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3 years ago

10 points, thanks for the help :)

Mathematics

1 answer:

Margaret [11]3 years ago

7 0

Answer:

Step-by-step explanation:

Factoring an expression is the process of undoing the multiplication.

Assume you have a function f(x):

$f(x)=x^2+2x-48$

This can be factored:

$f(x)=(x+8)(x-6)$

Using multiplication and the distributive property, you arrive back to:

$f(x)=x^2+2x-48$

Then you can see clearly that all we've done is reverse the multiplication.

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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

How many solutions exist for the given equation? 3x 13 = 3(x 6) 1 zero one two infinitely many

romanna [79]

An equation is formed of two equal expressions. There is no solution set of the equation 3x+13 = 3(x+6)+1.

<h3>What is an equation?</h3>

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The equation can be solved in the following manner,

$3x+13 = 3(x+6)+1\\3x+13=3x+18+1\\3x+13=3x+19$

Since both the sides of the equation are the same in terms of variable and the constant terms are not the same. Therefore, there is no solution set of the equation 3x+13 = 3(x+6)+1.

Learn more about Equation:

brainly.com/question/2263981

8 0

2 years ago

John needs to put tape around 40 windows in a building before the painters can get to work. Each window measures 3 feet by 4 fee

tangare [24]

600 feet of tape because 4 +4 for two sides of the window is 8 and 3+ 3 is 6, 14 plus the foot of overlap is 15 x 40 is 600.

3 0

3 years ago

A triangle has a base length given by the equation b = 2x + 4 and a height given by the equation h

Anna11 [10]

It’s 230 I hope this helps

7 0

3 years ago

PLEASE HELP MY ASSIGNMENT IS DUE IN 3 HOURS!!!!

Hatshy [7]

Answer:

76.3 degrees

Step-by-step explanation:

We use inverse cosine to find the angle.

arccos(1.9/8) = 76.26 deg

7 0

3 years ago