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tekilochka [14]
3 years ago
13

Rip van winkle sell asleep for a very long time when he fell asleep, his beard was 8 millimeters long and each passing week and

grew 2 additional millimeters
graph the relationship between the length of rip van winkle‘s beard (in millimeters) and time (in seconds)

please answer asap

Mathematics
2 answers:
Phoenix [80]3 years ago
8 0

Answer:

I am not sure how the graph works but the first green dot should be dragged down to the point where it is at 16 millimeters. The second green dot should stay where it is at 44 millimeters. Hope this helps!

Step-by-step explanation:

masya89 [10]3 years ago
4 0

Answer:

Time in weeks you mean not seconds.

His beard should be graphed at point xy 1, 8 and continue at a gradient rate 8 rise / 1 rise showing m = 8/1 . to show one week to be able to meet up with .

Step-by-step explanation:

There are 604800 seconds in a week so first multiply by 5.5 weeks to find the first green dot. 604800 x 5.5 = 3326400 so we know the .5 option shows a rounded next week number.

We can either work downwards to zero or start at 1,8 ever way they will be even balance as 8/32 = 4 8/36 = 4.4 growth and this for example would show a rounded amount, so that 8/8 would be 8 and show the first week, or can be skipped out and start with y = 2x + 10 and then when referring to show .5 growth it would still be a whole number within the equation representing 12 and still be a whole number representing 2 weeks.

The graph does not speak of seconds but weeks, but if you want to use the above and try for 604800 seconds as shown for 1 week, you will have a tough time graphing. Stick to 2,4,6 8, 10, 12, 14, 16, 18 weeks multiplied by 12 = y = 1 + 8 = 0  

y = 2x +8 +2 = 1

y = 3x + 8 +2 = 2  

etc etc....

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For each of the following vector fields F , decide whether it is conservative or not by computing curl F . Type in a potential f
Phantasy [73]

The key idea is that, if a vector field is conservative, then it has curl 0. Equivalently, if the curl is not 0, then the field is not conservative. But if we find that the curl is 0, that on its own doesn't mean the field is conservative.

1.

\mathrm{curl}\vec F=\dfrac{\partial(5x+10y)}{\partial x}-\dfrac{\partial(-6x+5y)}{\partial y}=5-5=0

We want to find f such that \nabla f=\vec F. This means

\dfrac{\partial f}{\partial x}=-6x+5y\implies f(x,y)=-3x^2+5xy+g(y)

\dfrac{\partial f}{\partial y}=5x+10y=5x+\dfrac{\mathrm dg}{\mathrm dy}\implies\dfrac{\mathrm dg}{\mathrm dy}=10y\implies g(y)=5y^2+C

\implies\boxed{f(x,y)=-3x^2+5xy+5y^2+C}

so \vec F is conservative.

2.

\mathrm{curl}\vec F=\left(\dfrac{\partial(-2y)}{\partial z}-\dfrac{\partial(1)}{\partial y}\right)\vec\imath+\left(\dfrac{\partial(-3x)}{\partial z}-\dfrac{\partial(1)}{\partial z}\right)\vec\jmath+\left(\dfrac{\partial(-2y)}{\partial x}-\dfrac{\partial(-3x)}{\partial y}\right)\vec k=\vec0

Then

\dfrac{\partial f}{\partial x}=-3x\implies f(x,y,z)=-\dfrac32x^2+g(y,z)

\dfrac{\partial f}{\partial y}=-2y=\dfrac{\partial g}{\partial y}\implies g(y,z)=-y^2+h(y)

\dfrac{\partial f}{\partial z}=1=\dfrac{\mathrm dh}{\mathrm dz}\implies h(z)=z+C

\implies\boxed{f(x,y,z)=-\dfrac32x^2-y^2+z+C}

so \vec F is conservative.

3.

\mathrm{curl}\vec F=\dfrac{\partial(10y-3x\cos y)}{\partial x}-\dfrac{\partial(-\sin y)}{\partial y}=-3\cos y+\cos y=-2\cos y\neq0

so \vec F is not conservative.

4.

\mathrm{curl}\vec F=\left(\dfrac{\partial(5y^2)}{\partial z}-\dfrac{\partial(5z^2)}{\partial y}\right)\vec\imath+\left(\dfrac{\partial(-3x^2)}{\partial z}-\dfrac{\partial(5z^2)}{\partial x}\right)\vec\jmath+\left(\dfrac{\partial(5y^2)}{\partial x}-\dfrac{\partial(-3x^2)}{\partial y}\right)\vec k=\vec0

Then

\dfrac{\partial f}{\partial x}=-3x^2\implies f(x,y,z)=-x^3+g(y,z)

\dfrac{\partial f}{\partial y}=5y^2=\dfrac{\partial g}{\partial y}\implies g(y,z)=\dfrac53y^3+h(z)

\dfrac{\partial f}{\partial z}=5z^2=\dfrac{\mathrm dh}{\mathrm dz}\implies h(z)=\dfrac53z^3+C

\implies\boxed{f(x,y,z)=-x^3+\dfrac53y^3+\dfrac53z^3+C}

so \vec F is conservative.

4 0
4 years ago
Pls solve question 4b. Verrry urgent . Ok tyy
kodGreya [7K]

Answer:

y = 3\left(x-\dfrac{3}{2}\right)^2+\dfrac{41}{4}

Step-by-step explanation:

Given equation:

y = 3x^2 - 9x + 17

Factor out 3 from the first 2 terms:

y = 3(x^2 - 3x) + 17

Divide the coefficient of x by 2 and square it:  (-3 ÷ 2)² = 9/4

Add this inside the parentheses and subtract the distributed value of it outside the parentheses:

y = 3\left(x^2 - 3x+\dfrac{9}{4}\right) + 17-\dfrac{27}{4}

Factor the parentheses and combine the constants:

y = 3\left(x-\dfrac{3}{2}\right)^2+\dfrac{41}{4}

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