2 years ago

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Mathematics

1 answer:

kozerog [31]2 years ago

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The length of a rectangle is 5 Inches more than its width, x. The area of a rectangle can be represented by the equation

Paul [167]

Answer:

Factor:

x^2+5x-300=0

(x-15)(x+20)=0

x=15 is the width

x+5=20 is the length

Step-by-step explanation:

4 0

3 years ago

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

I am Lyosha [343]

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

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

7 0

3 years ago

What type of polynomial is: 3x+x^2+4 <br>A.quadratic<br> B. quartic<br> C. linear <br>D. cubic

Svetradugi [14.3K]

Answer:

A.quadratic

Step-by-step explanation:

3x+x^2+4

Put in order from largest to smallest power of x

x^2 +3x+4

The highest power is 2

A.quadratic highest power 2

B. quartic highest power 4

C. linear highest power 1

D. cubic highest power 3

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2 years ago

What is 2.9 as a fraction

Pani-rosa [81]

Answer:

$\frac{29}{10}$

Step-by-step explanation:

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3 years ago

What is 6 minus 4 over seven

aalyn [17]

5 3/7 .. do you need to show your work?

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2 years ago