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xxMikexx [17]
3 years ago
15

Write the sentence as an inequality. A number (x) plus 10 is less than 34.

Mathematics
1 answer:
Ksenya-84 [330]3 years ago
5 0

Answer:

<em>X  + 10 < 34</em>

Step-by-step explanation:

X is the variable and variable represent a number in equations. Then this < is considered to be the less than symbol. The rest should be easy when you get the understanding.

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It's the expression times two and is technically equivalent.

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Which of the following predictions is most likely true
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A tank holds 300 gallons of water and 100 pounds of salt. A saline solution with concentration 1 lb salt/gal is added at a rate
Shkiper50 [21]

The amount of salt in the tank changes with rate according to

Q'(t)=\left(1\dfrac{\rm lb}{\rm gal}\right)\left(4\dfrac{\rm gal}{\rm min}\right)-\left(\dfrac{Q(t)}{300+(4-1)t}\dfrac{\rm lb}{\rm gal}\right)\left(1\dfrac{\rm gal}{\rm min}\right)

\implies Q'+\dfrac Q{300+3t}=4

which is a linear ODE in Q(t). Multiplying both sides by (300+3t)^{1/3} gives

(300+3t)^{1/3}Q'+(300+3t)^{-2/3}Q=4(300+3t)^{1/3}

so that the left side condenses into the derivative of a product,

\big((300+3t)^{1/3}Q\big)'=4(300+3t)^{1/3}

Integrate both sides and solve for Q(t) to get

(300+3t)^{1/3}Q=(300+3t)^{4/3}+C

\implies Q(t)=300+3t+C(300+3t)^{-1/3}

Given that Q(0)=100, we find

100=300+C\cdot300^{-1/3}\implies C=-200\cdot300^{1/3}

and we get the particular solution

Q(t)=300+3t-200\cdot300^{1/3}(300+3t)^{-1/3}

\boxed{Q(t)=300+3t-2\cdot100^{4/3}(100+t)^{-1/3}}

5 0
3 years ago
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