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
Answer:
The correct answer is D. 10.
Step-by-step explanation:
If Brandy earns 2 stars for every goal, and she scored 8 goals, then we need to multiply 8 by 2.
8 x 2 = 16
She looses 1/2 a star for every miss, and she missed the goal 12 times. Therefore, we need to multiply 1/2 by 12.
12 x 1/2 = 6
Therefore, Brandy lost 6 stars.
Now, we need to subtract the amount of stars Brandy earned by the amount that she lost.
16 - 6 = 10
Therefore, the correct answer is D. 10.
Hope this helps! :D
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The best and most correct answer among the choices provided by the question is <span>(D) f(n) = 0.9 * f(n - 1) + 10, f(0) = 175, n > 0 .</span> <span>
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Hope my answer would be a great help for you.</span>
Answer:
-422
Step-by-step explanation:
51[-2]³ - 21 + 7
51[-8] - 14
-408 - 14 = -422
I am joyous to assist you anytime.
Answer:
22.84, 5.83
Step-by-step explanation:
Pythagoras theorem states that: a^2+b^2=c^2
So, for red triangle, it will be: 9^2+21^2=b^2
81+441=b^2
522=b^2
square root of 522=b
22.84=b
For purple one,
3^2+5^2=a^2
9+25=a^2
34=a^2
square root of 34=a
5.83=a
