5.

Find a parametric representation for the surface. The plane through the origin that contains the vectors i - j and j - k

boyakko [2]

Answer:

parametric representation: x = u, y = v - u , z = - v

Explanation:

Given vectors :

i - j , j - k

represent the vector equation of the plane as:

r ( u, v ) = r₀ + <em>u</em>a + vb

where: r₀ = position vector

u and v = real numbers

a and b = nonparallel vectors

expressing the nonparallel vectors as :

a = i -j , b = j - k , r = ( x,y,z ) and r₀ = ( x₀, y₀, z₀ )

hence we can express vector equation of the plane as

r(u,v) = ( x₀ + u, y₀ - u + v, z₀ - v )

Finally the parametric representation of the surface through (0,0,0) i.e. origin = 0

( x, y , z ) = ( x₀ + u, y₀ - u + v, z₀ - v )

x = 0 + u ,

y = 0 - u + v

z = 0 - v

∴ parametric representation: x = u, y = v - u , z = - v

3 0

3 years ago

A piano tuner is using a 392 Hz tuning fork to tune the wire for a G-Natural note. She hears 4 beats per second. What are the tw

inysia [295]

A beat is an interference pattern between two sounds of slightly different frequencies, perceived as a periodic variation in volume whose rate is the difference of the two frequencies. Frequency beat is equal to,

$f_{beat} =| f_2\pm f_1 |$

The reference frequency in our case would be 392Hz, and since there is the possibility of the upper and lower range for the amount of beats per second that the two possible frequencies are heard would be

$f_{beat} =|392+4|= 396Hz$

$f_{beat} =|392-4|=388Hz$

Therefore the two possible frequencies the piano wire is vibrating at, would be 396Hz and 388Hz

5 0

3 years ago

You find a micrometer (a tool used to

MakcuM [25]

Explanation:

A micrometer is a measuring device or an instrument which is used to measure very minute measurements very accurately and precisely. It is mathematical tool used to provide accurate measurement for any mechanical components.

Now, if the micrometer that I have found is badly bent, it would provide faulty or wrong measurements both in terms of precision and accuracy when compared to a high quality meter stick.

3 0

3 years ago

If the distance between two asteroids is halved, the gravitational force they exert on each other will

mamaluj [8]

Answer:

e) Be four times greater

Explanation:

Here we have to use Newton's gravitational law that relates the gravitational force between two objects with their masses ( $m_{1}$ & $m_{2}$ ) and the distance between them ( $r$ ) in the next way:

$F=G\frac{m_{1}m_{2}}{r^{2}}$ (2)

Now if distance between asteroids is halved:

$F_{2}=G\frac{m_{1}m_{2}}{(\frac{r}{2})^{2}}$

$F_{2}=G\frac{m_{1}m_{2}}{\frac{r^{2}}{4}}$

$F_{2}=G\frac{4m_{1}m_{2}}{r^{2}}=4G\frac{m_{1}m_{2}}{r^{2}}$

Note that $G\frac{m_{1}m_{2}}{r^{2}}$ because (1) is F so:

$F_{2}=4F$

It's four times greater!

3 0

3 years ago

Hi everyone, I need help on the question: Why are humans the most dangerous creatures in the ocean

kozerog [31]

HUMAN ACTIVITIES ARE threatening the health of the world's oceans. More than 80 percent of marine pollution comes from land-based activities. From coral bleaching to sea level rise, entire marine ecosystems are rapidly changing.

Global warming is causing sea levels to rise, threatening coastal population centers. Many pesticides and nutrients used in agriculture end up in the coastal waters, resulting in oxygen depletion that kills marine plants and shellfish. Factories and industrial plants discharge sewage and other runoff into the oceans. Oil spills pollute the oceans, though U.S. water-sewage treatment plants discharge twice as much oil each year as tanker spills. Air pollution is responsible for almost one-third of the toxic contaminants and nutrients that enter coastal areas and oceans. The United Nations Food and Agriculture Organization estimates that 31.4 percent of fish stocks are either fished to capacity or over-fished.

7 0

3 years ago