dt}$ = 25 cm/min = 0.25 m/min

$\dfrac{dV}{dt} = \dfrac{ \dfrac{dV}{dh} }{ \dfrac{dt}{dh}} = \dfrac{dV}{dh} \times \dfrac{dh}{dt}$

$\dfrac{dV}{dt} = (64 + 8 \times 3 ) \times (0.25 ) = 22$

The rate at which water is being drawn from the through, $\dfrac{dV}{dt}$ = 22 m³/min.

Learn more here:

link

A horizontal trough is 16 m long, and its end are isosceles trapezoids with an altitude of 4 m, a lo

Answer from: sgslayerkingminecraf

0.28cm/min

Step-by-step explanation:

Given the horizontal trough whose ends are isosceles trapezoid

Volume of the Trough =Base Area X Height

=Area of the Trapezoid X Height of the Trough (H)

The length of the base of the trough is constant but as water leaves the trough, the length of the top of the trough at any height h is 4+2x (See the Diagram)

The Volume of water in the trough at any time

$Volume=\frac{1}{2} (b_{1}+4+2x)h X H$

$Volume=\frac{1}{2} (4+4+2x)h X 16$

=8h(8+2x)

V=64h+16hx

We are not given a value for x, however we can express x in terms of h from Figure 3 using Similar Triangles

x/h=1/4

4x=h

x=h/4

Substituting x=h/4 into the Volume, V

$V=64h+16h(\frac{h}{4})$

$V=64h+4h^2\\\frac{dV}{dt}= 64\frac{dh}{dt}+8h \frac{dh}{dt}$

h=3m,

dV/dt=25cm/min=0.25 m/min

$0.25= (64+8*3) \frac{dh}{dt}\\0.25=88\frac{dh}{dt}\\\frac{dh}{dt}=\frac{0.25}{88}$

=0.002841m/min =0.28cm/min

The rate is the water being drawn from the trough is 0.28cm/min.

Answer from: Quest

make sure you have version 2.50

try looking in the very back of the book : )

step-by-step explanation:

you can download it here

Answer from: Quest

J= r + 9 because since jessica rode 9 more miles than roger, you add 9 miles to rogers mileage.

Another question on Mathematics

Mathematics, 21.06.2019 18:40

If f(x) = x+8 and g(x) = 4x- 3, find (f+g)(x)

Answers: 1

Answer

Mathematics, 21.06.2019 19:30

Find the actual dimensions of the box. the side length are in meters and integers. the surface area of the box is 104 m2 and volume of the box is 60 m3.

Answers: 1

Answer

Mathematics, 21.06.2019 20:00

Afrequency table of grades has five classes (a, b, c, d, f) with frequencies of 3, 13, 14, 5, and 3 respectively. using percentages, what are the relative frequencies of the five classes?

Answers: 3

Answer

Mathematics, 21.06.2019 21:00

List x1, x2, x3, x4 where xi is the midpoint endpoint of the five equal intervals used to estimate the area under the curve of f(x) between x = 0 and x = 10.

Answers: 1

Answer

You know the right answer?

A horizontal trough is 16 m long, and its end are isosceles trapezoids with an altitude of 4 m, a lo...

Questions