We already know that the distance of all the planets are generally calculated by keeping the Sun as the main location point.
Explanation:
The distances of all the planets from the Sun in scientific notation and exponential form-
Mercury-
57
million kilometers.
Scientific notation-
5.7
⋅
10
7
km
Venus-
108
million kilometers.
Scientific notation-
1.08
⋅
10
8
km
Earth-
150
million kilometers
Scientific notation-
1.5
⋅
10
8
km
Mars-
228
million kilometers
Scientific notation-
2.28
⋅
10
8
km
Jupiter-
779
million kilometers
Scientific notation-
7.79
⋅
10
8
km
Saturn-
1.43
billion kilometers
Scientific notation-
1.43
⋅
10
9
km
Uranus-
2.88
billion kilometers
Scientific notation-
2.388
⋅
10
9
km
Neptune-
4.5
billion kilometers
Scientific notation-
4.5
⋅
10
9
km
y = 9ln(x)
<span>y' = 9x^-1 =9/x</span>
y'' = -9x^-2 =-9/x^2
curvature k = |y''| / (1 + (y')^2)^(3/2)
<span>= |-9/x^2| / (1 + (9/x)^2)^(3/2)
= (9/x^2) / (1 + 81/x^2)^(3/2)
= (9/x^2) / [(1/x^3) (x^2 + 81)^(3/2)]
= 9x(x^2 + 81)^(-3/2).
To maximize the curvature, </span>
we find where k' = 0. <span>
k' = 9 * (x^2 + 81)^(-3/2) + 9x * -3x(x^2 + 81)^(-5/2)
...= 9(x^2 + 81)^(-5/2) [(x^2 + 81) - 3x^2]
...= 9(81 - 2x^2)/(x^2 + 81)^(5/2)
Setting k' = 0 yields x = ±9/√2.
Since k' < 0 for x < -9/√2 and k' > 0 for x >
-9/√2 (and less than 9/√2),
we have a minimum at x = -9/√2.
Since k' > 0 for x < 9/√2 (and greater than 9/√2) and
k' < 0 for x > 9/√2,
we have a maximum at x = 9/√2. </span>
x=9/√2=6.36
<span>y=9 ln(x)=9ln(6.36)=16.66</span>
the
answer is
(x,y)=(6.36,16.66)
Answer:
69
Step-by-step explanation:
74/2
Answer:
Step-by-step explanation:
Rearrange each function to solve for x.
Switch x and y,
The resulting equation is the inverse function.
A:
f(x) = y = 5+x
x = y-5
y = x-5
f⁻¹(x) = x-5
g(x) = 5-x ≠ f⁻¹(x)
g(x) is not the inverse of f(x).
:::::
B:
f(x) = y = 2x-9
x = (y+9)/2
y = (x+9)/2
f⁻¹(x) = (x+9)/2
g(x) = (x+9)/2 = f⁻¹(x)
g(x) is the inverse of f(x).
:::::
C:
f(x) = y = 2/x - 6
x = 2/(y+6)
y = 2/(x+6)
f⁻¹(x) = 2/(x+6)
g(x) = (x+6)/2 ≠ f⁻¹(x)
:::::
D:
f(x) = y = x/3 + 4
x = 3y - 12
y = 3x - 12
f⁻¹(x) = 3x - 12
g(x) = 3x - 4 ≠ f⁻¹(x)
g(x) is not the inverse of f(x).
Answer:
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