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3 years ago

Which shapes can the composite figure be

Mathematics

1 answer:

olganol [36]3 years ago

4 0

Answer:

rectangle, triangle, trapezoid, and octagon.

Step-by-step explanation:

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A rectangular box is to have a square base and a volume of 12 ft3. If the material for the base costs $0.17/ft2, the material fo

katen-ka-za [31]

Answer:

(a)Length =2 feet

(b)Width =2 feet

(c)Height=3 feet

Step-by-step explanation:

Let the dimensions of the box be x, y and z

The rectangular box has a square base.

Therefore, Volume of the box $V=x^2z$

Volume of the box $=12 ft^3\\$

$Therefore, x^2z=12\\z=\frac{12}{x^2}$

The material for the base costs $\$0.17/ft^2$ , the material for the sides costs $\$0.10/ft^2$ , and the material for the top costs $\$0.13/ft^2$ .

Area of the base $=x^2$

Cost of the Base $=\$0.17x^2$

Area of the sides $=4xz$

Cost of the sides= $=\$0.10(4xz)$

Area of the Top $=x^2$

Cost of the Base $=\$0.13x^2$

Total Cost, $C(x,z) =0.17x^2+0.13x^2+0.10(4xz)$

Substituting $z=\frac{12}{x^2}$

$C(x) =0.17x^2+0.13x^2+0.10(4x)(\frac{12}{x^2})\\C(x)=0.3x^2+\frac{4.8}{x} \\C(x)=\dfrac{0.3x^3+4.8}{x}$

To minimize C(x), we solve for the derivative and obtain its critical point

$C'(x)=\dfrac{0.6x^3-4.8}{x^2}\\Setting \:C'(x)=0\\0.6x^3-4.8=0\\0.6x^3=4.8\\x^3=4.8\div 0.6\\x^3=8\\x=\sqrt[3]{8}=2$

Recall: $z=\frac{12}{x^2}=\frac{12}{2^2}=3\\$

Therefore, the dimensions that minimizes the cost of the box are:

(a)Length =2 feet

(b)Width =2 feet

(c)Height=3 feet

7 0

2 years ago

A parabola opening up or down has vertex (0,0) and passes through (12, -18). Write its

denis-greek [22]

The equation is y= -1/8x^2

4 0

3 years ago

-5(6v-w-1) <br> Distributive prot

krok68 [10]

Answer:

-30v + 5w + 5

Step-by-step explanation:

-5(6v - w - 1) =

Multiply -5 by each term inside the parentheses.

= -5 * 6v - (-5) * w - (-5) * (-1)

= -30v + 5w + 5

5 0

2 years ago

If one pair of opposite sides of a quadrilateral is both congruent and __________, then the quadrilateral is a parallelogram. AN

Sholpan [36]

Answer:

I think it’s parallel

Step-by-step explanation:

Correct me if this is wrong

7 0

2 years ago

Read 2 more answers

Evaluate the function<br>(x) = 11 – 3x<br>for -2).

il63 [147K]

Answer:

Step-by-step explanation:

f(x) = 11 - 3x

f(-2) - <em>put x = -2 to the f(x):</em>

<em />

f(-2) = 11 - 3(-2) = 11 + 6 = 17

3 0

2 years ago