Answer:
<h2>answer to this question is (c) </h2>
<h3>hope you are satisfied with my answer</h3>
A nebula is an enormous cloud of dust and gas occupying the space between stars and acting as a nursery for new stars. The roots of the word come from Latin nebula, which means a “mist, vapor, fog, smoke, exhalation.” Nebulae are made up of dust, basic elements such as hydrogen and other ionized gases.
Protective systems are methods of protecting workers from cave-ins of material that can fall or roll into an excavation, or from the collapse of nearby structures. As mentioned in earlier chapters, if an excavation is less than 5 feet deep, OSHA does not require a protective systems unless the competent person sees signs of a potential cave-in. (It is important to remember that a wall collapse in a trench four and 1/2 feet deep can still have serious results!) For trenches between 5 feet and 20 feet deep, shoring and sheeting, shielding, sloping and benching are all acceptable protective measures. It is up to the planners of the construction project and the competent person on site to determine which systems will work best. If an excavation is greater than 20 feet deep, a registered professional engineer must design the protective system.
Shoring systems are structures of timber, mechanical, or hydraulic systems that support the sides of an excavation and which are designed to prevent cave-ins.Sheeting is a type of shoring system that keeps the earth in position. It can be driven into the ground or work in conjunction with a shoring system. Driven sheeting is most frequently used for excavations open for long periods of time. Another type of sheeting, in which plates or shoring grade plywood (sometimes called Finland form) is used in conjunction with strutted systems such as hydraulic or timber shoring. These strutted systems are also referred to as active systems. The most frequently used strutted system involves aluminum hydraulic shoreswhich are lightweight, re-usable and installed and removed completely from above
Answer:
this pic is to blury sorry
Explanation:
Solution. To check whether the vectors are linearly independent, we must answer the following question: if a linear combination of the vectors is the zero vector, is it necessarily true that all the coefficients are zeros?
Suppose that
x 1 ⃗v 1 + x 2 ⃗v 2 + x 3 ( ⃗v 1 + ⃗v 2 + ⃗v 3 ) = ⃗0
(a linear combination of the vectors is the zero vector). Is it necessarily true that x1 =x2 =x3 =0?
We have
x1⃗v1 + x2⃗v2 + x3(⃗v1 + ⃗v2 + ⃗v3) = x1⃗v1 + x2⃗v2 + x3⃗v1 + x3⃗v2 + x3⃗v3
=(x1 + x3)⃗v1 + (x2 + x3)⃗v2 + x3⃗v3 = ⃗0.
Since ⃗v1, ⃗v2, and ⃗v3 are linearly independent, we must have the coeffi-
cients of the linear combination equal to 0, that is, we must have
x1 + x3 = 0 x2 + x3 = 0 ,
x3 = 0
from which it follows that we must have x1 = x2 = x3 = 0. Hence the
vectors ⃗v1, ⃗v2, and ⃗v1 + ⃗v2 + ⃗v3 are linearly independent.
Answer. The vectors ⃗v1, ⃗v2, and ⃗v1 + ⃗v2 + ⃗v3 are linearly independent.
