ΔABD and ΔACD are similar (By A-A-A) and The length of DA is 6.
The triangles where all the corresponding sides of the two triangles are in equal proportion are called similar triangles.
In triangle ΔABC ∠BAC=90°
Let ∠ABC=x
then ∠ACB=90°-x
In triangle ΔADC, ∠ADC =90°
∠ACB=∠ACD=90°-x
∠DAC= 180°-(∠ADC+∠ACD)= 180°-(90°+90°-x)= x
In triangle ΔADB , ∠ADB =90°
∠ABD=x
∠BAD=90°-x
Between triangles ΔABD and ΔACD
∠ABD=∠DAC (=X)
∠BAD∠ACD (=90°-x)
∠ADB=∠ADC (=90°)
from the above, it is clear that triangles ΔABD nad ΔACD is similar. (By A-A-A)
So sides are in equal proportion in 2 triangles,
AD/DC= BD/AD
⇒AD²= BD*DC
⇒AD²=9*4
⇒AD²=36
⇒AD=6
⇒DA=6
Therefore triangles ΔABD and ΔACD are similar (By A-A-A) and The length of DA is 6.
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The integral is path-independent if we can find a scalar function <em>f</em> such that grad(<em>f</em> ) = <em>A</em>. This requires


Take the first PDE and integrate both sides with respect to <em>x</em> to get

where <em>g</em> is assumed to be a function of <em>y</em> alone. Differentiating this with respect to <em>x</em> gives

which would mean <em>g</em> is *not* a function of only <em>y</em>, but also <em>x</em>, contradicting our assumption. So the integral is path-dependent.
Parameterize the unit circle (call it <em>C</em>) by the vector function,

with <em>t</em> between 0 and 2π.
Note that this parameterization takes <em>C</em> to have counter-clockwise orientation; if we compute the line integral of <em>A</em> over <em>C</em>, we can multiply the result by -1 to get the value of the integral in the opposite, clockwise direction.
Then

and the (counter-clockwise) integral over <em>C</em> is



and so the integral in the direction we want is -2π.
By the way, that the integral doesn't have a value of 0 is more evidence of the fact that the integral is path-dependent.
Answer:
Solution given:
1:
-1/8=
2. -64/27
=
Express in rational number
1. (-3/2)=-3/2*2/2=-(3*2)*(2/2)=-6/4
2. (1/5)=1/5*5/5=<u>5/25</u>
and
(-4/3)³(2/5)-⁴ ÷ (7/4)
(-4³/3³)(2-⁴/5-⁴)÷7/4
(-64/27)(5⁴/2⁴)÷7/4
(-64/27)(625/16)÷7/4
(-64*625/(27*16))*4/7
-2500/27*4/7
-10000/169
(-100/13)²
This is A (-16)... When looking for this use the fomula PEMDAS ( Parenthesis, Exponents, Multiply, Add, and Subtract)....... 5+4=9 and -7-9=-16... so the answer is A
Answer: 6
Step-by-step explanation: DE is 4+2 so EF would be the same if it is equal.