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Gnoma [55]
3 years ago
8

Lella will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $46 and costs an ad

ditional $0.14 per mile driven. The
second plan has an initial fee of $51 and costs an additional $0.10 per mile driven

Mathematics
1 answer:
Helen [10]3 years ago
6 0
The plans cost the same at 125 miles. the cost is $63.50
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Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its te
Aleonysh [2.5K]

Answer:

t=5.18 minute

Step-by-step explanation:

Using Newton's law of cooling

\frac{dT}{dt}=-k(T-T_{s})

T is temperature of a cup of coffee at any time t T_{s}, is the temperature of the surrounding and k is a constant of proportionality in this negative because temperature is decreasing.

T(0)=190\\T(1)=170\\T_{s}=66

\frac{dT}{dt}=-k(T-T_{s})\\\frac{dT}{(T-T_{s})}=-k*dt\\\int\limits {\frac{1}{T-T_{s} } } \, dT=-\int\limits {k} \, dt\\ln(T-T_{s})=k*t+C\\e*ln(T-T_{s})=e^{k*t+C} \\T-T_{s}=e^{k*t}*e^{C}\\e^{C}=C\\T-T_{s}=e^{k*t}*C\\T=T_{s}+e^{k*t}*C

To find constant knowing the time and the temperature the first step of the change of energy in cup of coffee

T=T_{s} +e^{-k*t}*C\\ C=190-66=124\\170=66+124*e^{-k*2}\\ 170-66=124*e^{-k*2}\\ln(\frac{104}{124})=ln*e^{-k*2}\\-0.175=-k*2\\k=0.08794

Now using the constant of decreasing can find the time to be a 145 temperature the cup of coffee

145=66+124*e^{-k*t} \\145-66=124*^{-0.087*t}

ln(0.637)=ln*e(-0.087*t)\\-0.45=-0.087*t\\t=5.18minutes

4 0
3 years ago
Which of the following accurately depicts the transformation of y= x^2 to the function shown below? y=2(x-3)^2+5
sweet [91]

Answer:

Which of the following accurately depicts the transformation of y= x^2 to the function shown below? y=2(x-3)^2+5

A. Shift left 3 units, shrink vertically to 1/2 of the original height, then shift up 5 units.

B. Shift right 3 units, stretch vertically by a factor of 2, then shift up 5 units.

C. Shift up 3 units, stretch horizontally by a factor of 2, then shift left 5 units.

D. Shift 5 units right, stretch vertically by a factor of 3, then shift up 2 units.

Step-by-step explanation:

For f(x) = 4x+1 and g(x)= x^2-5, find (f/g) (x).

6 0
3 years ago
A rectangle is 40 yards long and 30 yards wide. What is the length of the diagonal that cuts through the center?
choli [55]

Answer:

it should be 50

Step-by-step explanation:

Using the pythagorean theorem c = \sqrt{a^{2} +b^{2} } we get 50

4 0
3 years ago
The number of bees that visit a plant is 600 times the number of years the plant is alive, where t represents the number of year
zavuch27 [327]
C for sure, lock it down
7 0
3 years ago
Whats 2+2+2+2+2+2+2+2+2+2
eimsori [14]

Answer:

20

Step-by-step explanation:

there are 10 2s

2×10 =20

7 0
3 years ago
Read 2 more answers
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