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2 years ago

Determine the derivative of f(x) = -5x+3x from first principles first Calculate

Mathematics

1 answer:

ASHA 777 [7]2 years ago

8 0

Answer:

The derivative of the function f(x) = -5x+3x is ----> <u>-2</u>

Step-by-step explanation:

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How do you write the sum of one-sixth of n and one-fifth of g

kati45 [8]

Answer: $\frac{n}{6}+\frac{g}{5}$

Step-by-step explanation:

One-sixth of n is n/6.

One-fifth of g is g/5.

The sum means to add, so the expression is $\frac{n}{6}+\frac{g}{5}$ .

8 0

1 year ago

Can someone help me please

marysya [2.9K]

Answer:

Step-by-step explanation:

8 0

3 years ago

Solution for dy/dx+xsin 2 y=x^3 cos^2y

vichka [17]

Rearrange the ODE as

$\dfrac{\mathrm dy}{\mathrm dx}+x\sin2y=x^3\cos^2y$
$\sec^2y\dfrac{\mathrm dy}{\mathrm dx}+x\sin2y\sec^2y=x^3$

Take $u=\tan y$ , so that $\dfrac{\mathrm du}{\mathrm dx}=\sec^2y\dfrac{\mathrm dy}{\mathrm dx}$ .

Supposing that $|y|$ , we have $\tan^{-1}u=y$ , from which it follows that

$\sin2y=2\sin y\cos y=2\dfrac u{\sqrt{u^2+1}}\dfrac1{\sqrt{u^2+1}}=\dfrac{2u}{u^2+1}$
$\sec^2y=1+\tan^2y=1+u^2$

So we can write the ODE as

$\dfrac{\mathrm du}{\mathrm dx}+2xu=x^3$

which is linear in $u$ . Multiplying both sides by $e^{x^2}$ , we have

$e^{x^2}\dfrac{\mathrm du}{\mathrm dx}+2xe^{x^2}u=x^3e^{x^2}$
$\dfrac{\mathrm d}{\mathrm dx}\bigg[e^{x^2}u\bigg]=x^3e^{x^2}$

Integrate both sides with respect to $x$ :

$\displaystyle\int\frac{\mathrm d}{\mathrm dx}\bigg[e^{x^2}u\bigg]\,\mathrm dx=\int x^3e^{x^2}\,\mathrm dx$
$e^{x^2}u=\displaystyle\int x^3e^{x^2}\,\mathrm dx$

Substitute $t=x^2$ , so that $\mathrm dt=2x\,\mathrm dx$ . Then

$\displaystyle\int x^3e^{x^2}\,\mathrm dx=\frac12\int 2xx^2e^{x^2}\,\mathrm dx=\frac12\int te^t\,\mathrm dt$

Integrate the right hand side by parts using

$f=t\implies\mathrm df=\mathrm dt$
$\mathrm dg=e^t\,\mathrm dt\implies g=e^t$
$\displaystyle\frac12\int te^t\,\mathrm dt=\frac12\left(te^t-\int e^t\,\mathrm dt\right)$

You should end up with

$e^{x^2}u=\dfrac12e^{x^2}(x^2-1)+C$
$u=\dfrac{x^2-1}2+Ce^{-x^2}$
$\tan y=\dfrac{x^2-1}2+Ce^{-x^2}$

and provided that we restrict $|y|$ , we can write

$y=\tan^{-1}\left(\dfrac{x^2-1}2+Ce^{-x^2}\right)$

5 0

3 years ago

Rabies is an often-fatal disease typically transmitted through the bite of an infected animal. The state of Florida has been rec

slega [8]

Answer:

a) 3.6

b) 1.897

c)0.0273

d) 0.9727

Step-by-step explanation:

Rabies has a rare occurrence and we can assume that events are independent. So, X the count of rabies cases reported in a given week is a Poisson random variable with μ=3.6.

The mean of a Poisson random variable X is μ.

mean=E(X)=μ=3.6.

The standard deviation of a Poisson random variable X is √μ.

standard deviation=S.D(X)=√μ=√3.6=1.897.

The probability for Poisson random variable X can be calculated as

P(X=x)=(e^-μ)(μ^x)/x!

where x=0,1,2,3,...

So,

P(no case of rabies)=P(X=0)=e^-3.6(3.6^0)/0!

P(no case of rabies)=P(X=0)=0.0273.

P(at least one case of rabies)=P(X≥1)=1-P(X<1)=1-P(X=0)

P(at least one case of rabies)=1-0.0273=0.9727

8 0

2 years ago

Do you agree that, "Celebrities and sports figures should not be viewed as positive role models, because they are not always who

natita [175]

Answer:

over. The

remaining cake is split into 4 equa

Step-by-step explanation:

over. The

remaining cake is split into 4 equa

5 0

2 years ago

Determine the derivative of f(x) = -5x+3x from first principles first Calculate​

Determine the derivative of f(x) = -5x+3x from first principles first Calculate