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4 years ago

What is the slope of find the slope of the line described by 4x + 5y = 60?

1 answer:

5 0

1) isolate y

4x + 5y = 60
-4x -4x
_____________
5y = -4x + 60

2) make y so that is is alone with no numbers beside it

5y = -4x + 60
__________
5

y = -4/5x + 60

3) the slope is ALWAYS the number to the left of x, even if it's a fraction. It's it a decimal, convert to a fraction. The last number (in this case is 60) is where the slope crosses the y-axis on the coordinate plane.

The slope is -4/5x + 60

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Answer:

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The surface area of a given cone is 1,885.7143 square inches. What is the slang height?

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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:

$s \approx r$

And:

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

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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Answer:

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Step-by-step explanation:

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