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3 years ago

DOES ANYONE UNDERSTAND????

Mathematics

1 answer:

Mice21 [21]3 years ago

7 0

Answer:

let cost of each pound of trail mix be x any y respectively

For 2 pounds of trail mix and 5 pounds of jelly beans, the total cost is $10

2x +5y = 10.....(1)

For 8 pounds of trail mix and 3 pounds of jelly beans, the total cost is $23

8x +3y = 23.....(2)

2x +5y= 10 ....... × 4

8x +20y = 40.....(3)

8x +3y = 23 ( from (2))

(3) - (2)

17y = 17

y= 1

8x +3y = 23

8x +3 = 23

8x= 20

x= 2.5

Cost for each pound of trail mix= $2.5

Cost for each pound of jelly beans= $1

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3 years ago

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A 75-gallon tank is filled with brine (water nearly saturated with salt; used as a preservative) holding 11 pounds of salt in so

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Let $A(t)$ = amount of salt (in pounds) in the tank at time $t$ (in minutes). Then $A(0) = 11$ .

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$\left(0.6\dfrac{\rm lb}{\rm gal}\right) \left(3\dfrac{\rm gal}{\rm min}\right) = \dfrac95 \dfrac{\rm lb}{\rm min}$

and flows out at a rate

$\left(\dfrac{A(t)\,\rm lb}{75\,\rm gal + \left(3\frac{\rm gal}{\rm min} - 3.25\frac{\rm gal}{\rm min}\right)t}\right) \left(3.25\dfrac{\rm gal}{\rm min}\right) = \dfrac{13A(t)}{300-t} \dfrac{\rm lb}{\rm min}$

where 4 quarts = 1 gallon so 13 quarts = 3.25 gallon.

Then the net rate of salt flow is given by the differential equation

$\dfrac{dA}{dt} = \dfrac95 - \dfrac{13A}{300-t}$

which I'll solve with the integrating factor method.

$\dfrac{dA}{dt} + \dfrac{13}{300-t} A = \dfrac95$

$-\dfrac1{(300-t)^{13}} \dfrac{dA}{dt} - \dfrac{13}{(300-t)^{14}} A = -\dfrac9{5(300-t)^{13}}$

$\dfrac d{dt} \left(-\dfrac1{(300-t)^{13}} A\right) = -\dfrac9{5(300-t)^{13}}$

Integrate both sides. By the fundamental theorem of calculus,

$\displaystyle -\dfrac1{(300-t)^{13}} A = -\dfrac1{(300-t)^{13}} A\bigg|_{t=0} - \frac95 \int_0^t \frac{du}{(300-u)^{13}}$

$\displaystyle -\dfrac1{(300-t)^{13}} A = -\dfrac{11}{300^{13}} - \frac95 \times \dfrac1{12} \left(\frac1{(300-t)^{12}} - \frac1{300^{12}}\right)$

$\displaystyle -\dfrac1{(300-t)^{13}} A = \dfrac{34}{300^{13}} - \frac3{20}\frac1{(300-t)^{12}}$

$\displaystyle A = \frac3{20} (300-t) - \dfrac{34}{300^{13}}(300-t)^{13}$

$\displaystyle A = 45 \left(1 - \frac t{300}\right) - 34 \left(1 - \frac t{300}\right)^{13}$

After 1 hour = 60 minutes, the tank will contain

$A(60) = 45 \left(1 - \dfrac {60}{300}\right) - 34 \left(1 - \dfrac {60}{300}\right)^{13} = 45\left(\dfrac45\right) - 34 \left(\dfrac45\right)^{13} \approx 34.131$

pounds of salt.

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2 years ago

Of the last 20 balloons sold at a party store, 10 were blue. Considering this data, how many of the next 18 balloons sold would

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Answer:

9 blue balloons

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Let's create a proportion using the following set up.

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We know that 10 blue balloons were sold if 20 total balloons were sold. We don't know how many blue are are sold if 18 total are sold. Therefore, we can say x blue are sold for 18 total sold.

10 blue/20 total=x blue/18 total

10/20=x/18

We want to find out what x is. In order to do this, we have to get x by itself. Perform the opposite of what is being done to the equation. Keep in mind, everything done to one side, has to be done to the other.

x is being divided by 18. The opposite of division is multiplication. Multiply both sides by 18.

18*(10/20)=(x/18)*18

18*(10/20)=x

18*1/2=x

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3 years ago

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Answer:

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3 years ago

Mike is driving a boat at 12 mph and is increasing his speed by 0.2 mph each second. Hank is driving a boat at 26.4 mph and is d

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As per given,

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Subtract 12 from both sides

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Add 0.7xn on both sides , we get

0.2x+0.7x= 14.4

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Multiply 10 on both sides, we get

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Divide both sides by 9 , we get x= 16

Hence, after 16 seconds the boats will be traveling the same speed.

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3 years ago