Mathematics, 16.11.2020 22:50 mxwtwo

What are the coordinates of point B on AC such that the ratio of AB to AC is 5 : 6?

Answers: 2

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Answers

Answer from: jewelzoe49

=(x

⋅(x

−x

),y

⋅(y

−y

),z

⋅(z

−z

))

Step-by-step explanation:

Let suppose that A, B, and C have the following points with respect to origin in the Euclidean space:

\vec A = (x_{A}, y_{A}, z_{A})

=(x

)

\vec B = (x_{B}, y_{B}, z_{B})

=(x

)

\vec C = (x_{C}, y_{C}, z_{C})

=(x

)

Besides, let consider that locations of A and B are currently known. The ratio is:

\frac{AB}{AC} = \frac{5}{6}

AB = \frac{5}{6} \cdot ACAB=

⋅AC

Vectorially speaking, expression can be rewritten in the following terms:

\overrightarrow{AB} = \frac{5}{6}\cdot \overrightarrow{AC}

⋅

(x_{B}-x_{A}, y_{B}-y_{A}, z_{B}-z_{A}) = \frac{5}{6}\cdot (x_{C}-x_{A}, y_{C}-y_{A}, z_{C}-z_{A})(x

−x

−y

−z

⋅(x

−x

−y

−z

)

Now, each side of the equation is summed vectorially by \vec A

and coordinates of point B are finally found:

\vec B = \left(x_{A}+\frac{5}{6}\cdot (x_{C}-x_{A}), y_{A}+\frac{5}{6}\cdot (y_{C}-y_{A}), z_{A}+\frac{5}{6}\cdot (z_{C}-z_{A})\right)

=(x

⋅(x

−x

),y

⋅(y

−y

),z

⋅(z

−z

))

Answer from: Quest

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.

Answer from: Quest

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.

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