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2 years ago

Layla has 3/4 of a can of paint. She uses 2/3 of the paint for one wall in her bedroom. How much of the can did she use?

Mathematics

2 answers:

Scorpion4ik [409]2 years ago

8 0

Answer:

5/12

Step-by-step explanation:

Mark him brain

ki77a [65]2 years ago

4 0

Answer:

17/12 or 1 and 5/12.

Step-by-step explanation:

3/4 and 2/3 needs to have the same denomenator. So, what number does both 4 and 3 go into? 12. So, 4x3=12, so we multiply the numerator by 3 too, to get 9 --> 9/12. Then, we see that 4x3=12 for 3 too so we multiply 2 by 4 which gets us 8 --> 8/12. So, now we add 9/12 + 8/12 to get 17/12, which then we make into a mixed number to get 1 and 5/12.

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2 years ago

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2 years ago

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3 years ago

A tank contains 30 lb of salt dissolved in 300 gallons of water. a brine solution is pumped into the tank at a rate of 3 gal/min

sesenic [268]

$A'(t)=(\text{flow rate in})(\text{inflow concentration})-(\text{flow rate out})(\text{outflow concentration})$
$\implies A'(t)=\dfrac{3\text{ gal}}{1\text{ min}}\cdot\left(2+\sin\dfrac t4\right)\dfrac{\text{lb}}{\text{gal}}-\dfrac{3\text{ gal}}{1\text{ min}}\cdot\dfrac{A(t)\text{ lb}}{300+(3-3)t\text{ gal}}$
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We're given that $A(0)=30$ . Multiply both sides by the integrating factor $e^{t/100}$ , then

$e^{t/100}A'(t)+\dfrac1{100}e^{t/100}A(t)=6e^{t/100}+3e^{t/100}\sin\dfrac t4$
$\left(e^{t/100}A(t)\right)'=6e^{t/100}+3e^{t/100}\sin\dfrac t4$
$e^{t/100}A(t)=600e^{t/100}-\dfrac{150}{313}e^{t/100}\left(25\cos\dfrac t4-\sin\dfrac t4\right)+C$
$A(t)=600-\dfrac{150}{313}\left(25\cos\dfrac t4-\sin\dfrac t4\right)+Ce^{-t/100}$

Given that $A(0)=30$ , we have

$30=600-\dfrac{150}{313}\cdot25+C\implies C=-\dfrac{174660}{313}\approx-558.02$

so the amount of salt in the tank at time $t$ is

$A(t)\approx600-\dfrac{150}{313}\left(25\cos\dfrac t4-\sin\dfrac t4\right)-558.02e^{-t/100}$

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2 years ago

Find the factors prime or composite of 16

laiz [17]

The prime factorization of 16 is 2⋅2⋅2⋅2.

The factors of 16 are all numbers between -16 and 16 that divide 16 evenly.−16,−8,−4,−2,−1,1,2,4,8,16

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3 years ago