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lord [1]
3 years ago
7

Plz answer will give brainliest

Mathematics
1 answer:
Alex73 [517]3 years ago
7 0
Given quadratic equationx^2+6x+6=0
Using the usual conventions, 
a=1, b=6, c=6
Apply the quadratic formula,
x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}
substitute a,b & c with numerical values,
x=\frac{-6\pm\sqrt{6^2-4(1)(6)}}{2(1)}
simplify:
x=\frac{-6\pm\sqrt{12}}{2}
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From a thin piece of cardboard 30 in. by 30 in., square corners are cut out so that the sides can be folded up to make a box. Wh
Brilliant_brown [7]

Answer:

Dimensions 5in x 10in x 10in will yeild a box with a max. volume of  500 cubic inches

Step-by-step explanation:

Volume =  height x length x width

considering 'x' as the length of the square corners that has been cut out from the cardboard and also, that is height of the cardboard box.

square corners are cut out so that the sides can be folded up to make a box, cardboard sides would reduce by 2x

therefore,

V = x  (30-2x) (30-2x) ---> eq(1)

V=( 30x - 2x²) (30-2x)

V= 900x- 60x² - 60x² + 4x³

V=  4x³ - 120 x²+ 900x

Taking derivative w.r.t 'x'

dV/dx = 12x² - 240 x +900

dV/dx = 4 (3x² - 60x +225)

For maximum dV/dx, make it equal zero

dV/dx = 0

so,  4 (3x² - 60x +225)=0

3x² - 60x+225=0   (taking 3 common)

x² - 20x + 75 =0

Solving this quadratic equation

x² - 15x -5x + 75 =0

x(x-15) - 5(x-15) =0

Either (x-15)=0

x=15

Or x-5=0

x = 5

if we substitute x=15 in eq(1), volume becomes zero.

therefore, x cannot be 15

When x= 5

eq(1)=>V = 5  (30-2(5)) (30-2(5))

V= 5 (10) (10)

V= 500 cubic inches,

Therefore, Dimensions 5in x 10in x 10in will yeild a box with a max. volume of  500 cubic inches

7 0
3 years ago
B 95 C a e 75° 709 ITEM BANK: Move to Bottom 25° 30° 35° 50° 75° 85°​
den301095 [7]

Answer:

85 California spout alone 1

3 0
3 years ago
Please help me on this (picture)
MissTica
There isn't a picture to help you with.
8 0
3 years ago
Rewrite the expression as a single logarithm: <br> log 5 - log 7
Lady bird [3.3K]

Answer:

-0.146

Step-by-step explanation:

log 5 = 0.699

log 7 = 0.845

5 0
3 years ago
Read 2 more answers
!!please, please help me!!
grigory [225]

Answer:

Length: 12

Width: 2\sqrt{10\\}

Area: 24\sqrt{10\\}

Step-by-step explanation:

We first find the points of C and D to find the length.

C: (-4,-5)

D: (2,-3)

The distance is 2\sqrt{10\\.

Now for the height.

A: (2,9)

D: (2,-3)

The distance is 12.

Area: 2\sqrt{10\\×12 = 24\sqrt{10\\}

6 0
2 years ago
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