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3 years ago

Please help me with this system of inequalities!

Mathematics

1 answer:

erica [24]3 years ago

8 0

Part A: y<4x-8 is a dotted line intercepting the y-axis at -8, and increasing by a value of 4, with shading bellow the line. The Second equation (which I can't fully type out) is a solid line intercepting the y-axis at 5,decreasing by a value of -5/2, and has shading above the line.

Part B: It does not because the point (5,-8) doesn't appear where the shaded areas meet.

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2 years ago

What is the volume of this cone?

olchik [2.2K]

Answer:

The volume of the cone is approximately 453.0 cm³

Step-by-step explanation:

The volume of a cone is one third that of a cylinder with the same height and radius. That gives us 1/3 πr²h, where r is radius and h is height.

However, we are not given the height of the cone, but the side length. We can work out the height using the Pythagorean theorem, as we have a right triangle with the height, base radius, and length. You may recall that the Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of it's other two sides:

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So we can find the height of the cone with that:

$10.8^2 = 7.4^2 + h^2\\h^2 = 10.8^2 - 7.4^2\\h^2 = 116.64 - 54.76\\h^2 = 61.88\\h = \sqrt{61.88}\\h \approx 7.9$

Now that we have the cone's height, we can solve for its volume:

$v = \frac{1}{3} \pi r^2 h\\v = \frac{1}{3} \pi \times 7.4^2 \times 7.9\\v = \frac{1}{3} \pi \times 54.76 \times 7.9\\v = \frac{1}{3} \pi \times 432.6\\v = \pi \times 144.2\\v \approx 453.0 cm^3$

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Please help me with this system of inequalities​!

Please help me with this system of inequalities!