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3 years ago

Solve each equation by completing the square r² = –12r - 35

Mathematics

1 answer:

Fittoniya [83]3 years ago

7 0

Answer:

r = - 7, r = - 5

Step-by-step explanation:

Given

r² = - 12r - 35 ( add 12r to both sides )

r² + 12r = - 35

To complete the square

add ( half the coefficient of the r- term )² to both sides

r² + 2(6)r + 36 = - 35 + 36

(r + 6)² = 1 ← take the square root of both sides )

r + 6 = ± 1 ( subtract 6 from both sides )

r = - 6 ± 1, thus

r = - 6 - 1 = - 7 or r = - 6 + 1 = - 5

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2 years ago

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A rectangular box with a volume of 272ft^3 is to be constructed with a square base and top. The cost per square foot for the bot

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Answer:

The dimensions of the box is 3 ft by 3 ft by 30.22 ft.

The length of one side of the base of the given box is 3 ft.

The height of the box is 30.22 ft.

Step-by-step explanation:

Given that, a rectangular box with volume of 272 cubic ft.

Assume height of the box be h and the length of one side of the square base of the box is x.

Area of the base is = $(x\times x)$

$=x^2$

The volume of the box is = area of the base × height

$=x^2h$

Therefore,

$x^2h=272$

$\Rightarrow h=\frac{272}{x^2}$

The cost per square foot for bottom is 20 cent.

The cost to construct of the bottom of the box is

=area of the bottom ×20

$=20x^2$ cents

The cost per square foot for top is 10 cent.

The cost to construct of the top of the box is

=area of the top ×10

$=10x^2$ cents

The cost per square foot for side is 1.5 cent.

The cost to construct of the sides of the box is

=area of the side ×1.5

$=4xh\times 1.5$ cents

$=6xh$ cents

Total cost = $(20x^2+10x^2+6xh)$

$=30x^2+6xh$

Let

C $=30x^2+6xh$

Putting the value of h

$C=30x^2+6x\times \frac{272}{x^2}$

$\Rightarrow C=30x^2+\frac{1632}{x}$

Differentiating with respect to x

$C'=60x-\frac{1632}{x^2}$

Again differentiating with respect to x

$C''=60+\frac{3264}{x^3}$

Now set C'=0

$60x-\frac{1632}{x^2}=0$

$\Rightarrow 60x=\frac{1632}{x^2}$

$\Rightarrow x^3=\frac{1632}{60}$

$\Rightarrow x\approx 3$

Now $C''|_{x=3}=60+\frac{3264}{3^3}>0$

Since at x=3 , C''>0. So at x=3, C has a minimum value.

The length of one side of the base of the box is 3 ft.

The height of the box is $=\frac{272}{3^2}$

=30.22 ft.

The dimensions of the box is 3 ft by 3 ft by 30.22 ft.

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3 years ago

What number must be added to the expression below to complete the square? x2+x

iren2701 [21]

Answer:

answer is 1/4

Step-by-step explanation:

proof is (x-1/2)²= x²-2*1/2*x+1/4= x²-x+1/4

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3 years ago

Solve each equation by completing the square r² = –12r - 35​

Solve each equation by completing the square r² = –12r - 35