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Alchen [17]
4 years ago
8

In parts ​(a) through ​(e)​ below, mark the given statement as True or False. Justify each answer. All vectors are in set of rea

l numbers R Superscript nℝn. a. vtimes•vequals=Bold left norm v right normvsquared2 Choose the correct answer below. A. The given statement is false. It is not possible for it to be true because vtimes•v simplifies to a ​vector, whereas Bold left norm v right normvsquared2 simplifies to a scalar. B. The given statement is true. By the definition of the length of a vector v​, Bold left norm v right normvequals=StartRoot Bold v times Bold v EndRootv•v. C. The given statement is false. By the definition of the length of a vector ​v, Bold left norm v right normvequals=vtimes•v. It follows that Bold left norm v right normvsquared2equals=​(vtimes•v​)squared2. D. The given statement is true. By the definition of the length of a vector ​v, Bold left norm v right normvequals=vtimes•v. It follows that Bold left norm v right normvsquared2equals=​(vtimes•v​)squared2.
Mathematics
1 answer:
Oxana [17]4 years ago
5 0

Answer:

(c)

"The given statement is true, by definition of length of a vector v, ||v|| = \sqrt{v\bullet v}"

Step-by-step explanation:

(a) v  \bullet v = || v ||^2

That is completely correct Remember that if  v = (x_1,x_2,x_3)\\ then

v \bullet v = x_1*x_1+x_2*x_2+x_3*x_3 = x_1^2+x_2^2+x_3^2 = ||v||^2

Therefore the correct answer would be (c).

"The given statement is true, by definition of length of a vector v, ||v|| = \sqrt{v\bullet v}"

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A helicopter starting on the ground is rising directly
Serggg [28]

Answer:

Oook, quick setup: pick a cartesian plane, be (0;y(t))the position of the helicopter as time passes, and (x(t);0) your position as you start running. In my horrible sketch, the green line is the distance when you start running, the red line is the distance you need,  in general what you want is to move one end of the segment up, the other right, and stretch it.

That distance is easily found with the formula for the distance between two points in the plane, or d=\sqrt{(\Delta x)^2+(\Delta y)^2}= \sqrt{x^2(t)+y^2(t)} (playing a bit with the squares). At this point we need to write down expressions for both x(t), y(t) and find at what value of t we need to evaluate our distance.

For the sake of semplicity, let's start measuring times the moment you start running. Since speed is constant, both expressions will be of the form s=vt+s_0

The equation for the runner becomes simply x(t)=10t, since you haven't moved until the heli is high enough.

The equation of the helicopter is y=25t+30 since the heli is 30ft above ground when you start running.

Finally, we need to know how many seconds have passed when the heli is at 60 ft above ground. that happens when 60=25t+30 \rightarrow t=\frac{30}{25} = 1.20s. in this time, you are at  x(1.2)=10(1.2)=12ft from the origin.

Plugging it in the distance formula you get: \sqrt{12^2+60^2}= \sqrt{144+3600}=4\sqrt {234}\approx 61.2ft

8 0
3 years ago
The distance from the centroid of a triangle to its vertices are 16cm, 17cm, and 18cm. What is the length of the shortest median
Marizza181 [45]

Answer:

24 \text{cm}

Step-by-step explanation:

Given: The distance from the centroid of a triangle to its vertices are 16\text{cm}, 17\text{cm}, and 18\text{cm}.

To Find: Length of shortest median.

Solution:

Consider the figure attached

A centroid is an intersection point of medians of a triangle.

Also,

A centroid divides a median in a ratio of 2:1.

Let G be the centroid, and vertices are A,B and C.

length of \text{AG} =16\text{cm}

length of \text{BG} =17\text{cm}

length of \text{CG} =18\text{cm}

as centrod divides median in ratio of 2:1

length of \text{AD} =\frac{3}{2}\text{AG}

                                              =\frac{3}{2}\times16

                                              =24\text{cm}

length of \text{BE} =\frac{3}{2}\text{BG}

                                              =\frac{3}{2}\times17

                                              =\frac{51}{2}\text{cm}

length of \text{CF} =\frac{3}{2}\text{CG}

                                              =\frac{3}{2}\times18

                                              =27\text{cm}

Hence the shortest median is \text{AD} of length 24\text{cm}

7 0
3 years ago
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPpppppp
Reptile [31]

Answer:

Step-by-step explanation:

= 7850/12

= 654.66

= 7850+654.66*2

= 9158.33

4 0
3 years ago
Why is biking important like why should we bike instead of driving cars?
AlexFokin [52]
So we dont have to pay for car gas and biking doe not cause pollution
4 0
3 years ago
What is the length of DE in the right triangle below ?
olganol [36]
B.25
sorry if my writing is not clear 

3 0
3 years ago
Read 2 more answers
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