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Otrada [13]
3 years ago
7

Let v1=(-6,4) and v2=(-3,6) compute the following.

Mathematics
1 answer:
yan [13]3 years ago
5 0

a. We assume you want the dot product. That is the sum of the products of the corresponding components.

... V1•V2 = (-6)(-3) + (4)(6) = 18 + 24 = 42


b. V1•V2 = |V1|·|V2|·cos(α)

... α = arccos(V1•V2/(|V1|·|V2|)

... α = arccos(42/√(((-6)²+4²)((-3)²+6²)))

... α = arccos(42/√2340)

... α ≈ 29.74°


c. The scalar projection of V1 onto V2 is the dot product of V1 with the unit vector in the V2 direction.

... V1•V2/|V2| = 42/√45 = 42/(3√5) = (14/5)√5


d. The projection of V1 onto V2 is the result of part c multiplied by the unit vector in the direction of V2.

... projection of V1 onto V2 = (14/5)√5·(-3, 6)/(3√5) = (14/5)(-1, 2) = (-14/5, 28/5)

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Here is the answer with an explanation!

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3 years ago
Dont even know where to start
zalisa [80]

Answer:

\displaystyle M =  ( 3,1 )

Step-by-step explanation:

we are given the endpoint i.e P and Q of a line segment

we want to figure out the Midpoint of the Line segment

in order to do so we can use Midpoint formula given by

\displaystyle M =  \bigg( \frac{ x_{1} +  x_{2}  }{2}  , \frac{ y_{1} +  y_{2}}{2}  \bigg)

so let

x_1=-2\\x_2=8\\y_1=-2\\y_2=4

substitute

\displaystyle M =  \bigg( \frac{  - 2 +  8}{2}  , \frac{  - 2 +  4}{2}  \bigg)

simplify addition:

\displaystyle M =  \bigg( \frac{  6}{2}  , \frac{  2}{2}  \bigg)

simplify division:

\displaystyle M =  ( 3,1 )

hence,

the Midpoint of the line segment is (3,1)

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3 years ago
What is the total surface area of rectangular prism?
algol13

Answer:

162 [m²].

Step-by-step explanation:

required surface is:

A=(3*7+6*7+3*6)*2=162 [m²].

4 0
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Lexie has dimes and ten dollar bills in her pocket. The number of dimes is six more than two times the number of ten dollar bill
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Answer:

d=6+2t

Step-by-step explanation:

Let

t=number of ten dollar bills

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Number of dimes is six more than two times the number of ten dollar bills

d=6+2*t

d=6+2t

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