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An architect is planning the entryway into a courtyard as an arch in the shape of a semi-circle with a radius of 8 feet. The equation of the arch can be written as $(x-8)^{2}+y^{2}=64$ when the domain is the set of non-negative real numbers less than or equal to 16 and the range is the set of positive real numbers less than or equal to $8 .$a. Draw the arch on graph paper.b. Can a box in the shape of a cube edges measure 6 feet be moved through the arch?c. Can a box that is a rectangular solid that measures 8 feet by 8 feet be moved through the arch?

a) See graphb) Yesc) Yes

Algebra

Chapter 4

RELATIONS AND FUNCTIONS

Section 9

Circles

An Introduction to Geometry

Functions

Linear Functions

Polynomials

Missouri State University

Oregon State University

Harvey Mudd College

Idaho State University

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in this problem. We're using the equation. Give in. It just means that icon, uh, to your model and architects don't sort of thing. So between you layer, um so de dome is located at this equation shown. So the center of the dome would be off the form H comma K in thesent er standard form. So that would be eight comma zero from the equation to hear across eight losses, too 468 and then go out the radius, which is the root of 64 out the radius rid of 64 which is eight. And we go out three d skin too. 468 I'm sorry. And then let's just roughly sketch out the like semi circle. So there it is. And so the questions asked about these two cases. Ah, involving the semi circle. So it's whether or not a cube, uh, length. You're not sorry Q of ah, let me get my cube of length six. I pre made it, but it asked whether this cube of Link six is able to fit into D. Let me just until like that. But it asked whether this cube is able to fit into the dome, so if we just plug it in there, it can fit. So the answer is yes to the first part. And you can also find that algebraic Lee by doing that. Six is less than eight in all the radius direction, and then we take our other square and it's a length eight. And we say, Can this length eight square fit into the Don't? Well, you can see how it's like poking out a little bit at the edges so it definitely cannot fit into the dome this way. Um, so the answer should be No. There might be another way if we rotate the cure, but it's if you're trying to put it in the vertical way, the answer is no.

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