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Zanzabum
3 years ago
13

The floor of the school art closet is being tiled. The closet is shaped like a parallelogram. The parallelogram has a base of 17

.5 feet and the height of 6 feet. Each package of tile will cover 5 ft.² how many packages of tile will be needed to tile the music room floor?
Mathematics
1 answer:
andrey2020 [161]3 years ago
7 0
First we need to find the total area of the floor. Dividing the total area of floor by area of one package of tile will give us the number package of tiles that are needed to cover the floor.

The shape of floor is parallelogram with base 17.5 feet and height of 6 feet.
Area of parallelogram is the product of its base and height.

So,

Floor Area = 17.5 x 6 = 105 ft²

Area covered by 1 package of tile = 5 ft²

So, number of package of tiles that are needed = 105/5 = 21 package of tiles.

21 packages of tiles will be needed to fully tile the room.
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Answer:

1.\frac{dy}{dt}=ky

2.543.6

Step-by-step explanation:

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y(0)=200

Let y be the number of bacteria at any time

\frac{dy}{dt}=Number of bacteria per unit time

\frac{dy}{dt}\proportional y

\frac{dy}{dt}=ky

Where k=Proportionality constant

2.\frac{dy}{y}=kdt,y'(0)=100

Integrating on both sides then, we get

lny=kt+C

We have y(0)=200

Substitute the values then , we get

ln 200=k(0)+C

C=ln 200

Substitute the value of C then we get

ln y=kt+ln 200

ln y-ln200=kt

ln\frac{y}{200}=kt

\frac{y}{200}=e^{kt}

y=200e^{kt}

Differentiate w.r.t

y'=200ke^{kt}

Substitute the given condition then, we get

100=200ke^{0}=200 \;because \;e^0=1

k=\frac{100}{200}=\frac{1}{2}

y=200e^{\frac{t}{2}}

Substitute t=2

Then, we get y=200e^{\frac{2}{2}}=200e

y=200(2.718)=543.6=543.6

e=2.718

Hence, the number of bacteria after 2 hours=543.6

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