Answer:
Circular paraboloid
Step-by-step explanation:
Given ,
Here, these are the respective 
axes components.
- <em>Component along x axis
</em>
- <em>Component along y axis
</em>
- <em>Component along z axis
</em>
We see that , from the parameterised equation , 
This can also be written as :
This is similar to an equation of a parabola in 1 Dimension.
By fixing the value of z=0,
<u><em>We get 
which is equation of a parabola curving towards the positive infinity of y-axis and in the x-y plane.</em></u>
By fixing the value of x=0,
<u><em>We get 
which is equation of a parabola curving towards positive infinity of y-axis and in the y-z plane. </em></u>
Thus by fixing the values of x and z alternatively , we get a <u>CIRCULAR PARABOLOID. </u>
Answer:
7 is the answer.
Step-by-step explanation:
In equations like this, you would solve the numbers in the parenthesis first, and then gradually do: Multiplication -> Division -> addition -> subtraction.
Therefore, -18 / 9 is -2.
-2 * 2 would be -4,
11 + (-4) would be 7.
Answer : 7.
G(x)=2x+3
x <span>≥ 1
g(x)=5
x is bigger then 1
</span>
Answer:
a) <u>0.4647</u>
b) <u>24.6 secs</u>
Step-by-step explanation:
Let T be interval between two successive barges
t(t) = λe^λt where t > 0
The mean of the exponential
E(T) = 1/λ
E(T) = 8
1/λ = 8
λ = 1/8
∴ t(t) = 1/8×e^-t/8 [ t > 0]
Now the probability we need
p[T<5] = ₀∫⁵ t(t) dt
=₀∫⁵ 1/8×e^-t/8 dt
= 1/8 ₀∫⁵ e^-t/8 dt
= 1/8 [ (e^-t/8) / -1/8 ]₀⁵
= - [ e^-t/8]₀⁵
= - [ e^-5/8 - 1 ]
= 1 - e^-5/8 = <u>0.4647</u>
Therefore the probability that the time interval between two successive barges is less than 5 minutes is <u>0.4647</u>
<u></u>
b)
Now we find t such that;
p[T>t] = 0.95
so
t_∫¹⁰ t(x) dx = 0.95
t_∫¹⁰ 1/8×e^-x/8 = 0.95
1/8 t_∫¹⁰ e^-x/8 dx = 0.95
1/8 [( e^-x/8 ) / - 1/8 ]¹⁰_t = 0.95
- [ e^-x/8]¹⁰_t = 0.96
- [ 0 - e^-t/8 ] = 0.95
e^-t/8 = 0.95
take log of both sides
log (e^-t/8) = log (0.95)
-t/8 = In(0.95)
-t/8 = -0.0513
t = 8 × 0.0513
t = 0.4104 (min)
so we convert to seconds
t = 0.4104 × 60
t = <u>24.6 secs</u>
Therefore the time interval t such that we can be 95% sure that the time interval between two successive barges will be greater than t is <u>24.6 secs</u>
