So, f[x] = 1/4x^2 - 1/2Ln(x)
<span>thus f'[x] = 1/4*2x - 1/2*(1/x) = x/2 - 1/2x </span>
<span>thus f'[x]^2 = (x^2)/4 - 2*(x/2)*(1/2x) + 1/(4x^2) = (x^2)/4 - 1/2 + 1/(4x^2) </span>
<span>thus f'[x]^2 + 1 = (x^2)/4 + 1/2 + 1/(4x^2) = (x/2 + 1/2x)^2 </span>
<span>thus Sqrt[...] = (x/2 + 1/2x) </span>
9514 1404 393
Answer:
g(x) = x -1
Step-by-step explanation:
Translation of a function by (right, up) = (h, k) is accomplished by ...
g(x) = f(x -h) +k
Here the translation is 4 units left, so h=-4 and k=0. This means ...
g(x) = f(x +4) = (x+4) -5
g(x) = x -1
You need to determine how much paper you need to cover the lateral side of the cylinder shown in the picture. For this, you have to calculate the surface area of the cylinder, which you can do using the following formula:

Where
A is the area
π is the number pi, for the calculations we usually use up to the first two decimal values of this number, 3.14
r is the radius
h is the height of the cylinder
The given cylinder has a height of h=15m and a diameter of d=6m
To calculate the lateral area you need to use the radius. The diameter is twice the radius, so to determine the radius of the cylinder you have to divide the diameter by 2

Now you can calculate the lateral area as follows:

Charlie will need 282.6 m² to cover the lateral side of the cylinder.
Answer:
122+42x= 2( 61+21x)
4x+16x+24 = 4(5x+6)
24x+48-3x = 21x+48
3x+39-2x = x+29
Step-by-step explanation:
Answer:
64°
Step-by-step explanation:
First, we have to find the angle situated in R, the addition of all angles in a triangle is 180° so that means:
x + 68 + 48 = 180
x = 180-116 = 64°
Now, remember that this angle (64°) is the same as this one = ?, thanks to one property.
So basically, that angle has the same value as that one.
? = 64°
Hope it was helpful ;)