A FRANK RA FRANK FRANK riddle

Mathematics

2 answers:

podryga [215]3 years ago

6 0

what do you mean.. is this some other things not about math?

MakcuM [25]3 years ago

3 0

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What

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Evaluate the line integral ∫CF⋅dr, where F(x,y,z)=5sinxi+4cosyj−2xzk and C is given by the vector function r(t)=t3i−t2j+t1k , 0≤

pickupchik [31]

$\mathbf r(t)=x(t)\,\mathbf i+y(t)\,\mathbf j+z(t)\,\mathbf k$
$\implies\begin{cases}x(t)=t^3\\y(t)=-t^2\\z(t)=t\end{cases}$
$\implies\dfrac{\mathrm d\mathbf r}{\mathrm dt}=3t^2\,\mathbf i-2t\,\mathbf j+\mathbf k$

with $0\le t\le1$ . With this parameterization, the vector field can be written as

$\mathbf F(x,y,z)=\mathbf F(x(t),y(t),z(t))=5\sin(t^3)\,\mathbf i+4\cos(t^2)\,\mathbf j-2t^4\,\mathbf k$

Now the line integral is given by

$\displaystyle\int_C\mathbf F\cdot\mathrm d\mathbf r=\int_{t=0}^{t=1}\mathbf F(x(t),y(t),z(t))\cdot\dfrac{\mathrm d\mathbf r(t)}{\mathrm dt}\,\mathrm dt$
$=\displaystyle\int_0^1(15t^2\sin(t^3)-8t\cos(t^2)-2t^4)\,\mathrm dt$
$=-5\cos1-4\sin1+\dfrac{23}5$

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3 years ago

Can somebody help me with these math problems?

love history [14]

it would prob be be the letter c and u times 25 and 10 then divide the 5

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3 years ago

Define saturated and unsaturated fats

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$\fbox \red{Saturated fat}$

A saturated fat is a type of fat in which the fatty acid chains have all or predominantly single bonds. A fat is made of two kinds of smaller molecules: glycerol and fatty acids. Fats are made of long chains of carbon atoms. Some carbon atoms are linked by single bonds and others are linked by double bonds

$\fbox \red{unsaturated fat}$

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Thanku ❤️ have a great day ahead ✨☁️

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3 years ago

You are 3 times older than your younger sister and you are 12 years old. Write an equation to solve for your sister's age

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Answer: 3 x 12 Also, the answer to that is 36

Step-by-step explanation: Since you are three times older and you're 12 so we do 3 times 12.

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3 years ago

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The ratio of two number is 4:7 and their hcf is 6 .find their lcm

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