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4 years ago

What is the measure of MBN?

Mathematics

1 answer:

shusha [124]4 years ago

6 0

Answer:

180°

Step-by-step explanation:

The measure of MBN is equal to the measure of the central angle ahead it

that's mean the measure is 180° (90+90)

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Suppose that you are asked to conduct a study to determine whether smaller class

weeeeeb [17]

Answer:

a. correlation

b. inverse linear correlation exists If the higher the population of students lead to a decrease in test score,

c. yes

Step-by-step explanation:

a. Correlation is a measure of the amount of association existing between two variables.

b. For linear correlation, if points are plotted on a graph and all the points lie on a straight line, then perfect linear correlation is said to exist. When a straight line having a positive gradient can reasonably be drawn through points on a graph positive or direct linear correlation exists,

Similarly,when a straight line having a negative gradient can reasonably be drawn through points on a graph, negative or inverse linear correlation exists,

The results of this determination give values of r lying between +1 and −1, where +1 indicates perfect direct Positive linear correlation and −1 indicates perfect inverse correlation or Negative linear correlation and 0 indicates that no correlation exists.

If the higher the population of students lead to a decrease in test score, there will definitely be a negative correlation between class size and test score. i.e low class size result in high test score which consequently lead to high performance.

c. YES

A negative correlation means low class size result in high test score which consequently lead to better performance.

8 0

4 years ago

Use Stokes' Theorem to evaluate C F · dr F(x, y, z) = xyi + yzj + zxk, C is the boundary of the part of the paraboloid z = 1 − x

Serggg [28]

I assume $C$ has counterclockwise orientation when viewed from above.

By Stokes' theorem,

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S$

so we first compute the curl:

$\vec F(x,y,z)=xy\,\vec\imath+yz\,\vec\jmath+xz\,\vec k$

$\implies\nabla\times\vec F(x,y,z)=-y\,\vec\imath-z\,\vec\jmath-x\,\vec k$

Then parameterize $S$ by

$\vec r(u,v)=\cos u\sin v\,\vec\imath+\sin u\sin v\,\vec\jmath+\cos^2v\,\vec k$

where the $z$ -component is obtained from

$1-(\cos u\sin v)^2-(\sin u\sin v)^2=1-\sin^2v=\cos^2v$

with $0\le u\le\dfrac\pi2$ and $0\le v\le\dfrac\pi2$ .

Take the normal vector to $S$ to be

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

Then the line integral is equal in value to the surface integral,

$\displaystyle\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S$

$=\displaystyle\int_0^{\pi/2}\int_0^{\pi/2}(-\sin u\sin v\,\vec\imath-\cos^2v\,\vec\jmath-\cos u\sin v\,\vec k)\cdot(\vec r_v\times\vec r_u)\,\mathrm du\,\mathrm dv$