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2 years ago

Find three different surfaces that contain the curve r(t) = t^2 i + lnt j + (1/t)k

Mathematics

1 answer:

Viefleur [7K]2 years ago

7 0

solution:

Consider the curve: r(t) = t²i +(int)j + 1/t k

X= t² , y = int ,z = 1/t

Using, x = t², z = 1/t

X = (1/z)²

Xz²= 1

Using y = int, z= 1/t

Y = in│1/z│

Using x = t², y = int

Y = int

= in(√x)

Hence , the required surface are,

Xz² = 1

Y = in│1/z│

Y= in(√x)

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Answer:

The multiplicative rate of change is $\dfrac{2}{5}.$

Step-by-step explanation:

You are given the function

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If the exponential function is written in the form

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In your case, the multiplicative rate of change is $\dfrac{2}{5}.$

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1 year ago

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ZanzabumX [31]

Answer:

a) 22.94 psi

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$f(x)={\frac {1}{\sigma {\sqrt {2\pi }}}}e^{-{\frac {1}{2}}\left({\frac {x-\mu }{\sigma }}\right)^{2}}$

where x = 22.94, $\mu = 31, \sigma = 2$

$f(22.94)={\frac {1}{2 {\sqrt {2\pi }}}}e^{-{\frac {1}{2}}\left({\frac {22.94-31}{2 }}\right)^{2}}$

$f(22.94)=0.2e^{-8.12} = 5.93\times10^{-5}$

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2 years ago

Squaring both sides of an equation is irreversible. Is Cubing both sides of an equation reversible? Provide numerical examples t

nikitadnepr [17]

Answer:

<h2>Cubing both sides of an equation is reversible.</h2>

Step-by-step explanation:

Squaring both sides of an equation is irreversible, because the square power of negative number gives a positive result, but you can't have a negative base with a positive number, given that the square root of a negative number doesn't exist for real numbers.

In case of cubic powers, this action is reversible, because the cubic root of a negative number is also a negative number. For example

$\sqrt[3]{x} =-1$

We cube both sides

$(\sqrt[3]{x} )^{3} =(-1)^{3} \\x=-1$

If we want to reverse the equation to the beginning, we can do it, using a cubic root on each side

$\sqrt[3]{x}=\sqrt[3]{-1} \\\sqrt[3]{x}=-1$

There you have it, cubing both sides of an equation is reversible.

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CaHeK987 [17]

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2 years ago

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