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Usimov [2.4K]
3 years ago
6

Simplify the following expression. log(x^4) -log(x^3)

Mathematics
1 answer:
Paraphin [41]3 years ago
3 0
The answer would be log(x)
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I really need help with this​
vova2212 [387]
The correct answer to this question is B.
8 0
2 years ago
A tank with a capacity of 1000 L is full of a mixture of water and chlorine with a concentration of 0.02 g of chlorine per liter
faltersainse [42]

At the start, the tank contains

(0.02 g/L) * (1000 L) = 20 g

of chlorine. Let <em>c</em> (<em>t</em> ) denote the amount of chlorine (in grams) in the tank at time <em>t </em>.

Pure water is pumped into the tank, so no chlorine is flowing into it, but is flowing out at a rate of

(<em>c</em> (<em>t</em> )/(1000 + (10 - 25)<em>t</em> ) g/L) * (25 L/s) = 5<em>c</em> (<em>t</em> ) /(200 - 3<em>t</em> ) g/s

In case it's unclear why this is the case:

The amount of liquid in the tank at the start is 1000 L. If water is pumped in at a rate of 10 L/s, then after <em>t</em> s there will be (1000 + 10<em>t</em> ) L of liquid in the tank. But we're also removing 25 L from the tank per second, so there is a net "gain" of 10 - 25 = -15 L of liquid each second. So the volume of liquid in the tank at time <em>t</em> is (1000 - 15<em>t </em>) L. Then the concentration of chlorine per unit volume is <em>c</em> (<em>t</em> ) divided by this volume.

So the amount of chlorine in the tank changes according to

\dfrac{\mathrm dc(t)}{\mathrm dt}=-\dfrac{5c(t)}{200-3t}

which is a linear equation. Move the non-derivative term to the left, then multiply both sides by the integrating factor 1/(200 - 5<em>t</em> )^(5/3), then integrate both sides to solve for <em>c</em> (<em>t</em> ):

\dfrac{\mathrm dc(t)}{\mathrm dt}+\dfrac{5c(t)}{200-3t}=0

\dfrac1{(200-3t)^{5/3}}\dfrac{\mathrm dc(t)}{\mathrm dt}+\dfrac{5c(t)}{(200-3t)^{8/3}}=0

\dfrac{\mathrm d}{\mathrm dt}\left[\dfrac{c(t)}{(200-3t)^{5/3}}\right]=0

\dfrac{c(t)}{(200-3t)^{5/3}}=C

c(t)=C(200-3t)^{5/3}

There are 20 g of chlorine at the start, so <em>c</em> (0) = 20. Use this to solve for <em>C</em> :

20=C(200)^{5/3}\implies C=\dfrac1{200\cdot5^{1/3}}

\implies\boxed{c(t)=\dfrac1{200}\sqrt[3]{\dfrac{(200-3t)^5}5}}

7 0
3 years ago
-5X +1 92 - 321+13 - 12X
Bogdan [553]

Answer:

Step-by-step explanation:

There’s no equal sign.

8 0
3 years ago
Sarah brought her City car in for repairs and maintenance over the first three years she owned it she replace the brake pads in
Veseljchak [2.6K]

Answer: Average per year for the repairs and maintenance is $273.66

Step-by-step explanation:

She replace the brake pads in the third year for $98 and the preventive maintenance plan cost $723 

what did he average per year for repairs and maintenance?

The total cost of repairs and maintenance = 98 + 723 = 821

repairs and maintenance over the first three years 

Divide the answer by 3

821/ 3 = 273.67 dollars per year

3 0
3 years ago
A box have 5 beads of the same size, but all are different colors. Tina draws a bead randomly from the box, notes its color, the
Mila [183]
Since Tina replaces the beads after each pick:

P(R,G,R)=(1/5)(1/5)(1/5)=1/125
7 0
2 years ago
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