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3 years ago

identify the coordinates of four points on the line with each given slope and y-intercept. slope= -1 and that y-intercept = 8

Mathematics

1 answer:

faust18 [17]3 years ago

3 0

Answer:

747_7_7_7_7_7"7"++"_+$+3+38

Step-by-step explanation:

327$-$+$+_+_+_+_+4+

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What is 62.713 rounded to the nearest hundredth?

irina [24]

62.71 would be the answer

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3 years ago

Louis wants to carpet the rectangular floor of his basement. The basement has an area of 864 square feet. The width of the basem

Mice21 [21]

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3 years ago

A/ How many hours does it take to fill the pool?

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3 years ago

The circumference of a circle is 138.16 centimeters. What is the area of the circle?

vodomira [7]

Circumference formula tells you $C=2 \pi r$

 $C=2 \pi r$
 $138.16=2 \pi r$
 $21.99= r$
 $r=21.99cm$ 
The formula to find the area of a circle is $A= \pi r^2$

 $A= \pi r^2$
 $A= \pi (21.99)^2$
 $A= \pi (483.56)$
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6 0

3 years ago

Determine whether or not the vector field is conservative. if it is conservative, find a function f such that f = ∇f. (if the ve

Akimi4 [234]

A three-dimensional vector field is conservative if it is also irrotational, i.e. its curl is $\mathbf 0$ . We have

$\nabla\times\mathbf f(x,y,z)=-2e^{-x}\,\mathbf k$

so this vector field is not conservative.

- - -

Another way of determining the same result: We want to find a scalar function $f(x,y,z)$ such that its gradient is equal to the given vector field, $\mathbf f(x,y,z)$ :

$\nabla f(x,y,z)=\mathbf f(x,y,z)$

For this to happen, we need to satisfy

$\begin{cases}f_x=ye^{-x}\\f_y=e^{-x}\\f_z=2z\end{cases}$

From the first equation, integrating with respect to $x$ yields

$f_x=ye^{-x}\implies f(x,y,z)=-ye^{-x}+g(y,z)$

Note that $g$ *must* be a function of $y,z$ only.

Now differentiate with respect to $y$ and we have

$f_y=-e^{-x}+g_y=e^{-x}\implies g_y=2e^{-x}\implies g(y,z)=2ye^{-x}+\cdots$

but this contradicts the assumption that $g(y,z)$ is independent of $x$ . So, the scalar potential function does not exist, and therefore the vector field is not conservative.

8 0

3 years ago