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Harman [31]
3 years ago
15

A shelf will covered with veneer on all 6 sides. The shelf is 48 inches long, 12 inches wide and 1 inch thick. What is the surfa

ce area of the shelf?

Mathematics
1 answer:
Liono4ka [1.6K]3 years ago
6 0
So. hmmmm notice the first picture, that's a rectangular prism

is really just 6 rectangles stacked up to each other at the edges

now, notice the second picture, is a prism/shelf with a length of 48, width of 12 and height of 1

so, your shelf is really just 6 rectangles stacked up to each other at the edges

you have 2 rectangles of 48x1 on the sides
2 rectangles of 12x1 for the front and back
and 2 rectangles of 12x48, for the top and bottom

get the area of each of those rectangles, add them up, and that's the surface area of the shelf

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How do I do this table !!!
erma4kov [3.2K]

Answer:

Step-by-step explanation:

just mutiply  120 by 1,2,3,4,5,6,7,8

7 0
4 years ago
A piece of wire 19 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral tria
mr Goodwill [35]

Answer: 8.26 m

Step-by-step explanation:

$$Let s be the length of the wire used for the square. \\Let $t$ be the length of the wire used for the triangle. \\Let $A_{S}$ be the area of the square. \\Let ${A}_{T}}$ be the area of the triangle. \\One side of the square is $\frac{s}{4}$ \\Therefore,we know that,$$A_{S}=\left(\frac{s}{4}\right)^{2}=\frac{s^{2}}{16}$$

$$The formula for the area of an equilateral triangle is, $A=\frac{\sqrt{3}}{4} a^{2}$ where $a$ is the length of one side,And one side of our triangle is $\frac{t}{3}$So,We know that,$$A_{T}=\frac{\sqrt{3}}{4}\left(\frac{t}{3}\right)^{2}$$We have to find the value of "s" such that,$\mathrm{s}+\mathrm{t}=19$ hence, $\mathrm{t}=19-\mathrm{s}$And$$A_{S}+A_{T}=A_{S+T}$$

$$Therefore,$$\begin{aligned}&A_{T}=\frac{\sqrt{3}}{4}\left(\frac{(19-s)}{3}\right)^{2}=\frac{\sqrt{3}(19-s)^{2}}{36} \\&A_{T+S}=\frac{s^{2}}{16}+\frac{\sqrt{3}(19-s)^{2}}{36}\end{aligned}

$$Differentiating the above equation with respect to s we get,$$A^{\prime}{ }_{T+S}=\frac{s}{8}-\frac{\sqrt{3}(19-s)}{18}$$Now we solve $A_{S+T}^{\prime}=0$$$\begin{aligned}&\Rightarrow \frac{s}{8}-\frac{\sqrt{3}(19-s)}{18}=0 \\&\Rightarrow \frac{s}{8}=\frac{\sqrt{3}(19-s)}{18}\end{aligned}$$Cross multiply,$$\begin{aligned}&18 s=8 \sqrt{3}(19-s) \\&18 s=152 \sqrt{3}-8 \sqrt{3} s \\&(18+8 \sqrt{3}) s=152 \sqrt{3} \\&s=\frac{152 \sqrt{3}}{(18+8 \sqrt{3})} \approx 8.26\end{aligned}$$

$$The domain of $s$ is $[0,19]$.So the endpoints are 0 and 19$$\begin{aligned}&A_{T+S}(0)=\frac{0^{2}}{16}+\frac{\sqrt{3}(19-0)^{2}}{36} \approx 17.36 \\&A_{T+S}(8.26)=\frac{8.26^{2}}{16}+\frac{\sqrt{3}(19-8.26)^{2}}{36} \approx 9.81 \\&A_{T+S}(19)=\frac{19^{2}}{16}+\frac{\sqrt{3}(19-19)^{2}}{36}=22.56\end{aligned}$$

$$Therefore, for the minimum area, $8.26 \mathrm{~m}$ should be used for the square

8 0
2 years ago
» Solve for r.<br> 8r = 40<br> r=
Semmy [17]
The answer is ...

R = 5

8(5) = 40
5 0
4 years ago
Read 2 more answers
In the diagram, ΔGEF and ΔHEF are congruent. What is the value of x?
mojhsa [17]

Similar triangles are triangles that has all sides and angles to be equal. The value of x if , ΔGEF and ΔHEF are congruent is 28

<h3>Similar triangles</h3>

Similar triangles are triangles that has all sides and angles to be equal. From the given diagram;

<GFE = <EFH

Given

<GFE = 60 degrees

<EFH = 2(x+2)

Substitute

2(x+2) = 60
2x + 4 = 60

2x = 60 - 4

2x = 56

x = 28

Hence the value of x if , ΔGEF and ΔHEF are congruent is 28

Learn more on congruent shapes here: brainly.com/question/2644832

#SPJ1

8 0
2 years ago
What does chemical erosion do
matrenka [14]
It causes the breakdown and decay to the rocks. It occurs when the weather water is slightly acidic.
5 0
3 years ago
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