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3 years ago

Help please it’s needed

Mathematics

1 answer:

julia-pushkina [17]3 years ago

3 0

Answer:

The reasonings I provided are just examples (they are true, though!). Hope this helps!

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A closed, rectangular-faced box with a square base is to be constructed using only 36 m2 of material. What should the height h a

kkurt [141]

Answer:

$b=h=\sqrt{6}$ m

Step-by-step explanation:

Let

Bas length of box=b

Height of box=h

Material used in constructing of box=36 square m

We have to find the height h and base length b of the box to maximize the volume of box.

Surface area of box= $2b^2+4bh$

$2b^2+4bh=36$

$b^2+2bh=18$

$2bh=18-b^2$

$h=\frac{18-b^2}{2b}$

Volume of box, V= $b^2h$

Substitute the values

$V=b^2\times \frac{18-b^2}{2b}$

$V=\frac{1}{2}(18b-b^3)$

Differentiate w. r.t b

$\frac{dV}{db}=\frac{1}{2}(18-3b^2)$

$\frac{dV}{db}=0$

$\frac{1}{2}(18-3b^2)=0$

$\implies 18-3b^2=0$

$\implies 3b^2=18$

$b^2=6$

$b=\pm \sqrt{6}$

$b=\sqrt{6}$

The negative value of b is not possible because length cannot be negative.

Again differentiate w.r.t b

$\frac{d^2V}{db^2}=-3b$

At $b=\sqrt{6}$

$\frac{d^2V}{db^2}=-3\sqrt{6}$

Hence, the volume of box is maximum at $b=\sqrt{6}$ .

$h=\frac{18-(\sqrt{6})^2}{2\sqrt{6}}$

$h=\frac{18-6}{2\sqrt{6}}$

$h=\frac{12}{2\sqrt{6}}$

$h=\sqrt{6}$

$b=h=\sqrt{6}$ m

7 0

3 years ago

In the figure below. AB is a diameter of circle P.

valentinak56 [21]

Answer: on khan academy answer: 221

Step-by-step explanation:

5 0

3 years ago

Triangle QRP is congruent to triangle YXZ. What is the perimeter of triangle YXZ?

andre [41]

Answer:

Perimeter of XYZ = Perimeter of QRP

Step-by-step explanation:

Since congruent then

P of XYZ = P of QRP

7 0

3 years ago

What is the linear function of f-10)=12 and f(16)=-1

Natali5045456 [20]

f(-10)=12, x = -10, y = 12

f(16)=-1, x = 16, y = -1.

so, we have two points, let's check with that,

 $\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ -10 &,& 12~) 
% (c,d)
&&(~ 16 &,& -1~)
\end{array}
\\\\\\
% slope = m
slope = m\implies 
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-12}{16-(-10)}\implies \cfrac{-1-12}{16+10}
\\\\\\
\cfrac{-13}{26}\implies -\cfrac{1}{2}$

 $\bf \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)} y-12=-\cfrac{1}{2}[x-(-10)]
\\\\\\
y-12=-\cfrac{1}{2}(x+10)\implies y-12=-\cfrac{1}{2}x-5\implies y=-\cfrac{1}{2}x+7$

3 0

4 years ago

Solve for m in D m/v, if D= 5.1 and v = 0.3 the / is for a fraction.

Nataliya [291]

$D= 5.1 ,v = 0.3 
\\
\\ \frac{Dm}{v} =\frac{5.1m}{0.3} =17m$

5 0

3 years ago

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