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3 years ago

The temperature in frostville was at 50*F at midnight,and it dropped at a constant rate for the next 10 hours.

Mathematics

1 answer:

bazaltina [42]3 years ago

5 0

After 10 hours the temperature is shown on the graph as 30 degrees.

50 degrees - 30 degrees = 20 degrees.

The temperature dropped 20 degrees in 10 hours.

Divide the change by the time:

20 degrees / 10 hours = 2 degrees per hour.

Because the temperature dropped, the change would be negative.

The answer is D. -2 degrees per hour.

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Hadley paddled a canoe 2/3 mile in 1/4 hour. How fast did Hadley paddle, in miles per hour?

irina [24]

Answer:

Step-by-step explanation:

Hadley paddled a canoe 2/3 mile in 1/4 hour. it will be 4 times more in an hour because 1/4*4=4/4=1. 2/3*4=8/3=2 2/3

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3 years ago

A 100 gallon tank initially contains 100 gallons of sugar water at a concentration of 0.25 pounds of sugar per gallon suppose th

Vsevolod [243]

At the start, the tank contains

(0.25 lb/gal) * (100 gal) = 25 lb

of sugar. Let $S(t)$ be the amount of sugar in the tank at time $t$ . Then $S(0)=25$ .

Sugar is added to the tank at a rate of P lb/min, and removed at a rate of

$\left(1\frac{\rm gal}{\rm min}\right)\left(\dfrac{S(t)}{100}\dfrac{\rm lb}{\rm gal}\right)=\dfrac{S(t)}{100}\dfrac{\rm lb}{\rm min}$

and so the amount of sugar in the tank changes at a net rate according to the separable differential equation,

$\dfrac{\mathrm dS}{\mathrm dt}=P-\dfrac S{100}$

Separate variables, integrate, and solve for S.

$\dfrac{\mathrm dS}{P-\frac S{100}}=\mathrm dt$

$\displaystyle\int\dfrac{\mathrm dS}{P-\frac S{100}}=\int\mathrm dt$

$-100\ln\left|P-\dfrac S{100}\right|=t+C$

$\ln\left|P-\dfrac S{100}\right|=-100t-100C=C-100t$

$P-\dfrac S{100}=e^{C-100t}=e^Ce^{-100t}=Ce^{-100t}$

$\dfrac S{100}=P-Ce^{-100t}$

$S(t)=100P-100Ce^{-100t}=100P-Ce^{-100t}$

Use the initial value to solve for C :

$S(0)=25\implies 25=100P-C\implies C=100P-25$

$\implies S(t)=100P-(100P-25)e^{-100t}$

The solution is being drained at a constant rate of 1 gal/min; there will be 5 gal of solution remaining after time

$1000\,\mathrm{gal}+\left(-1\dfrac{\rm gal}{\rm min}\right)t=5\,\mathrm{gal}\implies t=995\,\mathrm{min}$

has passed. At this time, we want the tank to contain

(0.5 lb/gal) * (5 gal) = 2.5 lb

of sugar, so we pick P such that

$S(995)=100P-(100P-25)e^{-99,500}=2.5\implies\boxed{P\approx0.025}$

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3 years ago

Write an equation in point-slope form of the line that passes through (-4,1) and (4,3).

SVEN [57.7K]

Step-by-step explanation:

y-y₁=m(x-x₁)

1-(-4)=m(4-3)

5=m

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3 years ago

ILL MARK BRAINILEST (100 POINTS) !!! Factor the polynomial 7xy + 14x − 35y − 70 completely. 7(2x − 5)(y + 2) 7(x − 5)(y + 2) 7(x

Vlad [161]

Answer:

B. 7(x − 5)(y + 2)

Explanation:

A. 7(2x − 5)(y + 2) = 14xy + 28x − 35y − 70 (Wrong)

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C. 7(x − 2)(y + 5) = 7xy + 35x− 14y − 70 (Wrong)

D. 7(x − 10)(y + 2) = 7xy + 14x − 70y − 140 (Wrong)

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2 years ago

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Taya2010 [7]

Answer:

13.5%

Step-by-step explanation:

I hope this helps

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3 years ago