answer:
78
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Answer: The length of BC is 7
Step-by-step explanation: Assuming the lengths of the opposite sides of the quadrilateral are congruent, then
AB=DC and
AD=BC
Inputting the values of AB, DC and AD as given in the question:
x + 8 = 3x ...(1)
x + 3=? ...(2)
We have to solve for the value of x to get the actual lengths and thus ascertain BD.
From equation (1):
8 = 3x - x
8 = 2x
8/2 = x
Therefore, x = 4.
If x = 4 then equation(2) would be
4 + 3= 7.
Hence, the actual lengths of the quadrilateral are:
AB = 4 + 8. DC = 3(4)
=12. =12.
AD = 4 + 3. AD = BC
= 7. Therefore, BC = 7.
Hence, it is confirmed that quadrilateral ABCD is a parallelogram since both the opposite sides are proven to be congruent.
Answer:
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Step-by-step explanation:
Answer:
1,2 and 4 are conservatives
3 is not conservative
Step-by-step explanation:
We calculate the Curl F
Remember that:
Curl F = <
>
1. Curl F = <0,0,5-5> = <0,0,0>
The potential function f so that ∇f=F
f(x,y,z) = 
Then F is conservative
2. Curl F = < 0, 0 ,0>
The potential function f so that ∇f=F
f(x,y,z) = 
Then F is conservative
3. Curl F = <0 ,0, 10+3xsin(y) - (-cos(y))>
= <0 ,0 , 10 +3xsin(y) + cos(y)<
How the field's divergence is not zero the vector field is not conservative
4. Curl F = <0, 0, 0>
The potential function f so that ∇f=F
f(x,y,z) =
Then F is conservative
Given:
4:x::x:16
To find:
The value of x.
Solution:
We have,
4:x::x:16
It means, we have
4:x = x:16
It can be rewritten as

On cross multiplication, we get


Taking square root on both sides.


Since ratio can be negative or positive, therefore, the value of x is either -8 or 8.