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3 years ago

Solve the inequality. 12x<-144

Mathematics

2 answers:

Zepler [3.9K]3 years ago

5 0

Answer:

Step-by-step explanation:

x=-12

Irina18 [472]3 years ago

4 0

Answer:

x= -12

Step-by-step explanation:

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2 years ago

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QUESTION 9

netineya [11]

The radius of the shape is c. 3ft 3in

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2 years ago

How do u guys do a step by step explanation on this app sorry I’m new

sukhopar [10]

Answer:

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Step-by-step explanation:

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2 years ago

A cardboard box without a lid is to have a volume of 19,652 cm3. Find the dimensions that minimize the amount of cardboard used.

Effectus [21]

Answer:

The dimension of the cardboard is 34 cm by 34 cm by 17 cm.

Step-by-step explanation:

Let the dimension of the cardboard box be x cm by y cm by z cm.

The surface area of the cardboard box without lid is

f(x,y,z)= xy+2xz+2yz.....(1)

Given that the volume of the cardboard is 19,652 cm³.

Therefore xyz =19,652

$\Rightarrow z=\frac{19652}{xy}$ ......(2)

putting the value of z in the equation (1)

$f(x,y)=xy+2x(\frac{19652}{xy})+2y(\frac{19652}{xy})$

$\Rightarrow f(x,y)=xy+\frac{39304}{y})+\frac{39304}{x}$

The partial derivatives are

$f_x=y-\frac{39304}{x^2}$

$f_y=x-\frac{39304}{y^2}$

To find the dimension of the box set the partial derivatives $f_x=0$ and $f_y=0$ .Therefore $y-\frac{39304}{x^2}=0$

$\Rightarrow y=\frac{39304}{x^2}$ .......(3)

and $x-\frac{39304}{y^2}=0$

$\Rightarrow x=\frac{39304}{y^2}$ .......(4)

Now putting the x in equation (3)

$y =\frac {39304}{(\frac{39304}{y^2})^2}$

$\Rightarrow y=\frac{y^4}{39304}$

$\Rightarrow y^3= 39304$

⇒y=34 cm

Then $\Rightarrow x=\frac{39304}{34^2}$ =34 cm.

Putting the value of x and y in the equation (2)

$z=\frac{19652}{34 \times 24}$

=17 cm.

The dimension of the cardboard is 34 cm by 34 cm by 17 cm.

4 0

2 years ago

I need help with part a and b, please help

yarga [219]

A. so the entire length of the to would be 25. You know 9 of those feet are not rope so you would subtract that from 25
25-9=16
16 would be the all the rope on top and you only want one side, so you would divide it by 2. The top right piece of rope would be 8ft long
Part b is the picture

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3 years ago