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Jet001 [13]
3 years ago
6

What is the solution to the inequality 3(2-3x)<51

Mathematics
2 answers:
drek231 [11]3 years ago
7 0
The answer is x < -5.
Radda [10]3 years ago
5 0
<span>3(2-3x)<51 then
6 - 9x < 51
-9x < 51 - 6
-9x < 45
   x < 45/-9
   x < -5</span>
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A worker is to construct an open rectangular box with a square base and a volume of 196196 ft cubedft3. If material for the bott
Archy [21]

Answer:

Therefore the dimensions of the box is 7 ft by 7 ft by 4 ft.

Therefore the minimum cost to manufacture the box is $12936.

Step-by-step explanation:

Given the volume of the open box is 196 cube ft.

Let the one side of the base of the box be x.

Since the base of the box is square in shape.

The other side of the base is also x.

The area of the base of the box = x² square ft

Let the height of the box be h.

The volume of the box is = Area of the base× height

                                          =(x²×h) cube ft.

                                           =x²h cube ft.

According to the problem,

x²h=196

\Rightarrow h=\frac{196}{x^2}

The material cost for the bottom is $88 per square ft and the material cost for the sides $77  per square ft.

The material cost for the bottom of the box = $(88×x²)

                                                                         =$88x²

The area sides = 2(length+width)height

                       =2(x+x)h

                      =4xh square ft.

The material cost for the sides of the box =$(77×4xh)

                                                                    =$308 xh

Total cost to make the box is =$(88x²+308 xh)

∴C=88x²+308 xh    [ C is in dollar]

Now putting h=\frac{196}{x^2}

C=88x^2+308x\times \frac{196}{x^2}

\Rightarrow C=88x^2+ \frac{60368}{x}

Differentiating with respect to x

C'=176x- \frac{60368}{x^2}

Again differentiating with respect to x

C''=176+ \frac{120736}{x^3}

Now to find the minimum cost, we set C'=0

\therefore 176x- \frac{60368}{x^2}=0

\Rightarrow 176x= \frac{60368}{x^2}

\Rightarrow x^3= \frac{60368}{176}

\Rightarrow x^3=343

\Rightarrow x=7

Now, C''|_{x=7}=176+ \frac{120736}{7^3}>0

Therefore at x=7, the manufacturing cost will be minimum.

The height of the box is h=\frac{196}{7^2} = 4ft

Therefore the dimensions of the box is 7 ft by 7 ft by 4 ft.

The manufacturing cost is C=88.7^2+ \frac{60368}{7}   [ putting x=7]

                                             =$12936

Therefore the minimum cost to manufacture the box is $12936.

4 0
3 years ago
A sum of money invested at the compound interest payable yearly has interest in
jeka94

Answer:

49% and 30% respectively

Step-by-step explanation:

Step one:

Given data

Principal =  Rs. 4,200

Final Amount= Rs. 9282 respectively

time = 2 years and

time = 4 years

Required

The rate of interest for 2 and 4 years

Step two:

the compound interest formula is

A= P(1+r)^t

for 2 years

Substitute

9282= 4200(1+r)^2\\\\9282/4200= (1+r)^2

1+r= \sqrt{\frac{9282}{ 4200} }\\\\1+r= \sqrt{2.21} \\\\1+r= 1.49\\\\r=1.49-1\\\\r= 0.49\\\\

the rate is 49%

For 4 years we have

9282= 4200(1+r)^4\\\\9282/4200= (1+r)^4

1+r= \sqrt[4]{\frac{9282}{4500} } \\\\1+r=\sqrt[4]{2.21}  \\\\1+r= 1.30\\\\r=1.30-1\\\\r= 0.30\\\\

the rate is 30%

6 0
3 years ago
Work bout the height of this pyramid?
Olenka [21]

Answer:

20 cm.

Step-by-step explanation:

In order to find the height, we need the volume and the base area first. We are already given the volume so we need to find the base area.

A = 18 · 5 = 90

Now that we know the base area is 90 cm², we can substitute the information into the equation to solve for the height.

V = 1/3(A)(h)

600 = 1/3(90)(h) (Given)

600 = 30h (Simplified)

20 = h (Divided 30 on both sides)

Therefore, the height is 20 cm.

4 0
2 years ago
Read 2 more answers
Send help please thx you
mars1129 [50]
I think not that sure that it would be 2727
5 0
3 years ago
June served 4/9 of fruit punch.how many liters does she have left
Sladkaya [172]
Just take 9/9-4/9=5/9, we get 9/9 because that is how much fruit punch that there was when the container was full. Enjoy!=)
8 0
3 years ago
Read 2 more answers
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