Determine the maximum number of zeros of the polynomial function 5x^3-3x^2+2x+3.

Mathematics

2 answers:

serg [7]3 years ago

4 0

D)4 is the answer jcidifodofif

HACTEHA [7]3 years ago

3 0

D.4 the answer is D Hanns

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Show that if the vector field F = Pi + Qj + Rk is conservative and P, Q, R have continuous first-order partial derivatives, then

olchik [2.2K]

Answer:

It is proved that $\frac{\partial P}{\partial y}=\frac{\partial Q}{\partial x}, \frac{\partial P}{\partial z}=\frac{\partial R}{\partial x}, \frac{\partial Q}{\partial z}=\frac{\partial R}{\partial y}$

Step-by-step explanation:

Given vector field,

$F=P\uvec{i}+Q\uvec{j}+R\uvec{k}$

Where,

$P=f_x=\frac{\partial f}{\partial x}, Q=f_y=\frac{\partial f}{\partial y}, R=f_z=\frac{\partial f}{\partial z}$

To show,

$\frac{\partial P}{\partial y}=\frac{\partial Q}{\partial x}, \frac{\partial P}{\partial z}=\frac{\partial R}{\partial x}, \frac{\partial Q}{\partial z}=\frac{\partial R}{\partial y}$

Consider,

$\frac{\partial P}{\partial y}=\frac{\partial}{\partial y}(\frac{\partial f}{\partial x})=\frac{\partial^2 f}{\partial y\partial x}=\frac{\partial^2 f}{\partial x\partial y}=\frac{\partial }{\partial x}(\frac{\partial f}{\partial y})=\frac{\partial Q}{\partial x}$

$\frac{\partial P}{\partial z}=\frac{\partial}{\partial z}(\frac{\partial f}{\partial x})=\frac{\partial^2 f}{\partial z\partial x}=\frac{\partial^2 f}{\partial x\partial z}=\frac{\partial }{\partial x}(\frac{\partial f}{\partial z})=\frac{\partial R}{\partial x}$

$\frac{\partial Q}{\partial z}=\frac{\partial}{\partial z}(\frac{\partial f}{\partial y})=\frac{\partial^2 f}{\partial z\partial y}=\frac{\partial^2 f}{\partial y\partial z}=\frac{\partial}{\partial y}(\frac{\partial f}{\partial z})=\frac{\partial R}{\partial y}$

Hence proved.

4 0

3 years ago

Will ran 3.23 km the first week and 4.15 km the second week. Chuck ran 8.75 km in two weeks.

Lostsunrise [7]

Will ran 3.23 + 4.15 = 7.38 in those 2 weeks, which rounds up to 7.4 km.
Chuck ran 8.75, which rounds to 8.8.

8.8 - 7.4 = 1.4 km
This means that Chuck ran 1.4 km more than Will, therefore the answer is D. about 1.4 km.

Hope this helps :)

6 0

3 years ago

Read 2 more answers

3. Alex is enjoying playing in the pool. He enjoys jumping

hichkok12 [17]

Answer:

32 degrees celsius

Step-by-step explanation:

To find the difference between two numbers, take the end point and subtract the start point from it.

End point = 42 degrees

Start point = 10 degrees

42 - 10 = 32 degree difference