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3 years ago

9

Consider the differential equation dydx=6x, dydx=6x, with initial condition y(0)=4y(0)=4.

1 answer:

topjm [15]3 years ago

4 0

Formatting is kind of messed up. I'm assuming the differential equations is dy/dx = 6x

You need to get all the x's on one side and y'all on the other.

dy =6x dx

Integrate both sides.

y = 3x^2 + C

Now plug in the given values

y(0) = 4 = 3(0)^2 + C

C = 0

y = 3x^2

Plug 1 in for x to find the value of y(1)

y(1) = 3(1)^2 = 3

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What are the solutions of x^2-2x+5=0

sweet [91]

The solution of $x^{2}-2 x+5=0$ are 1 + 2i and 1 – 2i

<u>Solution:</u>

Given, equation is $x^{2}-2 x+5=0$

We have to find the roots of the given quadratic equation

Now, let us use the quadratic formula

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$ --- (1)

<em><u>Let us determine the nature of roots:</u></em>

Here in $x^{2}-2 x+5=0$ a = 1 ; b = -2 ; c = 5

$b^2 - 4ac = 2^2 - 4(1)(5) = 4 - 20 = -16$

Since $b^2 - 4ac < 0$ , the roots obtained will be complex conjugates.

Now plug in values in eqn 1, we get,

$x=\frac{-(-2) \pm \sqrt{(-2)^{2}-4 \times 1 \times 5}}{2 \times 1}$

On solving we get,

$x=\frac{2 \pm \sqrt{4-20}}{2}$

$x=\frac{2 \pm \sqrt{-16}}{2}$

$x=\frac{2 \pm \sqrt{16} \times \sqrt{-1}}{2}$

we know that square root of -1 is "i" which is a complex number

$\begin{array}{l}{\mathrm{x}=\frac{2 \pm 4 i}{2}} \\\\ {\mathrm{x}=1 \pm 2 i}\end{array}$

Hence, the roots of the given quadratic equation are 1 + 2i and 1 – 2i

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2 years ago

What’s the appropriate volume of the cone 8in and 20in

Tasya [4]

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2 years ago

The times of the runners in a marathon are normally distributed, with a mean of 3 hours and 50 minutes and a standard deviation

balu736 [363]

Answer: 0.16

Step-by-step explanation:

Given that the run times provided are normally distributed ;

Mean(x) of distribution = 3 hours 50 minutes

Standard deviation(s) = 30 minutes

The probability that a randomly selected runner has a time less than or equal to 3 hours 20 minutes

3 hours 20 minutes = (3 hrs 50 mins - 30 mins):

This is equivalent to :

[mean(x) - 1 standard deviation]

z 1 standard deviation within the mean = 0.84

z, 1 standard deviation outside the mean equals:

P(1 - z value , 1standard deviation within the mean)

1 - 0.8413 = 0.1587

= 0.16

7 0

2 years ago

The point K(−6,−1) is translated 5 units up. What are the coordinates of the resulting point K´.

exis [7]

Answer:

-6...................

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2 years ago

Read 2 more answers

The question is in the picture, PLEASE HELPPP!

Mumz [18]

Answer:

1=c

Step-by-step explanation:

1=c

2=d

3=e

4=a

5=b

I know 1 and 2 are correct, but I am not sure about the others

I'm not too sure how to explain this, sorry

8 0

2 years ago