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3 years ago

Please help with question number 3, please

Mathematics

1 answer:

Nadusha1986 [10]3 years ago

6 0

The ratio is 9 : 7 which means for every 9 pounds of Quartz you have 7 pounds Marble. For the second row Quartz is 72. For the third row it's 11 bags because 99/9 = 11 and 11 times 7 equals 77. The four one is 126 pounds Quartz. Finally the last one is 15 bags and 15 times 7 is 75 pounds of Marble. What you do with the ratio is multiply by the number of bags to figure out with this many bags how many Quartz or Marble. You can do the same thing to figure out how many bags.

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The sum of three consecutive integers is 108. Which equation would be used to solve this word problem? (HINT: The equation has b

Shtirlitz [24]

3 consecutive integers : x, x + 1, x + 2

x + (x + 1) + (x + 2) = 108...ur equation
3x + 3 = 108...ur equation that has been simplified some

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3 years ago

Read 2 more answers

Gina decided to order some clothes from a catalog she ordered three pairs of jeans at $39 each for t-shirts at $15 each and 2 st

Blizzard [7]

39 times 3 and 15 times 3 then 27 times 2 then add together to get 216

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3 years ago

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

Debora [2.8K]

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

Salt flows in at a rate

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

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

Sonia makes a wooden frame around a square picture. The frame is made of four congruent trapezoids. The shorter base is 9 in, th

sp2606 [1]

answer

congruent trapezoide for one

0,5(9+12)×1,5=15,75

area of picture frame =4×15,75=63

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2 years ago

A box is 50 cm long. how long is the box in feet

algol13

Answer:

____1.64042 foot____

8 0

3 years ago