Answer to Question #86505 in Calculus for Joshua

Question

3.ABCD is a square (quadrilateral) with T and U the mid points of SP and QR respectively. Which expressions is true?
a.PQ+RS =2TU

b.PQ−RS=2TU

c.PQ+RT=2TS
__ __ ___
d.PQ− RT= 2TS

4.In triangle ABC, the points L, M, N are the midpoints of the sides AB, BC and CA respectively. Which these expressions is true?
___ ___ __ ___
a.2AB+3BC+AC=2LC
___ ___ __ ___
b.2AB−3BC+AC=2LC
___ ___ __ ___
c.2AB−3BC-AC=2LC
___ ___ __ ___
d.2AB+3BC−AC=2LC

5.If i.i = 1, then i.j = …
a.−1
b.0.5
c.−0.5
d.zero

Answer 1

3)

First of all we know, that all sides are equal in square;

We have two variants:

Square PQRS and PRQS

I: PQRS

a)PQ = RS = TU, so PQ+RS= 2 TU. true

b) PQ-RS = 0, and 0!=TU. false

c)2TS = PS; And PQ = PS, so RT = 0. false

d)From c we have that -RT have to be equal 0. It is False

4)Let’s imagine that all assignments are true. So they are true for any triangle. Let’s look at right-angle triangle with sides 1,1,sqrt(2).

AB = AC = 1;

BC = sqrt(2).

AL = AN = 0.5

BC = sqrt(2)/2;

LC = sqrt(5)/2;

a)

2AB+3BC+AC= 2+3*sqrt(2) + 1 and it isn’t equal to 2*sqrt(5)/2 

false

b)

2AB−3BC+AC= 2 - 3*sqrt(2) + 1 not equal to 2*sqrt(5)/2

False;

c)2AB−3BC-AC=2LC

2 - 3*sqrt(2) - 1 not equal to 2*sqrt(5)/2

false

d)2AB+3BC−AC=2LC 

2+3*sqrt(2) - 1 not equal to 2*sqrt(5)/2

false

5) i = (1,0); j = (0,1)

i*i = 1*1+ 0 * 0 = 1;

i*j = 1*0 + 0*1 = 0;

Answer:d