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4 years ago

Chang made $144 for 9 hours of work.

Mathematics

2 answers:

adell [148]4 years ago

7 0

Answer:

144 dollars=9 hours of work

112 dollars= x hours of work

144/112=9/x

144x=112(9)

Cross Multiply

x=7

He'll have to work 7 hours.

marshall27 [118]4 years ago

6 0

Answer:

Chang has to work 9 hours to make $112

Step-by-step explanation:

Amount made in an hour = Total amount/total hours worked

$=\frac{144}{9}\\$

= $16

Duration he has work to make $112 = 112/16

= 9 hours

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Answer:

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Step-by-step explanation:

given,

radius of sphere = 3

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h is the height of the cone

here r = x and h = 3 + y

now, volume in term of x and y

$V = \dfrac{1}{3}\pi x^2(3+y)$

Applying Pythagoras theorem

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$V = \dfrac{1}{3}\pi ( \sqrt{9-y^2})^2(3+y)$

$V = \dfrac{1}{3}\pi ( 9-y^2)(3+y)$

$V = \dfrac{1}{3}\pi (27 + 9 y - 3 y^2-y^3)$

differentiating both side

$\dfrac{dV}{dy} =\dfrac{1}{3}\pi ( 9-6y- 3y^2)$

for maxima $\dfrac{dV}{dy} = 0$

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(y+3)(y-1)=0

y = 1,-3

y cannot be negative so, volume at y = 1

$V = \dfrac{1}{3}\pi (27 + 9 (1)- 3(1)^2-(1)^3)$

$V =\dfrac{32}{3}\pi$

Hence, the largest cone which can be inscribed in the spheres of the radius 3 has volume $V =\dfrac{32}{3}\pi$

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