The angle between the planes is the same as the angle between their normal vectors, which are
<em>n</em><em>₁</em> = ⟨1, 1, 1⟩
<em>n</em><em>₂</em> = ⟨4, 3, 1⟩
The angle <em>θ</em> between the vectors is such that
⟨1, 1, 1⟩ • ⟨4, 3, 1⟩ = ||⟨1, 1, 1⟩|| ||⟨4, 3, 1⟩|| cos(<em>θ</em>)
Solve for cos(<em>θ</em>) :
4 + 3 + 1 = √(1² + 1² + 1²) √(4² + 3² + 1²) cos(<em>θ</em>)
8 = √3 √26 cos(<em>θ</em>)
cos(<em>θ</em>) = 8/√78
Answer:
850
Step-by-step explanation:
400+550+850=1800. 1800/3= 600
Since Emily is walking at a constant speed, we can solve this using proportions, equating ratios of distance/time.
The first ratio is 3/4 miles/1/4 hour
The second ratio is 1 mile/ x hour
Equating the two ratios: 3/4 / 1/4 = 1/x
3 = 1/x
x = 1/3 hour
Answer:
a. a = 1, b = -5, c = -14
b. a = 1, b = -6, c = 9
c. a = -1, b = -1, c = -3
d. a = 1, b = 0, c = -1
e. a = 1, b = 0, c = -3
Step-by-step explanation:
a. x-ints at 7 and -2
this means that our quadratic equation must factor to:
FOIL:
Simplify:
a = 1, b = -5, c = -14
b. one x-int at 3
this means that the equation will factor to:
FOIL:
Simplify:
a = 1, b = -6, c = 9
c. no x-int and negative y must be less than 0
This means that our vertex must be below the x-axis and our parabola must point down
There are many equations for this, but one could be:
a = -1, b = -1, c = -3
d. one positive x-int, one negative x-int
We can use any x-intercepts, so let's just use -1 and 1
The equation will factor to:
This is a perfect square
FOIL:
a = 1, b = 0, c = -1
e. x-int at 
our equation will factor to:
This is also a perfect square
FOIL and you will get:
a = 1, b = 0, c = -3
Answer:
x=-3, and y=2
Step-by-step explanation:
Since both equations are equal to y, set them equal to each other and solve for x, that way you can solve for y:
x+5=-2x-4
3x+5=-4
3x=-9
x=-3
Plugging in x=-3 into one of the original equations:
y = x + 5
y = -3 + 5
y = 2
Therefore, x=-3 and y=2. You can also write as the ordered pair (-3,2) since that's where the two equations would intercept on a graph.
