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Pani-rosa [81]
3 years ago
14

What is the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve y = 27 - x2?

Mathematics
2 answers:
Likurg_2 [28]3 years ago
6 0

Answer:

108 units squared

Step-by-step explanation:

Length is 2x , width is y

area = 2x * y

sub for y

area = 2x(27 - x^2)

area = 54x - 2x^3

1st derivative: 54 - 6x^2

54 - 6x^2 = 0

6(9 - x^2) = 0

6(3 - x)(3 + x) = 0

so, x = 3

solve for y: 27 - 3^2 = 18

area = (3*2)* 18 = 108 units squared

statuscvo [17]3 years ago
5 0
The answer is 54 square units.
let the vertex in quadrant I be (x,y) 
<span>then the vertex in quadratnt II is (-x,y) </span>
<span>base of the rectangle = 2x </span>
<span>height of the rectangle = y </span>
<span>Area = xy </span>
<span>= x(27 - x</span>²<span>) </span>
<span>= -x</span>³<span> + 27x </span>
<span>d(area)/dx = 3x</span>²<span> - 27 </span><span>= 0 for a maximum of area </span>
<span>3x</span>²<span> = 3 x 3</span>² = <span>27 </span>
<span>x</span>²<span> = 9 </span>
<span>x = ±3 </span>
<span>y = 27-9 = 18 </span>
So, the largest area = 3 x 18 = 54 square units
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If EF bisects CD.CG = 5x - 1, GD = 7x-13, EF = 6x - 4, and GF = 13. find EG.
Iteru [2.4K]

Answer:

EG = 19

Step-by-step explanation:

* Lets explain how to solve the problem

- If a line bisects another line that means the point of intersection

 divides the second line into two equal parts

∵ EF bisects CD at G

∴ CG = GD

∵ CG = 5x - 1

∵ GD = 7x - 13

∴ 7x - 13 = 5x - 1

* Lets solve the equation

∵ 7x - 13 = 5x - 1

- Subtract 5x from both sides and add 13 to both sides

∴ 7x - 5x = 13 - 1

∴ 2x = 12

- Divide both sides by 2

∴ x = 6

- Point G divides EF into two parts EG and GF

∴ EF = EG + GF

∵ EF = 6x - 4

- Substitute the value of x to find EF

∵ x = 6

∴ EF = 6(6) - 4 = 36 - 4 = 32

∴ EF = 32

∵ GF = 13

- Substitute the values of EF and GF in the equation of EF

∴ 32 = EG + 13

- Subtract 13 from both sides

∴ 19 = EG

* EG = 19

3 0
3 years ago
What is the difference between the smallest 6-digit whole number and the greatest four digit whole number
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Answer:

x^{3} -5x^{2} -6x +8 \frac{-2}{x + 3}

Step-by-step explanation:

            x^{3} -5x^{2} -6x +8 \frac{-2}{x + 3}

x + 3 / x^{4} - 2x^{3}-21x^{2} -10x +22

         -(x^{4} + 3x^{3})

                 -5x^{3} -21x^{2} -10x +22

                 -(-5x^{3} -15x^{2})

                              -6x^{2} -10x +22

                            -(-6x^{2} -18x)

                                            8x +22

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4 0
3 years ago
Point A is the midpoint of side XZ and point B is the
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Answer:

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Step-by-step explanation:

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What is the solution set of x2 + 5x + 1 = 0?
DerKrebs [107]

Answer:

\huge\boxed{\left\{-\dfrac{5+\sqrt{21}}{2};\ \dfrac{-5+\sqrt{21}}{2}\right\}}

Step-by-step explanation:

x^2+5x+1=0\\\\\text{Use the quadratic formula:}\\\\\text{For}\ ax^2+bx+c=0\\\\\Delta=b^2-4ac\\\\\text{if}\ \Delta < 0,\ \text{then the equation has no real solution}\\\text{if}\ \Delta=0,\ \text{then the equation has one real solution}\ x=\dfrac{-b}{2a}\\\text{if}\ \Delta>0,\ \text{then the equation has two real solution}\ x=\dfrac{-b\pm\sqrt{\Delta}}{2a}

\text{We have}\\\\a=1,\ b=5,\ c=1\\\\\Delta=5^2-4(1)(1)=25-4=21>0\\\\x=\dfrac{-5\pm\sqrt{21}}{2(1)}=\dfrac{-5\pm\sqrt{21}}{2}

3 0
3 years ago
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