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3 years ago

The graph of a linear function is shown on the grid.

Mathematics

2 answers:

Len [333]3 years ago

8 0

Answer:

Step-by-step explanation:

Elza [17]3 years ago

6 0

Answer:

Option (A)

Step-by-step explanation:

Let the equation of the line passing through a point (x', y') and slope 'm' is,

y - y' = m(x - x')

Slope of the line passing through two points (0, 5) and (4, -7),

m = $\frac{y_2-y_1}{x_2-x_1}$

= $\frac{5+7}{0-4}$

= -3

As slope of the line is negative, Options (A) and (B) will be the possible options.

Therefore, equation of the line passing through (4, -7) will be,

y - (-7) = -3(x - 4)

y + 7 = -3(x - 4)

Therefore, Option (A) will be the correct option.

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Let f(x,y,z) = ztan-1(y2) i + z3ln(x2 + 1) j + z k. find the flux of f across the part of the paraboloid x2 + y2 + z = 3 that li

Sophie [7]

Consider the closed region $V$ bounded simultaneously by the paraboloid and plane, jointly denoted $S$ . By the divergence theorem,

$\displaystyle\iint_S\mathbf f(x,y,z)\cdot\mathrm dS=\iiint_V\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV$

And since we have

$\nabla\cdot\mathbf f(x,y,z)=1$

the volume integral will be much easier to compute. Converting to cylindrical coordinates, we have

$\displaystyle\iiint_V\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV=\iiint_V\mathrm dV$
$=\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}\int_{z=2}^{z=3-r^2}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta$
$=\displaystyle2\pi\int_{r=0}^{r=1}r(3-r^2-2)\,\mathrm dr$
$=\dfrac\pi2$

Then the integral over the paraboloid would be the difference of the integral over the total surface and the integral over the disk. Denoting the disk by $D$ , we have

$\displaystyle\iint_{S-D}\mathbf f\cdot\mathrm dS=\frac\pi2-\iint_D\mathbf f\cdot\mathrm dS$

Parameterize $D$ by

$\mathbf s(u,v)=u\cos v\,\mathbf i+u\sin v\,\mathbf j+2\,\mathbf k$
$\implies\mathbf s_u\times\mathbf s_v=u\,\mathbf k$

which would give a unit normal vector of $\mathbf k$ . However, the divergence theorem requires that the closed surface $S$ be oriented with outward-pointing normal vectors, which means we should instead use $\mathbf s_v\times\mathbf s_u=-u\,\mathbf k$ .

Now,

$\displaystyle\iint_D\mathbf f\cdot\mathrm dS=\int_{u=0}^{u=1}\int_{v=0}^{v=2\pi}\mathbf f(x(u,v),y(u,v),z(u,v))\cdot(-u\,\mathbf k)\,\mathrm dv\,\mathrm du$
$=\displaystyle-4\pi\int_{u=0}^{u=1}u\,\mathrm du$
$=-2\pi$

So, the flux over the paraboloid alone is

$\displaystyle\iint_{S-D}\mathbf f\cdot\mathrm dS=\frac\pi2-(-2\pi)=\dfrac{5\pi}2$

6 0

3 years ago

1.Which equation gives the direct variation if y=8 when x=2?

Mama L [17]

First one is y=4x and the second one is y=2x

3 0

3 years ago

Is " what is the typical amount of rainfall in Canada " a statistical question?

AysviL [449]

Answer:

Yes

Step-by-step explanation:

Yes, the question asks for an average not the rainfall on one specific day, therefore it is a statistical question.

(accidentally answered as a comment)

5 0

3 years ago

In a lab, a substance was cooked by 42 C over a period of 7 hours at a constant rate. What was the change in temperature each ho

Mekhanik [1.2K]

Given that we have the change in temperature over 7 hours and we are looking for the change over 1 hour, we can divide the total change in temperature by 7. Thus, the change in temperature would be $\frac{42}{7} C^{\circ}$ .

Additionally, this can be solved by equations:

$\dfrac{42 \,\textrm{C}^{\circ}}{7 \,\textrm{hours}} = \dfrac{x \,\textrm{C}^{\circ}}{1 \,\textrm{hour}}$

$1 \,\textrm{hour} \cdot \dfrac{42 \,\textrm{C}^{\circ}}{7 \,\textrm{hours}} = x \,\textrm{C}^{\circ}$

$\dfrac{42}{7} \,\textrm{C}^{\circ} = x \,\textrm{C}^{\circ}$

$\dfrac{42}{7} = x$

By using two different methods, we can determine that the change each hour was equal to 42/7 C° per hour.

6 0

3 years ago

Please help me with this problem

Nookie1986 [14]

In order for two lines to be perpendicular, their slopes must multiply together to equal to negative one
So we do negative one divided by 2/5 to get the slope of the red line
Which is -5/2
To check, we do 2/5 multiplied by -5/2 which equals to -1 so our answer is correct

8 0

3 years ago

Read 2 more answers