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2 years ago

Isaiah ran 100 meters on a 200 meter track. He started running on the 19 meter mark. On what Mark did he finish his run

Mathematics

2 answers:

guapka [62]2 years ago

5 0

Answer:

119

Step-by-step explanation:

19+100=119

masha68 [24]2 years ago

4 0

Depends on the amount of marks but if there are 200 then the answer would be 119

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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

What is 6 thousandths of a meter of a decimal

Svetllana [295]

0.006
That's you're answer

5 0

2 years ago

Read 2 more answers

kinata goes for swimming lessons every 5 days while wayo goes every 6 days. if both kinata and wayo had lessons together at the

Yakvenalex [24]

Answer:
30th day
Step-by-step explanation:
5*6=30
and 6*5=30
basically we have to take Lcm of 5 and 6=30
30th day they both will be together

3 0

3 years ago

Quadrilateral ABCD is reflected across the x-axis and then reflect across the y-axis to form quadrilateral A?B?C?D?. If the coor

Dmitriy789 [7]

Answer:

A'(7,-3)

Step-by-step explanation:

We were given the coordinates, A(-7,3) of quadrilateral ABCD and we want to find the image of A after a reflection across the x-axis followed by a reflection in the y-axis.

When we reflect A(-7,3) across the x-axis we negate the y-coordinate to obtain: (-7,-3).

When the image is again reflected in the across the y-axis, we negate the x-coordinate to get (--7,-3).

Therefore the coordinates of A' after the composed transformation is (7,-3).

8 0

2 years ago

Little Johnny is fleeing from a horde of zombies. He is 4000 feet from a safe zone where a gate will be closed in 3 minutes. If

Free_Kalibri [48]

Answer:

Johnny will be able to reach the safe zone before the gate is closed.

Step-by-step explanation:

Given that:

Distance of Little Johnny from safe zone = 4000 feet

Time = 3 minutes

Speed = 22 mph

To find:

Will Johnny be able to reach the safe zone ?

Solution:

Johnny can only be safe if he can travel 4000 feet in 3 minutes with the given speed.

Let us try to find out, the distance that he can travel in 3 minutes at speed of 22 mph.

Let us have a look at the formula of distance traveled:

$Distance = Speed \times Time$

Time = 3 minutes = $\frac{3}{60}$ hrs

Speed = 22 mph

$Distance = 22 \times \frac{3}{60}\\\Rightarrow Distance = \dfrac{22}{20}\ miles \\\Rightarrow Distance = 1.1\ miles$

We know that 1 mile = 5280 feet

Therefore 1.1 miles = 5280 $\times$ 1.1 feet = 5808 feet

Distance traveled by Little Johnny is greater than 4000 feet.

Therefore Johnny will be able to reach the safe zone before the gate is closed.

8 0

2 years ago