Workout the following divisions.

Mathematics

1 answer:

IgorC [24]3 years ago

4 0

Answer:

Here. Tell me if you don't understand my writing.

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Find the Probability of pulling a green marble from a bag with six green and eight blue marbles.

jeka57 [31]

Answer:

6/14 or in its simplest form 3/7

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3 years ago

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Use synthetic substitution to find f(3) and f(-4) for f(x)= x^4 - 8x- 11.

AveGali [126]

Answer:

f(3)=56, f(-4)=277

Step-by-step explanation:

f(x)=x^4-8x-11

f(3)=3^4-8(3)-11=3*3*3*3-24-11=9*3*3-35=27*3-25=81-25=56

f(-4)=(-4)^4-8(-4)-11=(-4)(-4)(-4)(-4)+32-11=(16)(16)+32-11=256+32-11=288-11=277

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3 years ago

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Use the substitution of x=e^{t} to transform the given Cauchy-Euler differential equation to a differential equation with consta

kherson [118]

By the chain rule,

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm dt}\dfrac{\mathrm dt}{\mathrm dx}\implies\dfrac{\mathrm dy}{\mathrm dt}=x\dfrac{\mathrm dy}{\mathrm dx}$

which follows from $x=e^t\implies t=\ln x\implies\dfrac{\mathrm dt}{\mathrm dx}=\dfrac1x$ .

$\dfrac{\mathrm dy}{\mathrm dt}$ is then a function of $x$ ; denote this function by $f(x)$ . Then by the product rule,

$\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1x\dfrac{\mathrm dy}{\mathrm dt}\right]=-\dfrac1{x^2}\dfrac{\mathrm dy}{\mathrm dt}+\dfrac1x\dfrac{\mathrm df}{\mathrm dx}$