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PilotLPTM [1.2K]
2 years ago
12

Given the vectors w = <-5, 3> and z = <1, 4>, find the results of the vector subtractions. -w − z = z − w = w − z =

Mathematics
1 answer:
Elodia [21]2 years ago
4 0

Answer:

Concept: Linear Algebra

  1. Given two linearly independent vectors w and z
  2. We want -w-z
  3. Hence apply a negative gradient to w
  4. w=-<-5,3> =<5,-3>
  5. So <5,-3>-<1,4> = (<5-1>,<-3-4>)
  6. The answer is <4,-7>
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small cubes with edge lengths of 1/4 inch will be packed into the right rectangular prism shown.( the base is 4 1/2, the width i
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General Idea:

We need to find the volume of the small cube given the side length of the small cube as 1/4 inch.

Also we need to find the volume of the right rectangular prism with the given dimension (the height is 4 1/2, the width is 5, and the length is 3 3/4).

To find the number of small cubes that are needed to completely fill the right rectangular prism, we need to divide volume of right rectangular prism by volume of each small cube.

Formula Used:

Volume \; of \; Cube = a^3 \; \\\{where \; a \; is \; side \; length \; of \; cube\}\\\\Volume \; of  \; Right \; Rectangular  \; Prism=L \times W \times H\\\{Where  \; L \; is \; Length, \; W \; is \; Width, \;and  \; H \; is \; Height\}

Applying the concept:

Volume of Small Cube:

V_{cube}= (\frac{1}{4}  )^3= \frac{1}{64} \; in^3\\\\V_{Prism}=  3 \frac{3}{4}  \times 5 \times  4 \frac{1}{2}  = \frac{15}{4}  \times \frac{5}{1}  \times \frac{9}{2}  = \frac{675}{8}  \\\\Number \; of \; small \; cubes= \frac{V_{Prism}}{V_{Cube}}   = \frac{675}{8}  \div \frac{1}{64}  \\\\Flip \; the \; second \; fraction\; and \; multiply \; with \; the \; first \; fraction\\\\Number \; of \; small \; cubes \;= \frac{675}{8} \times \frac{64}{1}   = 5400

Conclusion:

The number of small cubes with side length as 1/4 inches that are needed to completely fill the right rectangular prism whose height is 4 1/2 inches, width is 5 inches, and length is 3 3/4 inches is <em><u>5400 </u></em>

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Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.
Keith_Richards [23]

Answer:

8.0 seconds to the nearest tenth,

Step-by-step explanation:

h=-16t^2 +vt + c.

-16t^2 + 116t + 101 = 0

t =  [ -116 + /- √(116^2 - 4*-16*101) ] / (-32)

t = (-116 +/- √19920) / (-32)

t = -0.79, 8.036  (we ignore the negative root)

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3 years ago
Given a force of 10N and an acceleration of 5m/s? What is the mass?
likoan [24]

Answer:

<h3>2kg = mass</h3>

Step-by-step explanation:

<h3>What is the mass?</h3>

Mass is a body of matter without definite shape.

Use the Newton's second law of motion formula.

Note: \longrightarrow \sf{F=M*A}

<u>Given:</u>

  • Force = 10N
  • Acceleration = 5m/s

First thing you do is divide.

10/5=2

= 2kg (mass)

Therefore, the final answer is 2kg (mass).

I hope this helps, let me know if you have any questions.

To learn more about the mass:

brainly.com/question/7580108

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