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3 years ago

A manufacturer of shipping boxes has a box

Mathematics

1 answer:

MissTica3 years ago

6 0

then ship that f...... box somewhere becuase all i can think of unless your trying to steal it.

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The top and bottom margins of a poster are each 12 cm and the side margins are each 8 cm. The area of printed material on the po

grin007 [14]

Answer:

Dimensions of printed poster are

length is 32 cm

width is 48 cm

Step-by-step explanation:

Let's assume

length of printed poster is x cm

width of printed poster is y cm

now, we can find area of printed poster

so, area of printed poster is

$=xy$

we are given that area as 1536

so, we can set it to 1536

$xy=1536$

now, we can solve for y

$y=\frac{1536}{x}$

now, we are given

The top and bottom margins of a poster are each 12 cm and the side margins are each 8 cm

so, total area of poster is

$A=(8+x+8)\times (12+y+12)$

$A=(x+16)\times (y+24)$

now, we can plug back y

$A=(x+16)\times (\frac{1536}{x}+24)$

now, we have to minimize A

so, we will find derivative

$A'=\frac{d}{dx}\left(\left(x+16\right)\left(\frac{1536}{x}+24\right)\right)$

we can use product rule

$A'=\frac{d}{dx}\left(x+16\right)\left(\frac{1536}{x}+24\right)+\frac{d}{dx}\left(\frac{1536}{x}+24\right)\left(x+16\right)$

$=\frac{d}{dx}\left(x+16\right)\left(\frac{1536}{x}+24\right)+\frac{d}{dx}\left(\frac{1536}{x}+24\right)\left(x+16\right)$

now, we can simplify it

$A'=-\frac{24576}{x^2}+24$

now, we can set it to 0

and then we can solve for x

$A'=-\frac{24576}{x^2}+24=0$

$-\frac{24576}{x^2}x^2+24x^2=0\cdot \:x^2$

$-24576+24x^2=0$

$x=32,\:x=-32$

Since, x is dimension

and dimension can never be negative

so, we will only consider positive value

$x=32$

now, we can solve for y

$y=\frac{1536}{32}$

$y=48$

so, dimensions of printed poster are

length is 32 cm

width is 48 cm

5 0

3 years ago

You are working with a quadratic equation and construct the following table.

Alecsey [184]

Answer:

a) Vertex is at (-3, -1)

b) y-intercept is at (0,8)

c) x intercept is at (-4,0) and (-2,0)

d) x=-3

Step-by-step explanation:

We know the vertex is the lowest or highest part of a parabola meaning all the points are reflected across. It is the only y value without a matching pair

E.x. -1 and 1, -3 and 3

The only point without a corresponding y value is (-3,-1) therefore the vertex is at (-3,-1)

The y-intercept is where the parabola meets the y axis or the x value is equal to 0, we just have to find when x = 0 to find the y intercept

y intercept: (0,8)

For the x intercept's it is just the reverse, you need to find where the parabola crosses the x axis or when y = 0

x intercept 1:(-4,0)

x intercept 2: (-2,0)

The axis of symmetry is also the x coordinate of the vertex which is 3 so

x = 3

6 0

4 years ago

Pls help if you only know the correct answer! Thanks! :)

FromTheMoon [43]

Yes yes yes yes yes yes yes that is the makers Ik the answer it’s easy do you need help if so tell me

3 0

3 years ago

How about: 37×13×78. Simplify this, if you please.

Natasha2012 [34]

Answer:

37518

Step-by-step explanation:

Clear your calculator. Enter 37, followed by ×, and then 13, followed by ×, and then 78 and the ENTER key. Result: 37518.

5 0

2 years ago

Help me pls!<br> Find f( - 3) × g(4), for f(x) = x^ - 3 and g(x) = x^½ .

madreJ [45]

Answer:

-54

Step-by-step explanation:

Find f( - 3) × g(4),

for f(x) = x^ - 3

f(-3) = -3^ - 3= -3 × -3 × -3= -27

and g(x) = x^½

g(4) = 4^½ = 2^2^½ = 2 ^1 = 2

f( - 3) × g(4) = -27 ×2 = -54

8 0

3 years ago