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mylen [45]
3 years ago
9

A local clothing store sells t-shirts for $8 each, sweaters for $12 each, jeans for $15 each. Let x represent the number of t-sh

irts sold, y represents the number of sweaters sold, and z represent the number of jeans sold. Write an expression to represent the total amount of sales from t-shirts, sweaters, and jeans
Mathematics
1 answer:
Svetlanka [38]3 years ago
7 0

Answer:

8x + 12y + 15z

Step-by-step explanation:

Given the sales rate of three items: 8$ for t-shirts, 12$ for sweaters, and 15$ for jeans. It also states that these rates are represented by the corresponding variables being x for t-shirts, y for sweaters, and z for jeans.

To complete the expression, just combine the rate with the corresponding variables. i.e <u>8</u>$ for t-shirts, and <u>x</u> for shirts = 8x, <u>12</u>$ for sweaters and <u>y</u> for sweaters = 12y, <u>15</u>$ for jeans, and <u>z</u> for jeans = 15z. Finally, sum them together.

<u>8x</u> + <u>12y</u> + <u>15z</u>

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(If the discriminant = 0, then there is one root
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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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See attachment for math work and answer.

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8 0
3 years ago
Read 2 more answers
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