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3 years ago

An automobile purchased for 22000 is worth 2500 after 5 years what’s the value 3 years after it is purchased

Mathematics

1 answer:

ohaa [14]3 years ago

6 0

(17,000-2,500)/5=14,500/5=$2,900 is the annual depreation.

17,000-2,900*3

17,000-8,700=$8,300 value after 3 years.

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A cylindrical can without a top is made to contain 25 3 cm of liquid. What are the dimensions of the can that will minimize the

Basile [38]

Answer:

Therefore the radius of the can is 1.71 cm and height of the can is 2.72 cm.

Step-by-step explanation:

Given that, the volume of cylindrical can with out top is 25 cm³.

Consider the height of the can be h and radius be r.

The volume of the can is V= $\pi r^2h$

According to the problem,

$\pi r^2 h=25$

$\Rightarrow h=\frac{25}{\pi r^2}$

The surface area of the base of the can is = $\pi r^2$

The metal for the bottom will cost $2.00 per cm²

The metal cost for the base is =$(2.00× $\pi r^2$ )

The lateral surface area of the can is = $2\pi rh$

The metal for the side will cost $1.25 per cm²

The metal cost for the base is =$(1.25× $2\pi rh$ )

$=\$2.5 \pi r h$

Total cost of metal is C= 2.00 $\pi r^2$ + $2.5 \pi r h$

Putting $h=\frac{25}{\pi r^2}$

$\therefore C=2\pi r^2+2.5 \pi r \times \frac{25}{\pi r^2}$

$\Rightarrow C=2\pi r^2+ \frac{62.5}{ r}$

Differentiating with respect to r

$C'=4\pi r- \frac{62.5}{ r^2}$

Again differentiating with respect to r

$C''=4\pi + \frac{125}{ r^3}$

To find the minimize cost, we set C'=0

$4\pi r- \frac{62.5}{ r^2}=0$

$\Rightarrow 4\pi r=\frac{62.5}{ r^2}$

$\Rightarrow r^3=\frac{62.5}{ 4\pi}$

⇒r=1.71

Now,

$\left C''\right|_{x=1.71}=4\pi +\frac{125}{1.71^3}>0$

When r=1.71 cm, the metal cost will be minimum.

Therefore,

$h=\frac{25}{\pi\times 1.71^2}$

⇒h=2.72 cm

Therefore the radius of the can is 1.71 cm and height of the can is 2.72 cm.

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As x decreases y also decreased

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3 years ago

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Answer:

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3 years ago

1. The diameter of a sphere is 21.6 cm. The volume of the sphere is __

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Detailed Answers:

Volume of a Sphere (V) = 4/3 πr^3

1. Diameter (d) = 21.6 cm
Radius (r) = 21.6/2 = 10.8 cm

Therefore,
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= 4/3 * 22/7 * 1259.712
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Volume (V) = 5278.79 cm^3

2. Diameter (d) = 16 cm
Radius (r) = 16/2 = 8 cm

Therefore,
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= 4/3 * 22/7 * (8)^3
= 4/3 * 22/7 * 512
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=> 2145.52

Volume (V) = 2145.52 cm^3

3. Diameter (d) = 24 cm
Radius (r) = 24/2 = 12 cm

Therefore,
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= 4/3 * 22/7 * (12)^3
= 4/3 * 22/7 * 1728
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Volume (V) = 7241.14 cm^3

4. Diameter (d) = 6 cm
Radius (r) = 6/2 = 3 cm

Therefore,
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