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3 years ago

Help please? ASAP :)

Mathematics

1 answer:

Juliette [100K]3 years ago

7 0

Answer: The Z-value is a test statistic for Z-tests that measures the difference between an observed statistic and its hypothesized population parameter in units of the standard deviation. ... A mold with a depth of 12 cm has a Z-value of 2, because its depth is two standard deviations greater than the mean

Step-by-step explanation:

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Panel 1 is the answer choice<br><br> Panel 2 is the question

Ierofanga [76]

D is the midpoint of A and B
A = (0,s)
B = (r,0)

Add up the x coordinates to get 0+r = r. Then cut that in half to get r/2
Similarly, do the same for the y coordinates: s+0 = s ---> s/2

So the location of point D is (r/2, s/2)

Answer: Choice C

8 0

3 years ago

Given the definitions of f (x) and g(x) below, find the value of (g • f)(9).

Stells [14]

9514 1404 393

Answer:

(g·f)(9) = 496

Step-by-step explanation:

One way to do this is to find the values of g(9) and f(9).

g(9) = (3x -1)x +14 = (3(9) -1)(9) +14 = 26(9) +14 = 248

f(9) = -(9) +11 = 2

Then ...

(g·f)(9) = g(9)·f(9) = 248·2

(g·f)(9) = 496

8 0

3 years ago

The perimeter of the entire garden.

Leno4ka [110]

Add up all the lengths of the garden and you will be able to get the perimeter.

8 0

1 year ago

Problem 4: Let F = (2z + 2)k be the flow field. Answer the following to verify the divergence theorem: a) Use definition to find

Viktor [21]

Given that you mention the divergence theorem, and that part (b) is asking you to find the downward flux through the disk $x^2+y^2\le3$ , I think it's same to assume that the hemisphere referred to in part (a) is the upper half of the sphere $x^2+y^2+z^2=3$ .

a. Let $C$ denote the hemispherical <u>c</u>ap $z=\sqrt{3-x^2-y^2}$ , parameterized by

$\vec r(u,v)=\sqrt3\cos u\sin v\,\vec\imath+\sqrt3\sin u\sin v\,\vec\jmath+\sqrt3\cos v\,\vec k$

with $0\le u\le2\pi$ and $0\le v\le\frac\pi2$ . Take the normal vector to $C$ to be

$\vec r_v\times\vec r_u=3\cos u\sin^2v\,\vec\imath+3\sin u\sin^2v\,\vec\jmath+3\sin v\cos v\,\vec k$

Then the upward flux of $\vec F=(2z+2)\,\vec k$ through $C$ is

$\displaystyle\iint_C\vec F\cdot\mathrm d\vec S=\int_0^{2\pi}\int_0^{\pi/2}((2\sqrt3\cos v+2)\,\vec k)\cdot(\vec r_v\times\vec r_u)\,\mathrm dv\,\mathrm du$

$\displaystyle=3\int_0^{2\pi}\int_0^{\pi/2}\sin2v(\sqrt3\cos v+1)\,\mathrm dv\,\mathrm du$

$=\boxed{2(3+2\sqrt3)\pi}$

b. Let $D$ be the disk that closes off the hemisphere $C$ , parameterized by

$\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath$

with $0\le u\le\sqrt3$ and $0\le v\le2\pi$ . Take the normal to $D$ to be

$\vec s_v\times\vec s_u=-u\,\vec k$

Then the downward flux of $\vec F$ through $D$ is

$\displaystyle\int_0^{2\pi}\int_0^{\sqrt3}(2\,\vec k)\cdot(\vec s_v\times\vec s_u)\,\mathrm du\,\mathrm dv=-2\int_0^{2\pi}\int_0^{\sqrt3}u\,\mathrm du\,\mathrm dv$

$=\boxed{-6\pi}$

c. The net flux is then $\boxed{4\sqrt3\pi}$ .

d. By the divergence theorem, the flux of $\vec F$ across the closed hemisphere $H$ with boundary $C\cup D$ is equal to the integral of $\mathrm{div}\vec F$ over its interior:

$\displaystyle\iint_{C\cup D}\vec F\cdot\mathrm d\vec S=\iiint_H\mathrm{div}\vec F\,\mathrm dV$

We have

$\mathrm{div}\vec F=\dfrac{\partial(2z+2)}{\partial z}=2$

so the volume integral is

$2\displaystyle\iiint_H\mathrm dV$

which is 2 times the volume of the hemisphere $H$ , so that the net flux is $\boxed{4\sqrt3\pi}$ . Just to confirm, we could compute the integral in spherical coordinates:

$\displaystyle2\int_0^{\pi/2}\int_0^{2\pi}\int_0^{\sqrt3}\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=4\sqrt3\pi$

4 0

3 years ago

Divide 54 into two parts so that four times the greater equals five time the less

LUCKY_DIMON [66]

Let the both the parts be 'x' and 'y'
x>y
We know that 4x = 5y
so x = 5y/4
x + y = 54
Replacing x we get
(5y/4) + y = 54
(5y +4y)/4 = 54
9y = 216
y = 24
Replacing y in ' x+y = 54'
we get x = 30

Hence the larger part is 30 whereas the smaller part is 24

5 0

2 years ago