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2 years ago

MATHEMATICS if the diagonal of a square is 12cm, calculate the area and the perimeter of the square. 72cm

Mathematics

1 answer:

nata0808 [166]2 years ago

6 0

Answer:

$diagonal \: of \: square = a \sqrt{2} \\ 12 = a \sqrt{2} \\ \frac{12}{ \sqrt{2} } = a \\ \: a = 6 \sqrt{2} \\ now \: area \: of \: square = {l}^{2} \\ = (6 \sqrt{2) {}^{2} } \\ = 72cm {}^{2} \\ again \: perimeter \: of \: square = 4l \\ = 4 \times (6 \sqrt{2} ) \\ = 33.94cm$

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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

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3 years ago

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I am Lyosha [343]

Answer:

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Step-by-step explanation:

We can get the answer by subtracting the decimal by one.

2/5 = 0.4

1 - 0.4 = 0.6

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2 years ago

Help me answer these PLEASE ASAP

Hoochie [10]

Answer:

Answered below

Step-by-step explanation:

Sheet 1: Question 3

Vertically opposite angles are equal so you will equate the angles given,

∠LPN = ∠OPM

7 + 13x = -20 + 16x

27 = 3x

x = 9

Sheet 1: Question 4

Vertically opposite angles are equal so you will equate the angles given,

∠ABD = ∠EBC

2x + 20 = 3x + 15

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x = 5

Sheet 1: Question 5

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Vertically opposite angles are equal so you will equate the angles given,

∠SOP = ∠ROQ

5x = 4x + 10

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Sheet 1: Question 6

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∠4 + ∠1 + 41 = 180° (because all angles on a straight line are equal to 180°)

∠4 + 72 + 41 = 180

∠4 = 67°

∠3 = 41° (because vertically opposite angles)

∠2 = 67° (because vertically opposite angles)

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Step 1: Find the value of x

Sum of complementary angles is equal to 90°

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7x + 4 + 4x + 9 = 90°

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Angle A: 7x + 4

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Angle B: 4x + 9

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Angle B = 37°

Sheet 3: Question 3

Step 1: Find the value of x

Sum of supplementary angles is equal to 180°.

Angle A + Angle B = 180°

3x - 7 + 2x + 2 = 180°

5x = 185

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Step 2: Find angle A and angle B using x

Angle A: 3x - 7

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Sum of supplementary angles is equal to 180°.

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Sheet 4: Question 2

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Sheet 4: Question 3

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MATHEMATICS if the diagonal of a square is 12cm, calculate the area and the perimeter of the square. 72cm​

MATHEMATICS if the diagonal of a square is 12cm, calculate the area and the perimeter of the square. 72cm