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Over [174]
3 years ago
10

I need this for today

Mathematics
1 answer:
stiks02 [169]3 years ago
7 0

Answer: The Last option is the only option equivalent to that equation.

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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
Help plzzz<br>Select the correct answer.<br>​
Morgarella [4.7K]
<h3>Answer:  C) 3</h3>

=========================================================

Explanation:

f(x) is the outer function, so the final output -8 corresponds to f(x)

We see that f(-4) = -8 in the first column of the table. I'm starting with the output and working my way backward to get the input. So we started with -8 and worked back to -4.

Then we move to the g(x) function to follow the same pattern: start with the output and move to the input. We start at -4 in the g(x) bubble and move to 3 in the x bubble.

In short, g(3) = -4

So,

f(g(x)) = f(g(3)) = f(-4) = -8

We see that x = 3 leads to f(g(x)) = -8

3 0
3 years ago
Which number line represents the solution to 2.5 – 1.2x &lt; 6.5 – 3.2x?
tensa zangetsu [6.8K]
<span>2.5 – 1.2x < 6.5 – 3.2x

-1.2x + 3.2x < 6.5 - 2.5

3.2x - 1.2x < 4

2x < 4

x < 4/2

x < 2</span>
3 0
3 years ago
Read 2 more answers
Alyssa has 50 quarters and dimes. She has a total of $9.80. How many dimes does she have? Explain your steps.
Debora [2.8K]

Answer:

t $9.50 of it is quarters and 30 cents of it is dimes so 3 dimes

Step-by-step explanation:

8 0
2 years ago
Choose the product. -5p 3(4p 2 + 3p - 1) -20p 5 - 15p 4 + 5p 3 -20p 6 - 15p 4 - 5p 3 -20p 5 + 3p - 1 20p 5 + 15p 4 - 5p 3
Likurg_2 [28]
<span>-5p^3(4p^2 + 3p - 1) = -20p^5 - 15p^4 + 5p^3

answer is

A. first one
  </span>-20p^5 - 15p^4 + 5p^3
5 0
3 years ago
Read 2 more answers
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