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3 years ago

Can someone help me with this? Please leave an explanation too, if possible.

Mathematics

2 answers:

Anika [276]3 years ago

7 0

the surface area of the collar is 12.3

lesya [120]3 years ago

6 0

Answer:

Lateral surface area = 287.11 in^2

Step-by-step explanation:

An Elizabethan collar is a conical frustum. In this problem, you'll want to find the lateral surface area, which does not include either base, because the collar does not have bases. To calculate this, the formula is

$la = \pi(r1 + r2)s$

$\sqrt{ {(r1 - r2)}^{2} + {h}^{2} }$

where r1 equals the radius of the larger base, r2 the radius of the smaller base, h the height of the conical frustum, and s is the side length.

s= approximately 8.308...

r1 = 8

r2 = 3

8 + 3 is 11

11 × pi × 8.308... = 287.1108... in^2

Sorry for any confusion or mistakes! By the time I realized this was a bit above my math level I'd already typed out all those formulas, so I was invested.

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Read 2 more answers

Dilate the the triangle, scale factor = 3 (positive 3, ignore the

HACTEHA [7]

Answer:

The rule of dilation is $P'(x,y) = 3\cdot P(x,y)$ .

The vertices of the dilated triangle are $A'(x,y) = (-21, -18)$ , $B'(x,y) = (-15,-10)$ and $C'(x,y) = (-3,-15)$ , respectively.

Step-by-step explanation:

From Linear Algebra, we define the dilation by the following definition:

$P'(x,y) = O(x,y) + k\cdot[P(x,y)-O(x,y)]$ (1)

Where:

$O(x,y)$ - Center of dilation, dimensionless.

$k$ - Scale factor, dimensionless.

$P(x,y)$ - Original point, dimensionless.

$P'(x,y)$ - Dilated point, dimensionless.

If we know that $O(x,y) = (0,0)$ , $k = 3$ , $A(x,y) = (-7,-6)$ , $B(x,y) = (-5,-2)$ and $C(x,y) =(-1,-5)$ , then dilated points of triangle ABC are, respectively: