Answer:
8 ohms
Step-by-step explanation:
given that y varies inversely as x then the equation relating them is
y =
← k is the constant of variation
To find k use either of the given conditions
y = 10 when x = 12 or y = 5 when x = 24, hence
k = 10 × 12 = 120
y =
← equation of variation
when x = 15, then
y =
= 8
Answer:
cool
Step-by-step explanation:
is this a question?
Answer:
c=9
d=3
Step-by-step explanation:
We have been asked:
What value of c makes x2 + 6x + c a perfect square trinomial?
c =
If x2 + 6x + c = (x + d)2, then d =
First step we have to do is divide the coefficient of x by 2. The coefficient is 6
6/2 = 3
Now take the square of 3 = 3^2
3^2 = 3*3 =9
The value of c is 9
If x^2 + 6x + c = (x + d)^2, then d =?
Put the value of c in the equation:
x^2+6x+9
Take the square root of 1st and third term. Then the expression can be written as:
x^2+6x+9 = (x+3)^2
Thus the value of d is 3.
If x^2 + 6x + 9 = (x + 3)^2, then d = 3 .....
Answer:
Step-by-step explanation:
In Raphael's example, the robot moves in a perfect triangle. A perfect triangle is known to have three equal sides and three equal angles of 60° each. Raphael's example mentions the length of two sides of the triangle as 3m and 4m and it also mentions the angle the robot turns 120°
Therefore the angle created is 180°-120°= 60° which is an angle of a perfect triangle.
The distance that the robot has to calculate would be equal to the length of the third side of the triangle
lets assume the length of the third side of the triangle to be
and the two remaining angles to be a and b.
To get the distance
, let's list out what we know about this triangle.
side a = 3m
side b = 4m
side c =<em> β</em>
Angle 1 = Angle made between side 2 and 3 = A
Angle 2 = Angle made between side 1 and 3 = B
Angle β = Angle made between side 1 and 2 = 60°
The law of cosines states that
=
+
- 2ab(cosβ)
=
+
- 2×3×4(cos 60)
= 9 + 16 - 24(0.5)
= 9 + 16 - 12
= 13
<em>β</em> = 
<em>β</em> = 3.6055512755 m
The distance the robot will compute is 3.61 meter to the nearest hundredth.