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1 year ago

I need help with question 10

Mathematics

1 answer:

Luden [163]1 year ago

7 0

Answer:

Step-by-step explanation:

pythagorean theorem: a²+b² = c²

area of square = length²

c = side opposite right angle = length of square Z

thus, area of square Z = c²

area of square X = a² (or b², it doesn't matter)

area of square Y = b² (or a²)

a² + b² = c²

region x + region y = region z

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3 years ago

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A cold drink is poured out at 52°F. After 2 minutes of sitting in a 72°F room, its temperature has risen to 55°F. Find an equati

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Answer:

The model for the temperature of the drink can be written as

$T=72-20e^{-0.08t}$

Step-by-step explanation:

For a cold drink in a hotter room, we can say that the rate of change of temperature of the drink is proportional to the difference of temperature between the drink and the room.

We can model that in this way

$\frac{dT}{dt}=k*(T_r-T)$

If we rearrange and integrate

$\int\frac{dT}{(T-Tr)} =-k*\int dt\\\\ln(T-T_r)=-kt+C1\\\\T-T_r=Ce^{-kt}\\\\T=T_r+Ce^{-kt}$

We know that at time 0, the temperature of the drink was 52°F. Then we have:

$T=T_r+Ce^{-kt}\\\\52=72+Ce^0=72+C\\\\C=-20$

We also know that at t=2, T=55°F

$T=T_r+Ce^{-kt}\\\\55=72-20e^{-k*2}\\\\e^{-k*2}=(72-55)/20=0.85\\\\-2k=ln(0.85)=-0.1625\\\\k=0.08$

The model for the temperature of the drink can be written as

$T=72-20e^{-0.08t}$

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3 years ago

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2 years ago

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Answer:

See the detailed answers below

Step-by-step explanation:

Given data

Ratio= 1:4:7

combined ratio= 1+4+7= 12

Total amount= $636,000

Apply the part to all method

The first person will take

1/12= x/ 636,000

cross multiply

12x= 636,000*1

x= 636,000/12

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cross multiply

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2 years ago