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3 years ago

State the value of the discriminate. Then determine the number of real roots of the equation.

Mathematics

1 answer:

nika2105 [10]3 years ago

8 0

Answer:

no real solutions

Step-by-step explanation:

Given a quadratic equation in standard form

ax² + bx + c = 0 : a ≠ 0

Then the nature of the roots can be determined from the discriminant

b² - 4ac

• If b² - 4ac > 0 then 2 real and distinct roots

• If b² - 4ac = 0 then 2 real and equal roots

• If b² - 4ac < 0 then no real roots

Given

n(7n + 8) = - 10 ← distribute left side

7n² + 8n = - 10 ( add 10 to both sides )

7n² + 8n + 10 = 0 ← in standard form

with a = 7, b = 8 and c = 10, thus

b² - 4ac = 8² - (4 × 7 × 10) = 64 - 280 = - 216

Since b² - 4ac < 0 the equation has no real roots

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In a lab experiment, 2200 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to do

ratelena [41]

The answer would be 5866 because after it multiplied twice it would be at 8800 at that rate it would be gaining 1466.66 an hour so add that to 4400 and u get 5866

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3 years ago

Suppose that a spherical droplet of liquid evaporates at a rate that is proportional to its surface area: where V = volume (mm3

Alex

Answer:

V = 20.2969 mm^3 @ t = 10

r = 1.692 mm @ t = 10

Step-by-step explanation:

The solution to the first order ordinary differential equation:

$\frac{dV}{dt} = -kA$

Using Euler's method

$\frac{dVi}{dt} = -k *4pi*r^2_{i} = -k *4pi*(\frac {3 V_{i} }{4pi})^(2/3)\\ V_{i+1} = V'_{i} *h + V_{i} \\$

Where initial droplet volume is:

$V(0) = \frac{4pi}{3} * r(0)^3 = \frac{4pi}{3} * 2.5^3 = 65.45 mm^3$

Hence, the iterative solution will be as next:

i = 1, ti = 0, Vi = 65.45

$V'_{i} = -k *4pi*(\frac{3*65.45}{4pi})^(2/3) = -6.283\\V_{i+1} = 65.45-6.283*0.25 = 63.88$

i = 2, ti = 0.5, Vi = 63.88

$V'_{i} = -k *4pi*(\frac{3*63.88}{4pi})^(2/3) = -6.182\\V_{i+1} = 63.88-6.182*0.25 = 62.33$

i = 3, ti = 1, Vi = 62.33

$V'_{i} = -k *4pi*(\frac{3*62.33}{4pi})^(2/3) = -6.082\\V_{i+1} = 62.33-6.082*0.25 = 60.813$

We compute the next iterations in MATLAB (see attachment)

Volume @ t = 10 is = 20.2969

The droplet radius at t=10 mins

$r(10) = (\frac{3*20.2969}{4pi})^(2/3) = 1.692 mm\\$

The average change of droplet radius with time is:

Δr/Δt = $\frac{r(10) - r(0)}{10-0} = \frac{1.692 - 2.5}{10} = -0.0808 mm/min$

The value of the evaporation rate is close the value of k = 0.08 mm/min

Hence, the results are accurate and consistent!

5 0

3 years ago

Divide £12 between mick and sharon in the ratio 2:4

antiseptic1488 [7]

Answer:mick share is £4 while Sharon share is £8

Step-by-step explanation:

Money to be shared=£12

Mick : sharon=2:4

Sum of ratio=2+4=6

Mick share=2/6 x 12

Mick share=(2x12)/6

Mick share=24/6

Mick share=4

Sharon share=4/6 x 12

Sharon share=(4x12)/6

Sharon share=48/6

Sharon share=8

6 0

3 years ago

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horrorfan [7]

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2 years ago

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2 years ago

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