we know that
The conjugate of a complex number is the number with equal real part and imaginary part equal in magnitude but opposite in sign
so
In this problem we have
the conjugate is equal to-------->
therefore
<u>the answer is the option</u>
10+3i
Let the speed of walking of James = x mile/hour
speed of jogging = 2x mile/hour
9/2x + 1.5/x = 2
or, (9 + 3)/2x = 2
or, 12 = 4x
or, x = 3
Average speed of walking = 3 mile/hour
Average speed of jogging = 2 * 3 = 6 mile/hour
If A=w(50-w)
A=50w-w^2
dA/dw=50-2w
d2A/dw2=-2
Since the acceleration is a constant negative, that means that when velocity, dA/dw=0, it is at an absolute maximum for A(w)...
dA/d2=0 only when 50=2w, w=25
So as the case with any rectangle, the perfect square will enclose the greatest area possible with respect to a given amount of material to enclose that area...
So the greatest area occurs when W=L=25 in this case:
A(25)=50w-w^2
Area maximum is thus:
Amax=50(25)-(25)^2=625 u^2
The height of the kite above the ground is 90.63 feet.
<u>Step-by-step explanation:</u>
The angle of elevation of the kite is (θ) 65°.
The distance between the kite and its end is (hypotenuse)100 feet.
To find the height (x) of the kite flying above the ground.
we know that sin(θ) =.
sin 65°=
sin 65° = 0.90631.
0.90631 ×100=x.
90.63=x.
∴The height of the kite above the ground is 90.63 feet.
Add the two equations
since the 5x and -5x cancel out
you get y=-4
plug y=-4 into the first equation
solve for x
x=2
THE ANSWER IS: (2,-4)