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3 years ago

Cone shaped container with a diameter of 7.5 and a hieght of 3.5 to feed his tropical fish

Mathematics

1 answer:

jeka943 years ago

6 0

Volume of a cone = 1/3 πr²h

Volume = 1/3π(7.5÷2)²(3.5) = 51.54 unit³

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The length of a rectangle is 4 cm longer than its width. If the perimeter of the rectangle is 44 cm, find its area.

adell [148]

Length: w+4
Width:w
Perimeter:44
Area: L times w
P=44
44=2(w)+2(w+4)
44=2w+2w+8
44=4w+8
36=4w
w=9
L=w+4
L=9+4
L=13
Area should equal 117 cm squared

5 0

3 years ago

A tank contains 1600 L of pure water. Solution that contains 0.04 kg of sugar per liter enters the tank at the rate 2 L/min, and

goldfiish [28.3K]

Let S(t) denote the amount of sugar in the tank at time t. Sugar flows in at a rate of

(0.04 kg/L) * (2 L/min) = 0.08 kg/min = 8/100 kg/min

and flows out at a rate of

(S(t)/1600 kg/L) * (2 L/min) = S(t)/800 kg/min

Then the net flow rate is governed by the differential equation

$\dfrac{\mathrm dS(t)}{\mathrm dt}=\dfrac8{100}-\dfrac{S(t)}{800}$

Solve for S(t):

$\dfrac{\mathrm dS(t)}{\mathrm dt}+\dfrac{S(t)}{800}=\dfrac8{100}$

$e^{t/800}\dfrac{\mathrm dS(t)}{\mathrm dt}+\dfrac{e^{t/800}}{800}S(t)=\dfrac8{100}e^{t/800}$

The left side is the derivative of a product:

$\dfrac{\mathrm d}{\mathrm dt}\left[e^{t/800}S(t)\right]=\dfrac8{100}e^{t/800}$

Integrate both sides:

$e^{t/800}S(t)=\displaystyle\frac8{100}\int e^{t/800}\,\mathrm dt$

$e^{t/800}S(t)=64e^{t/800}+C$

$S(t)=64+Ce^{-t/800}$

There's no sugar in the water at the start, so (a) S(0) = 0, which gives

$0=64+C\impleis C=-64$

and so (b) the amount of sugar in the tank at time t is

$S(t)=64\left(1-e^{-t/800}\right)$

As $t\to\infty$ , the exponential term vanishes and (c) the tank will eventually contain 64 kg of sugar.

7 0

3 years ago

-3.6,-5.4,-8.1,-12.15 arithmetic or geometric or neither.

Brums [2.3K]

Answer:

Geometric Sequence

Step-by-step explanation:

1. Check the difference.

The difference between the 1st and 2nd term

$( - 5.4) - ( - 3.6) = - 1.8$

The difference between the 2nd and 3rd term

$( - 8.1) - ( - 5.4) = - 2.7$

The difference is not the same. Therefore, it is not an arithmetic sequence.

2. Check the ratio

The ratio between the 1st and 2nd term

$( - 5.4) \div ( - 3.6) = 1.5$

The ratio between the 2nd and 3rd term

$( - 8.1) \div ( - 5.4) = 1.5$

The ratio is the same. Therefore, it is a geometric sequence.

8 0

3 years ago

How do you dilate a figure on the coordinate plane and determine its scale factor?

levacccp [35]

Answer:

All you have to do is scale up the coordinates of the plane by the factor. Multiply the values of each coodinate by the scale factor.

Step-by-step explanation:

3 0

3 years ago

10 less than the product of 8 and 5

Nastasia [14]

The answer is 30.

8 x 5 =40

40 - 10 = 30

3 0

3 years ago

Read 2 more answers