D(x) = 1375 - 110x.....where x is the hrs traveled and d(x) is the distance in miles left to travel
(a) after 8 hrs....so x = 8
d(8) = 1375 - 110(8)
d(8) = 1375 - 880
d(8) = 495...so after 8 hrs, u r 495 miles short of ur destination
(b) before reaching its destination...its destination is 1375 miles....and if u r traveling 110 miles per hr....1375/110 = 12.5....so after 12.5 hrs, u should reach ur destination.
Answer:
There are no real solutions. The complex solutions are ...
(x, y) = (2.5-i√1.75, -2.5+i√1.75) or (2.5+i1.75, -2.5-i1.75)
Step-by-step explanation:
Subtract the first equation from the second.
y -y = (x^2 -6x +8) -(-x)
0 = x^2 -5x +8
Rewrite to facilitate completing the square:
x^2 -5x = -8
x^2 -5x +6.25 = -1.75 . . . . . add 6.25 to complete the square
(x -2.5)^2 = -1.75 . . . . . write as a square
x -2.5 = ±i√1.75 . . . . . . take the square root
x = 2.5 ± i√1.75 . . . . . . add 2.5; y is the opposite of this
Solutions are ...
- x = 2.5 +i√1.75, y = -2.5 -i√1.75
- x = 2.5 -i√1.75, y = -2.5 +i√1.75
_____
The graph shows the equations have no point of intersection, meaning there are no real solutions. The complex solutions are shown above.
The magnitude of the resulting vector, u - v, is approximately 5.83
and its angle of direction is approximately 59.04°.
<h3>How to find the magnitude of the resulting vector?</h3>
We want to subtract vector v from vector u.
We are given;
v = <2, -3> = 2i - 3j
u = <5, 2> = 5i + 2j
u - v = 5i + 2j - (2i - 3j)
= 5i + 2j - 2i + 3j
= 3i + 5j
Resultant vector = √(3² + 5²)
Resultant vector = √34 ≈ 5.83
Angle of direction of resultant vector is;
tan θ = (5/3)
θ = tan⁻¹(5/3)
θ = 59.04°
Read more about Magnitude of Vector at; brainly.com/question/3184914
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Point slope is nicer
y-y1=m(x-x1)
goes through the point (x1,y1) and has a slope of m
slope itnercept
y=mx+b
m=slope
b=y intercept
first find slope
slope between 2 points (x1,y1) and (x2,y2) is (y2-y1)/(x2-x1)
given
(7,82) and (4,18)
slope=(18-82)/(4-7)=-64/-3=64/3
point slope
point is (7,82) or you can do (4,18)
I'll do both
y-82=(64/3)(x-7) or
y-18=(64/3)(x-4)
those both work
slope intercept
slope is 64/3
y=64/3x+b
find b
input a point
(4,18)
18=64/3(4)+b
18=256/3+b
minus 256/3 from both sides
note: 18=54/3
-202/3=b
y=64/3x-202/3 is equation in slpe intercept
