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2 years ago

Mrs. Womack wants to make 22 mini pizzas for her favorite math class party. She

Mathematics

2 answers:

Shkiper50 [21]2 years ago

4 0

Answer:

She can only make 4 whole mini pizzas and needs 70 more cups of flour and will not have any leftover after that.

Step-by-step explanation:

18/4= 4.5

22*4=88

88-18= 70

alex41 [277]2 years ago

4 0

Answer:

Step-by-step explanation:

Mrs. Womack need 22 mini pizzas and each requires 4 cups and when you do the math 22 times 4 is 88, and she only has 18 cups so she would only have enough to make 4 full pizzas. So in total she needs 88 cups meaning she needs 70 more.

22x4=88

88-18=70

18÷4= 4.5

Answer:70 more cups are needed

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A tank contains 1600 L of pure water. Solution that contains 0.04 kg of sugar per liter enters the tank at the rate 2 L/min, and

goldfiish [28.3K]

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and flows out at a rate of

(S(t)/1600 kg/L) * (2 L/min) = S(t)/800 kg/min

Then the net flow rate is governed by the differential equation

$\dfrac{\mathrm dS(t)}{\mathrm dt}=\dfrac8{100}-\dfrac{S(t)}{800}$

Solve for S(t):

$\dfrac{\mathrm dS(t)}{\mathrm dt}+\dfrac{S(t)}{800}=\dfrac8{100}$

$e^{t/800}\dfrac{\mathrm dS(t)}{\mathrm dt}+\dfrac{e^{t/800}}{800}S(t)=\dfrac8{100}e^{t/800}$

The left side is the derivative of a product:

$\dfrac{\mathrm d}{\mathrm dt}\left[e^{t/800}S(t)\right]=\dfrac8{100}e^{t/800}$

Integrate both sides:

$e^{t/800}S(t)=\displaystyle\frac8{100}\int e^{t/800}\,\mathrm dt$

$e^{t/800}S(t)=64e^{t/800}+C$

$S(t)=64+Ce^{-t/800}$

There's no sugar in the water at the start, so (a) S(0) = 0, which gives

$0=64+C\impleis C=-64$

and so (b) the amount of sugar in the tank at time t is

$S(t)=64\left(1-e^{-t/800}\right)$

As $t\to\infty$ , the exponential term vanishes and (c) the tank will eventually contain 64 kg of sugar.

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