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Vlada [557]
3 years ago
10

An expression is shown below

Mathematics
1 answer:
Leno4ka [110]3 years ago
4 0

Answer:

B) It is irrational and equal to = 4\sqrt{2}

Step-by-step explanation:

The expression, \sqrt{18} + \sqrt{2} , is an irrational expression because it contains two irrational numbers, \sqrt{18} and \sqrt{2} . Both number are not perfect square. there is no whole number that would be squared that will give you 18 nor 2.

The expression can be equals the following:

\sqrt{18} + \sqrt{2}

= \sqrt{9*2} + \sqrt{2}

= \sqrt{9}*\sqrt{2} + \sqrt{2}

= 3\sqrt{2} + \sqrt{2}

= 4\sqrt{2}

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Answer:

If r >> h, the slang height of the cone is approximately 23.521 inches.

Step-by-step explanation:

The surface area of a cone (A) is given by this formula:

A = \pi \cdot r^{2} + 2\pi\cdot s

Where:

r - Base radius of the cone, measured in inches.

s - Slant height, measured in inches.

In addition, the slant height is calculated by means of the Pythagorean Theorem:

s = \sqrt{r^{2}+h^{2}}

Where h is the altitude of the cone, measured in inches. If r >> h, then:

s \approx r

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Given that A = 1885.7143\,in^{2}, the following second-order polynomial is obtained:

\pi \cdot r^{2} + 2\pi \cdot r -1885.7143\,in^{2}  = 0

Roots can be found by the Quadratic Formula:

r_{1,2} = \frac{-2\pi \pm \sqrt{4\pi^{2}-4\pi\cdot (-1885.7143)}}{2\pi}

r_{1,2} \approx -1\,in \pm 24.521\,in

r_{1} \approx 23.521\,in \,\wedge\,r_{2}\approx -25.521\,in

As radius is a positive unit, the first root is the only solution that is physically reasonable. Hence, the slang height of the cone is approximately 23.521 inches.

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Step-by-step explanation:

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