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2 years ago

Please help me find the area!!!!!

Mathematics

2 answers:

Gre4nikov [31]2 years ago

8 0

Answer:

5) 162

6) 61.6

Step-by-step explanation:

Area of triangle = $\frac{1}{2} b*h$

Area of rectangle = w * l

Left triangle Area = $\frac{1}{2} 4*3$

= 2*3

Right triangle Area = $\frac{1}{2} 7*8$

= $\frac{56}{2}$

=28

Rectangle Area = 16*8 = 128

Total Area = 128+28+6 = 162

12-10 = 2

base of each traingle is 2/2 = 1

Left triangle = right triangle = $\frac{1}{2} 5.6*1$ = 2.8

Rectangle = 10*5.6 = 56

Total = 2.8+2.8+56 = 61.6

Karo-lina-s [1.5K]2 years ago

7 0

For 5 the area is 162 ft

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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

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3 years ago

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Answer:

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3 years ago

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