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Stels [109]
3 years ago
7

In the given right triangle, find the length of the hypotenuse, AB, if BC = 6 and AC = 5.

Mathematics
1 answer:
wolverine [178]3 years ago
6 0
*Use the Pythagorean Theorem

a^2 + b^2 = c^2

6^2 + 5^2 - c^2
36 + 25 = c^2
61 = c^2     *Square root 61

c^2 (c squared) = about 7.8
 
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6. A tank contains 100-gallon of pure water. At time t = 0, a solution containing 2 lb of salt per gallon flows into the tank at
SOVA2 [1]

Answer:

The answer is below

Step-by-step explanation:

Let Q represent the amount of salt in the tank at time t.

\frac{dQ}{dt}= flow\ in - flow\ out\\ \\flow\ in=3\ gal/min*2\ lb/gal=6\ lb/min\\\\net\ gain\ in\ tank\ volume=3-4=-1, henceflow\ out= \frac{4Q}{100-t} \\\\\frac{dQ}{dt}= 6-\frac{4Q}{100-t} \\\\\frac{dQ}{dt}+ \frac{4Q}{100-t}=6\\\\The \ integrating\ factor\ is:\\\\IF=e^{\int\limits {\frac{4}{100-t} } \, dt }=e^{-4\int\limits {\frac{-1}{100-t}}=e^{-4ln(100-t)}=(100-t)^{-4}}\\\\Multiplying\ through  \ by\ IF: \\\\(100-t)^{-4}\frac{dQ}{dt}+ (100-t)^{-4}\frac{4Q}{100-t}=6(100-t)^{-4}\\\\

Integrating:\\\\A(100-t)^{-4}=-2(100-t)^{-3}+c\\\\A=-2(100-t)+\frac{c}{(100-t)^{-4}} \\\\at, t=0,A=0\\\\0=-2(100-0)+\frac{c}{(100-0)^{-4}}\\\\c=0.02\\\\A=-2(100-t)+\frac{0.02}{(100-t)^{-4}}

7 0
3 years ago
Alicia borrowed $15,000 to buy a car. She borrowed the money at 8% for 6 years
myrzilka [38]

Answer:

She have to pay the bank at the end of the 6 years = 222000$

Step-by-step explanation:

Formula applied in this case where price, interest rate and time duration is mentioned.

Interest = prt/100

Substituting all the given values in the formula.

interest = 15000 * 6 * 8/100

150 * 6 * 8 = 7200

Interest + 15000 = 15000 + 7200 = 222000$ has to pay the total.

In this question amount is 15000 multiply by 6 and by 8 then divide it by 100 so we get the interest then we add it in to amount so we get an answer that is total amount which he has to pay.                                                                           Hope this helps! :P PLZ GIVE ME BRAINLIST

7 0
3 years ago
What is 9\3x=5\8 to find the answer i need to ?
tatuchka [14]
9/3x = 5/8 

Using the reciprocal, multiply each side by 3/9. 

5/8 * 3/9 = 15/72
Simplify it : 5/24

x = 5/24

Hope this helps :)
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3 years ago
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Step-by-step explanation:

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