Answer:
c
Step-by-step explanation:
math
Answer:
DA/dt = 75.27 cm²
Step-by-step explanation:
Cube Volume = V(c) = 683 cm³
DV(c) /dt = 824 cm³
V(c,x) = x³
Then
DV(c,x)/ dt = 3x² Dx/dt
( DV(c,x)/ dt )/ 3x² = Dx/dt (1)
Now as V(c,x) = x³ when V(c,x) = 683 cm³ x = ∛683
x = 8.806 ( from excel)
And by subtitution of this value in equation (1)
Dx/dt = ( DV(c,x)/ dt )/ 3x² ⇒ Dx/dt = 824 / 3*x²
Dx/dt = 824 /3*77.55
Dx/dt = 824/232,64
Dx/dt = 3,542
Then we got Dx/dt where x is cube edge. The area of the face is x² then
the rate of change of the suface area is
DA/dt = ( Dx/dt )²*6 ( 6 faces of a cube)
DA/dt = (3.542)²*6
DA/dt = 75.27 cm²
6x + 4 - x = 2(x+1)
First combine like terms on the left side:
6x-x - 5x
So you have 5x+4 on the left side.
Then use the distributive property on the right side:
2(x+1) becomes 2x +2
Now you have 5x +4 = 2x +2
Subtract 4 from each side:
5x = 2x -2
Subtract 2x from each side:
3x = -2
Divide both sides by 3:
x = -2/3
Volume is in cubic units, meaning the volume ix raised to the 3rd power.
If the cube is scaled by 5, then the volume is scaled by 5^3.
5^3 = 5*5*5 = 125
The new volume would be the original volume multiplied by the total increase:
64 x 125 = 8,000 cubic meters.
4^x + 6^x = 9^x
4^x + 6^x - 9^x = 0
2^2x + (2×3)^x - 3^2x = 0
2^2x + 2^x×3^x - 3^2x = 0
(⅔)^2x + (⅔)^x - 1 = 0
let t = ( ⅔)^x
t² + t - 1 = 0
t = (-1+√5 ) / 2
(⅔)^x = (-1+√5 ) / 2
x = Log base ⅔ ((-1+√5 ) / 2 )
x = 1.18681
