Answer: 2 / 15
Step-by-step explanation:
3 red / 10 total
4 white / 9 total
3/10 * 4/9 = 12/90 = 2/15
Answer:
x = 1 - 5t
y = t
z = 1 - 5t
Step-by-step explanation:
For the equation of a line, we need a point and a direction vector. We are given a point (1, 0, 1).
Since the line is suppose to be a tangent to the given curve at the point (1, 0, 1), we need to find a tangent vector for which the curve passes through that point.
We have x = e^(-5t)cos5t
at t = 1, x = e^(-5)cos5
at t = 0, x = 1
y = e^(-5t)sin5t
at t = 1, y = e^(-5)sin5
at t = 0, y = 0
z = e^(-5t)
at t = 1, z = e^(-5)
at t = 0, z = 1
Clearly, the only parameter value for which the curve passes through the point (1, 0, 1) is t = 0.
In vector notation, the curve
r(t) = xi + yj + zk
= e^(-5t)cos5t i + e^(-5t)sin5t j + e^(-5t) k
r'(t) = [-5e^(-5t)cos5t - e^(-5t)sin5t] i +[e^(-5t)cos5t - 5e^(-5t)sin5t] j - 5e^(-5t) k
r'(0) = -5i + j - 5k
is a vector tangent at the point.
We get the parametric equation from this.
x = x(0) + tx'(0)
= 1 - 5t
y = y(0) + ty'(0)
= t
z = z(0) + tz'(0)
= 1 - 5t
The answer i think is A hope that help
Answer:
2/3
Step-by-step explanation:
Answer:
The correct option is D.
Step-by-step explanation:
The slope of a line is the change in y with respect to x.
If the slope of a line is undefined it means it is a vertical line and a vertical line can not passes through three quadrants. So, option A is incorrect.
If the slope of a line is 0 it means it is a horizontal line and a horizontal line can not passes through three quadrants. So, option B is incorrect.
If the slope of a line is positive it means the value of y increases as x increases.
Since it is an increasing line, therefore after a certain period both x and y will positive. It means the line will passes through first quadrant. So, option C is incorrect.
If the slope of a line is negative it means the value of y decreases as x increases. It can passes through each of Quadrants II, III, and IV.
Therefore the correct option is D.
