X = {(2, 4), (3, 4), (4,4), (5, 4)) Is x a function and why?

Mathematics

2 answers:

egoroff_w [7]2 years ago

6 0

Answer:

x is a function

since it forms a horizontal line it passes the vertical line test and is a function

kow [346]2 years ago

4 0

Because they all have a different x number. Even though the y numbers are the same you can tell wether a set of numbers are a function by the x numbers. So since there are different x numbers it is a function. I hope this helps!

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What is the value of x?

Elanso [62]

Since all the angles are congruent, the sides must be congruent too.

So, just have one equation on one side equal to another.

5x= 3x+6

Subtract 3x from both sides.

2x=6

Divide 2 into both sides.

x=3.

We can check this by seeing if all the sides are the same.

5(3)= 15

6(3)-5= 15

3(3)+6= 15

I hope this helps!
~cupcake

7 0

3 years ago

Find the following: F(x, y, z) = e^(xy) sin z j + y tan^−1(x/z)k Exercise Find the curl and the divergence of the vector field.

natulia [17]

$\vec F(x,y,z)=e^{xy}\sin z\,\vec\jmath+y\tan^{-1}\dfrac xz\,\vec k$

Divergence is easier to compute:

$\mathrm{div}\vec F=\dfrac{\partial(e^{xy}\sin z)}{\partial y}+\dfrac{\partial\left(y\tan^{-1}\frac xz\right)}{\partial z}$

$\mathrm{div}\vec F=xe^{xy}\sin z-\dfrac{xy}{x^2+z^2}$

Curl is a bit more tedious. Denote by $D_t$ the differential operator, namely the derivative with respect to the variable $t$ . Then

$\mathrm{curl}\vec F=\begin{vmatrix}\vec\imath&\vec\jmath&\vec k\\D_x&D_y&D_z\\0&e^{xy}\sin z&y\tan^{-1}\frac xz\end{vmatrix}$

$\mathrm{curl}\vec F=\left(D_y\left[y\tan^{-1}\dfrac xz\right]-D_z\left[e^{xy}\sin z\right]\right)\,\vec\imath-D_x\left[y\tan^{-1}\dfrac xz\right]\,\vec\jmath+D_x\left[e^{xy}\sin z}\right]\,\vec k$