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kolezko [41]
2 years ago
8

Working together, Shawn and Hector can install a tile floor in 6 hours. It would take Shawn 9 hours to do the job alone. What is

the value of r, the part of the tile that Hector could install in 1 hour?
Mathematics
2 answers:
laiz [17]2 years ago
3 0
The product of the sum of the their rates and the time it took them to finish the job should be equal to one whole job. This may be expressed by the equation,
                            (1/9 + r) x 6 = 1
Solving for the value of r gives an answer of r = 1/18. Thus, Hector does 1/18 of the job in 1 hour.
Umnica [9.8K]2 years ago
3 0

Answer:

a. 1/18

Step-by-step explanation: just took the test

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Sometimes a change of variable can be used to convert a differential equation y′=f(t,y) into a separable equation. One common ch
enot [183]

Answer:

y=\frac{-7t^2+22t-7}{7t-22}

Step-by-step explanation:

We are given that

Initial value problem

y'=(t+y)^2-1, y(3)=4

Substitute the value z=t+y

When t=3 and y=4 then

z=3+4=7

y'=z^2-1

Differentiate z w.r.t t

Then, we get

\frac{dz}{dt}=1+y'

z'=1+z^2-1=z^2

z^{-2}dz=dt

Integrate on both sides

-\frac{1}{z}dz=t+C

z=-\frac{1}{t+C}

Substitute t=3 and z=7

Then, we get

7=-\frac{1}{3+C}

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C=-\frac{22}{7}

Substitute the value of C then we get

z=-\frac{1}{t-\frac{22}{7}}

z=\frac{-7}{7t-22}

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y=\frac{-7}{7t-22}-t

y=\frac{-7-7t^2+22t}{7t-22}

y=\frac{-7t^2+22t-7}{7t-22}

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