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Ostrovityanka [42]
4 years ago
9

Consider the following rectangle with a perimeter of 38ft. Find x Answer in units of feet.

Mathematics
2 answers:
Lilit [14]4 years ago
5 0

X = 8

18-(2x8) = 18 - 16 = 2

8+9=17

Perimeter = 2x width + 2x length

Length = 2x2 = 4

Width = 2x17 =34 34 + 4 = 38

Ahat [919]4 years ago
5 0

Let's turn this into an equation. Since we use 2L+2W=P to find the perimeter, we need to use that equation but fill in the information we know.

2(18-2x)+2(x+9)=38; let's distribute the parenthesis. 36-4x+2x+18=38; let's add like terms. 54-2x=38; let's subtract 54 from both sides. -2x=-16; divide both sides by -2. x=8 Let's check to make sure 8 is the correct answer. We need plug it in to both sides.

x+9=8+9=17; that's the length of one side, let's find the other. 18-2(x)=18-2(8)=18-16=2; that's the length of the other side.

17+17+2+2=34+4=38

So, x=8 ft.

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find the surface areas of the larger cone and the smaller cone in terms of pi. compare the surface areas using a percent. (the m
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ANSWER :

Surface area of larger cone : 24π units^2

Surface area of smaller cone : 6π units^2

The surface area of the smaller cone is 25% of that of the larger cone.

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AB = 3 is the radius of the larger cone and the slanted height is BC = 5

DE = 1.5 is the radius of the smaller cone and the slanted height is EC = 2.5

Recall the surface area of the cone :

A=\pi r^2+\pi rL

where r = radius and L = slanted height.

For the larger cone, r = 3 and L = 5

\begin{gathered} A=\pi(3)^2+\pi(3)(5) \\ A=24\pi \end{gathered}

For the smaller cone, r = 1.5 and L = 2.5

\begin{gathered} A=\pi(1.5)^2+\pi(1.5)(2.5) \\ A=6\pi \end{gathered}

Comparing the surface areas :

The area of the smaller cone compared to the larger cone is :

\begin{gathered} \frac{smaller}{larger}\times100=\frac{6\pi}{24\pi}\times100 \\  \\ =25\% \end{gathered}

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