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expeople1 [14]
3 years ago
9

Can someone please explain Linear Inequalities to me?​

Mathematics
2 answers:
Arisa [49]3 years ago
8 0

A linear inequality is similar to a linear equation ( y=2x+5) where there is a relation between 2 variables and when plotted on the graph it is always a straight line, taking the example given earlier, y=2x+5 when plotted on a graph would give us this line ( added as attachment), a linear equations or inequalities do not have a power above, like x^2+3x+9=y is not a linear equation as there is a power above 1, in this case 2 involved, coming to linear inequalities, only the '=' symbol is replaced with \geq, \leq,. so instead of y=2x+5, a linear <u>inequality</u> would be :-

y\leq 2x+5\\ y\geq 2x+5\\ y2x+5

Now all of these have seperate meanings, starting with the first one it states y is less than or equal to 2x+5, second is y is greater than or equal to 2x+5, third is y is less than 2x+5 and lastly the fourth is y is greater than 2x+5. All 4 of these inequalities are graphed on the graph similarly to the original equation ( y=2x+5) however shading the right area according to the inquality is important.

In the graphs attached below, there is a solid line for \leq,\geq but a dashed line for <,> this is because the value of y in the first 2 equations may be equal to 2x+5, it may be on the line or any where in the shaded regions, however in the second too it cannot be on the line but it can only be in the shaded region hence the line is dashed

I hope I made sense for you, let me know if anything confused it, i'll elaborate it further

Zarrin [17]3 years ago
6 0
Ok so an equation like y<_x+2 is not completely equal. a linear inequality is like that but just graphed, so basically a graphed unequal equation (<_ means equal to or greater) i hope this helped!
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Using differential calculus, maximize the volume of a box made of cardboard (top is open) as shown in Figure A. 15, subject to t
lana [24]

The maximum volume of the box is 40√(10/27) cu in.

Here we see that volume is to be maximized

The surface area of the box is 40 sq in

Since the top lid is open, the surface area will be

lb + 2lh + 2bh = 40

Now, the length is equal to the breadth.

Let them be x in

Hence,

x² + 2xh + 2xh = 40

or, 4xh = 40 - x²

or, h = 10/x - x/4

Let f(x) = volume of the box

= lbh

Hence,

f(x) = x²(10/x - x/4)

= 10x - x³/4

differentiating with respect to x and equating it to 0 gives us

f'(x) = 10 - 3x²/4 = 0

or, 3x²/4 = 10

or, x² = 40/3

Hence x will be equal to 2√(10/3)

Now to check whether this value of x will give us the max volume, we will find

f"(2√(10/3))

f"(x) = -3x/2

hence,

f"(2√(10/3)) = -3√(10/3)

Since the above value is negative, volume is maximum for x = 2√(10/3)

Hence volume

= 10 X 2√(10/3)  -  [2√(10/3)]³/4

= 2√(10/3) [10 - 10/3]

= 2√(10/3) X 20/3

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Complete Question

(Image Attached)

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3 years ago
Write an equation of the line shown. Then use the equation to find the value of x when y=112
PtichkaEL [24]

Answer:

y = 8x + 16

x = 12

Step-by-step explanation:

Given two points on the line (0, 16) and (3, 40), an equation for the line can be written using the slope-intercept line equation which takes the format y = mx + b.

Where,

m = slope = \frac{y_2 - y_1}{x_2 - x_1}

b = y-intercept or the point at which the line cuts the y-axis.

Let's find slope (m) using the slope formula:

Let,

(0, 16) = (x_1, y_1)

(3, 40) = (x_2, y_2)

slope (m) = \frac{40 - 16}{3 - 0}

slope (m) = \frac{24}{3}

slope (m) = 8

Find b. Substitute the values of x = 0, y = 16, and m = 8 in the slope-intercept formula to find b.

y = mx + b

16 = 8(0) + b

16 = 0 + b

16 = b

b = 16

Plug in the values of m and b into the slope-intercept formula to get the equation of the line.

y = mx + b

y = 8x + 16

Let's use the equation to find x when y = 112.

y = 8x + 16

Substitute y = 112 in the equation

112 = 8x + 16

112 - 16 = 8x

96 = 8x

Divide both sides by 8

12 = x

x = 12

8 0
3 years ago
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