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Leto [7]
3 years ago
10

Solve using substitution. y = -10x-10 y = -3x + 4

Mathematics
1 answer:
Nikolay [14]3 years ago
4 0
-10x-10 = -3x+4
+3x +3x
————————
-7x-10 = 4
+10 +10
————————
-7x = 14
then divide -7 on both side of the equal sign
you’ll get x=-2

then plug in -2 as x into one of the equations ( it doesn’t matter which one)

y= -10(-2)-10 = 20-10= 10

so y=10


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You are creating an open top box with a piece of cardboard that is 16 x 30“. What size of square should be cut out of each corne
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\frac{10}{3} \ inches of square should be cut out of each corner to create a box with the largest volume.

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Lets assume the cut out size of each corner be "x".

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Using distributive property of multiplication

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Next using differentiative method to find box largest volume, we will have \frac{dv}{dx}= 0

\frac{d (4x^{3} -92x^{2} +480x)}{dx} = \frac{dv}{dx}

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solving quadratic equation inside the parenthesis.

⇒12(x^{2} -12x-\frac{10x}{x} +40)=0

Dividing 12 on both side

⇒[x(x-12)-\frac{10}{3} (x-12)]= 0

We can again take common as (x-12).

⇒ x(x-12)[x-\frac{10}{3} ]=0

∴(x-\frac{10}{3} ) (x-12)= 0

We have two value for x, which is 12 and \frac{10}{3}

12 is invalid as, w= (16-2x)= 16-2\times 12

∴ 24 inches can not be cut out of 16 inches width.

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Volume(v)= (30-2x)\times (16-2x)\times x

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⇒ Volume(v)= (30-\frac{20}{3} ) (16-\frac{20}{3}) (\frac{10}{3} )

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