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3 years ago

7-2 1/2 for woodshop real quick?

Mathematics

1 answer:

Nutka1998 [239]3 years ago

5 0

Answer:

Buy HFS (R) Quick Release Woodworking Vice Size Wood Vise(7 INCH): Bench Vises - Amazon.com ✓ FREE DELIVERY possible on eligible purchases.

Step-by-step explanation:

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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

3. Consider the following statement.

Kitty [74]

Answer:

rarely correct

for f(x) = 6, g(x) = 2; f(g(x)) = 6, g(f(x)) = 2 ≠ f(g(x))

Step-by-step explanation:

The order in which functions operate on each other can rarely be reversed with the same result. If the functions are inverses of each other and both have the same domain as range, then their order can be reversed.

Not so, in most other cases. An example is shown above.

4 0

4 years ago

Read 2 more answers

If C is the midpoint of BD, what is the coordinate of point C if point B is at 0?

Agata [3.3K]

Answer:

It depends on where point D is placed so C > 0

Step-by-step explanation:

As i said above

8 0

3 years ago

Complete the statement to describe the expression ab+cd+ef+gh.

BigorU [14]

Answer with explanation:

The given expression is

=ab+cd+ef+gh

The meaning of expression is equal to terms which contains variables and constants and operation between them is Addition, Subtraction, Multiplication and Division.

→The expression consists of four terms which are, ab, cd, ef, and gh.

→Each term contains

Two factors.

8 0

4 years ago

Read 2 more answers

kenny6666 [7]

Answer:

(x=days) g(x)=15x+200

Step-by-step explanation:

the 200 is a base fee, meaning you cant tag a variable on it and in this case it works as a y-intercept, the 15 dollars a day would be 15x because x is the number of days and to calculate how much it costs to work a few days you multiply the daily rate and the number of days, then add 200 to get your cost.

5 0

3 years ago