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3 years ago

If matrix A is of the size 2×3 and we are able to add matrix B to A. what must be the size of B be?

Mathematics

1 answer:

tankabanditka [31]3 years ago

5 0

Answer:

6 be because 2×3 =6 so B it will be the given answer

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Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains liters of a dye solution with a

Alja [10]

Answer:

t = 460.52 min

Step-by-step explanation:

Here is the complete question

Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 200 liters of a dye solution with a concentration of 1 g/liter. To prepare for the next experiment, the tank is to be rinsed with fresh water flowing in at a rate of 2 liters/min, the well-stirred solution flowing out at the same rate.Find the time that will elapse before the concentration of dye in the tank reaches 1% of its original value.

Solution

Let Q(t) represent the amount of dye at any time t. Q' represent the net rate of change of amount of dye in the tank. Q' = inflow - outflow.

inflow = 0 (since the incoming water contains no dye)

outflow = concentration × rate of water inflow

Concentration = Quantity/volume = Q/200

outflow = concentration × rate of water inflow = Q/200 g/liter × 2 liters/min = Q/100 g/min.

So, Q' = inflow - outflow = 0 - Q/100

Q' = -Q/100 This is our differential equation. We solve it as follows

Q'/Q = -1/100

∫Q'/Q = ∫-1/100

㏑Q = -t/100 + c

$Q(t) = e^{(-t/100 + c)} = e^{(-t/100)}e^{c} = Ae^{(-t/100)}\\Q(t) = Ae^{(-t/100)}$

when t = 0, Q = 200 L × 1 g/L = 200 g

$Q(0) = 200 = Ae^{(-0/100)} = Ae^{(0)} = A\\A = 200.\\So, Q(t) = 200e^{(-t/100)}$

We are to find t when Q = 1% of its original value. 1% of 200 g = 0.01 × 200 = 2

$2 = 200e^{(-t/100)}\\\frac{2}{200} = e^{(-t/100)}$

㏑0.01 = -t/100

t = -100㏑0.01

t = 460.52 min

6 0

3 years ago

Tju [1.3M]

Answer:

Step-by-step explanation:

Rationalize the denominator of b. So, multiply the numerator and denominator by $\sqrt{x}$

$b = \frac{(1-2\sqrt{x}) *\sqrt{x}}{\sqrt{x}*\sqrt{x} }=\frac{1*\sqrt{x} -2\sqrt{x} *\sqrt{x} }{\sqrt{x} *\sqrt{x} }\\\\=\frac{\sqrt{x} -2x}{x}\\$

Now, find a +b

$a +b = \frac{2x+\sqrt{x} }{x}+\frac{\sqrt{x} -2x}{x}\\\\=\frac{2x+\sqrt{x} +\sqrt{x} -2x}{x}$

Combine like terms

$= \frac{2x-2x+\sqrt{x} +\sqrt{x} }{x}\\\\=\frac{2\sqrt{x} }{x}$

Now find (a + b)²

(a +b)² = $(\frac{2\sqrt{x} }{x})^{2}$

$= \frac{2^{2}*(\sqrt{x} )^{2}}{x^{2}}\\\\= \frac{4* x}{x^{2}}\\\\= \frac{4}{x}$

Hint: $\sqrt{x} *\sqrt{x} =\sqrt{x*x}=x$

5 0

3 years ago

Find the midpoint of a and b where a has coordinates (2,3) and b has coordinates (8,9).

kupik [55]

It should be about (5,5.5)

6 0

3 years ago

Read 2 more answers

HEY!!! YES, YOU!!! WANNA HELP OUT A FELLOW SUFFERING VICTIM OF MATH? NOWS YOUR CHANCE!!! PLEASE HELP! 10 PTS!!!

rosijanka [135]

Answer:

16 cm

Step-by-step explanation:

Suppose that x is the original width. If that original width is enlarged by a scale factor 5/2 that means that x is multiplied by 5/2 and after that multiplication we obtained new width, 40 cm.

Therefore,

x*(5/2) = 40

We multiply the equation by 2 and obtain:

x*5 = 40*2

5x = 80

Now we divide the equation by 5 and obtain:

x = 80/5

x = 16

We obtained that x, the original width was 16 cm

5 0

3 years ago

Alex has 3 times as many pets as Roman. If they have 24 altogether ,how many do they have ?

Viefleur [7K]

A= 3R
R = A/3
24= A + R
24= 3R + R
24 = 4R
6= R
A= 18

Roman = 6
Alex = 18

6+18 = 24

5 0

3 years ago

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If matrix A is of the size 2×3 and we are able to add matrix B to A. what must be the size of B be?​

If matrix A is of the size 2×3 and we are able to add matrix B to A. what must be the size of B be?