Answer:
y = x-4
Step-by-step explanation:
y = -x-5
Slope of line is -1.
Slope of perpendicular to line is 1.
Point-slope equation for line of slope 1 that passes through (6,2):
y-2 = 1(x-6)
Rearrange equation to slope-intercept form:
y = 1(x-6) + 2
y = x-4
The volume of the first cube is (5h^2)^3, while the volume of the second cube is (3k)^3, so their total volume is (5h^2)^3 + (3k)^3. We can use the special formula for factoring a sum of two cubes:
x^3 + y^3 = (x + y)(x^2 - xy + y^2)
(5h^2)^3 + (3k)^3 = (5h^2 + 3k)((5h^2)^2 - (5h^2)(3k) + (3k)^2)
= (5h^2 + 3k)(25h^4 - 15(h^2)(k) + 9k^2)
This is the second of the given choices.
Assume that each material in each category has an equal chance of being selected.
Categories:
(a) Type of wood used to make the cabinet: birch, maple, cherry.
Each type of wood has a probability of 1/3 to be selected.
(b) Type of finish: transparent, semi-transparent.
Each type of finish has a probability of 1/2 to be selected.
(c) Knob: bronze, steel, wood.
Each material has 1/3 probability to be selected.
Each event (selecting material for the cabinet, for the finish, and for the knob) is an independent event.
Therefore
Probablity(birch wood AND bronze knob) = (1/3)*(1/3) = 1/9
Probability(wood knob) = 1/3
Probability(transparent stain) = 1/2
Probability(cheryy wood AND semi-transparent stain) = (1/3)*(1/2) = 1/6
Answer: 
Step-by-step explanation:
To find: The vector parametric equations for the line through the points (−1,−4,2) and (−1,0,−3).
Let A (−1,−4,2) and B(−1,0,−3)
First we find direction vectors : 
Now, the parametric equations of the line:
Hence, the vector parametric equations for the line through the points (−1,−4,2) and (−1,0,−3):
