Which graph represents x

Mathematics

2 answers:

Paraphin [41]3 years ago

6 0

Hey!

First, we need to multiply both sides of the equation by 3 to give us x on its own.

Equation :
$\frac{3x}{3} \leq 2 * 3$

Solution {Equation Solved} :
$x \leq 6$

So the given number for our new inequality is 6 so that's where we'll plot our point.

REMEMBER IT HAS TO BE A CLOSED POINT

Now we need to find the direction of the arrow. Since the "teeth" of the symbol are facing right, this means our arrow will be going left.

So, this means the correct graph to the given is the second number line.

Hope this helps!

- Lindsey Frazier ♥

Maurinko [17]3 years ago

4 0

The answer is the second graph.

$\frac{x}{3} \leq 2$
You need to isolate x, in order to do this you need to multiply both sides by 3, or 3/1
2*3 = 6
x/3 * 3 = x
Your equation should now be
$x \leq 6$

So the circle should be filled in and pointing towards the left starting from 6

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The coordinates of the endpoints of line segment C D are C(3, 8) and D(6, -1). Express the length of line segment C D in simples

8_murik_8 [283]

$\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
C&({{ 3}}\quad ,&{{ 8}})\quad 
% (c,d)
D&({{ 6}}\quad ,&{{ -1}})
\end{array}\qquad 
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
CD=\sqrt{(6-3)^2+(-1-8)^2}\implies CD=\sqrt{3^2+(-9)^2}
\\\\\\
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3 0

3 years ago

A bin is constructed from sheet metal with a square base and 4 equal rectangular sides. if the bin is constructed from 48 square

kondaur [170]

This is a problem of maxima and minima using derivative.

In the figure shown below we have the representation of this problem, so we know that the base of this bin is square. We also know that there are four square rectangles sides. This bin is a cube, therefore the volume is:

V = length x width x height

That is:

$V = xxy = x^{2}y$

We also know that the bin is constructed from 48 square feet of sheet metal, so:

Surface area of the square base = $x^{2}$

Surface area of the rectangular sides = $4xy$

Therefore, the total area of the cube is:

$A = 48 ft^{2} = x^{2} + 4xy$

Isolating the variable y in terms of x:

$y = \frac{48- x^{2} }{4x}$

Substituting this value in V:

$V = x^{2}( \frac{48- x^{2} }{x}) = 48x- x^{3}$

Getting the derivative and finding the maxima. This happens when the derivative is equal to zero:

$\frac{dv}{dx} = 48-3x^{2} =0$

Solving for x:

$x = \sqrt{\frac{48}{3}} = \sqrt{16} = 4$

Solving for y:

$y = \frac{48- 4^{2} }{(4)(4)} = 2$

Then, the dimensions of the largest volume of such a bin is:

Length = 4 ft
Width = 4 ft
Height = 2 ft

And its volume is:

$V = (4^{2} )(2) = 32 ft^{3}$