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Anna71 [15]
2 years ago
6

The bed of a pick up truck measures 4' x 8" to the nearest inch what is the length of the longest thin metal bar that will lie f

lat in the bed
Mathematics
1 answer:
Andru [333]2 years ago
6 0
Ok so what y ou want to do it to max space, lie it diagonally
use pythagoren theorem
first convert the units

4'=4 feet
8''=8 inches
convert to inches
4 feet times 12=48 inches

so
pythagorea theorem is
a^2+b^2=c^2
c=hypotonuse
a and b are legs
in a right triangle

8 and 48 are the legs
fidn hypotonuse

8^2+48^2=c^2
64+2304=c^2
2368=c^2
8√37=c
aprox
48.66=c
4 feet amd 0.66 inches
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Let x= Time taken by Ximena to paint the fence alone .

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As per given , we have

\dfrac{1}{x}+\dfrac{1}{x-12}=\dfrac{1}{8}\\\\\Rightarrow\ \dfrac{x-12+x}{x(x-12)}=\dfrac{1}{8}\\\\\Rightarrow\ 8(2x-12)=x^2-12x\\\\\Rightarrow\ 16x-96=x^2-12x\\\\\Rightarrow\ x^2-12x-16x+96=0\\\\\Rightarrow\ x^2-28x+96=0\\\\\Rightarrow\ x^2-4x-24x+96=0\\\\\Rightarrow\ x(x-4)-24(x-4)=0\\\\\Rightarrow\ (x-4)(x-24)=0\\\\\Rightarrow x=4, 24

if x= 4

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Therefore, x= 24

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Time taken by Ximena to paint the fence alone  = 24 hours

Time taken by Candice to paint the fence alone = 24-12=12 hours

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3 years ago
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