NEED HELP ASAP 70 POINTS

Mathematics

2 answers:

Viefleur [7K]3 years ago

8 0

Answer:

x = 24 inches

Step-by-step explanation:

We can use similar triangles to solve this problem. Put the same side of the small triangle over the same side of the large triangle

5 in 8 in

--------- = ------------

15 in x in

Using cross products

5x = 8*15

Divide by 5

5x/5 = 8*15/5

x = 8*3

x = 24 inches

Vera_Pavlovna [14]3 years ago

7 0

Look at the picture.

We have the similar triangles (AAA). Therefore the lengths of the sides are in proportion:

$\dfrac{x}{8}=\dfrac{15}{5}$

$\dfrac{x}{8}=3$ <em>multiply both sides by 8</em>

$\boxed{x=24\ in}$

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KiRa [710]

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8 0

2 years ago

Suppose a tank contains 400 gallons of salt water. If pure water flows into the tank at the rate of 7 gallons per minute and the

Strike441 [17]

Answer:

Step-by-step explanation:

This is a differential equation problem most easily solved with an exponential decay equation of the form

$y=Ce^{kt}$ . We know that the initial amount of salt in the tank is 28 pounds, so

C = 28. Now we just need to find k.

The concentration of salt changes as the pure water flows in and the salt water flows out. So the change in concentration, where y is the concentration of salt in the tank, is $\frac{dy}{dt}$ . Thus, the change in the concentration of salt is found in

$\frac{dy}{dt}=$ inflow of salt - outflow of salt

Pure water, what is flowing into the tank, has no salt in it at all; and since we don't know how much salt is leaving (our unknown, basically), the outflow at 3 gal/min is 3 times the amount of salt leaving out of the 400 gallons of salt water at time t:

$3(\frac{y}{400})$