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Sever21 [200]
3 years ago
5

Find the dimensions of the shaded region so that its area is maximized. x= y=

Mathematics
1 answer:
musickatia [10]3 years ago
3 0
1.  Find the equation of the line AB.  For reference, the answer is y=(-2/3)x+2.
2.  Derive a formula for the area of the shaded rectange.  It is A=xy (where x is the length and y is the height).
3.  Replace "y" in A=xy with the formula for y:  y= (-2/3)x+2:
       
                 A=x[(-2/3)x+2]    This is a formula for Area A in terms of x only.
4.  Since we want to maximize the shaded area, we take the derivative with respect to x of    A=x[(-2/3)x+2] , or, equivalently, A=(-2/3)x^2 + 2x.
This results in   (dA/dx) = (-4/3)x + 2.
5.  Set this result = to 0 and solve for the critical value:  

(dA/dx) = (-4/3)x + 2=0, or (4/3)x=2   This results in x=(3/4)(2)=3/2

6.  Verify that this critical value x=3/2 does indeed maximize the area function.
7.  Determine the area of the shaded rectangle for x=3/2, using the previously-derived formula          A=(-2/3)x^2 + 2x.

The result is the max. area of the shaded rectangle.
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Solve y=3x+4 and y=-2x-6 using substitution method
Ivan
3x + 4 = -2x - 6
5x = -6 - 4
x = -2

y = (3*-2) + 4
y = -6 + 4
y = -2
7 0
2 years ago
The point (4, -8.5) is reflected across the y axis on a coordinate plane to create a new point. What is the distance between the
Shalnov [3]

Answer:

8units

Step-by-step explanation:

If the coordinate (x,y) is reflected over the y axis, the resulting coordinate will be (-x, y)

For the coordinate (4,-8.5), the resulting point after reflection will be (-4, -8.5)

Using the distance formula;

D = √(x₂-x₁)²+(y₂-y₁)²

D = √(-8.5+8.5)²)²+(-4-4)²

D =√(-8)²

D = √64

D = 8

Hence the required distance is 8units

5 0
2 years ago
3/19 of [7/9+{3/4/(1/2-1/3)}] simplify
kifflom [539]

Answer:

simplify to get the answer i think it would be 0.2

Step-by-step explanation:

6 0
2 years ago
Jill got an 85% on a math test if there were 40 questions in total,how many did she get wrong?
GrogVix [38]
You can solve this by setting up a proportion. You can put the number of items correct over the total number. and substitute the unknown number with x.

\frac{85}{100} = \frac{x}{40}   Cross-multiply
3400 = 100x   Divide both sides by 100
34 = x

40 - 34 = 6

So, Jill got 6 questions wrong.
3 0
3 years ago
Read 2 more answers
An angle is supplementary and one measures 70° what is the measurement of the other angle?
alexandr1967 [171]

Answer:

x= 110

Step-by-step explanation:

Supplementary angles add to 180

Let x be the other angle

x +70 =180

Subtract 70 from each side

x+70-70=180-70

x = 110

5 0
3 years ago
Read 2 more answers
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