Help me with this please

Mathematics

1 answer:

RUDIKE [14]3 years ago

5 0

Answer: 24

Step-by-step explanation: The first side is 2 by 4 by 1 which equals 8. The middle is 2 by 2 by 2 which equals 8. The last side is 2 by 4 by 1 which equals 8. 8 plus 8 plus 8 equals 24.

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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

7(x+2)+3(x+5)=14(x+1)+2

shtirl [24]

7x + 14 + 3x + 15 = 14x + 14 + 2 10x + 14 = 14x + 16 14 - 16 = 14x - 10x -2 = 4x X = - 2/4 X = - 1/2 OR X = - 0.5

8 0

3 years ago

Read 2 more answers

If (x+2) is a factor of x^3-6x^2+kx+10, k=

Alja [10]

If a binomial $(x-a)$ is a factor of a polynomial, then $a$ is a root of this polynomial.

$(x+2)=(x-(-2)) \Rightarrow a=-2\\\\
(-2)^3-6\cdot(-2)^2+k\cdot(-2)+10=0\\
-8-24-2k+10=0\\
-2k=22\\\
\boxed{k=-11}
$

3 0

3 years ago

If 3/x= 4/5, then what is the value of x?

vitfil [10]

3 4
—- = —-
x 5

cross multiply 3 and 5 = 15
and 4 and x = 4x
you get 15=4x

x= 15/4

5 0

3 years ago

On a map, 3 centimeters represents 150 kilometers. If a line between two cities measures 4.5 centimeters, how many kilometers ap

SCORPION-xisa [38]

Answer: 225km

Step-by-step explanation:

3cm --- 150

1cm ---- 50

Therefore 4.5cm * 50 = 225km

7 0

2 years ago