One A
y = e^x
dy/dx = e^x The f(x) = the differentiated function. Any value that e^x can have, the derivative has the same value. x is contained in all the reals.
One B
y = x*e^x
y' = e^x + xe^x Using the multiplication rule.
You want the slope and the value of the of y to be the same. The slope is y' of the tangent line
xe^x = e^x + xe^x
e^x = 0
This happens only when x is very "small" like x = - 4444444
y = e^x * ln(x) Using the multiplication rule again, we need the slope of the line with is y'
y1 = e^x
y1' = e^x
y2 = ln(x)
y2' = 1/x
y' = e^x*ln(x) + e^x/x So at x = 1 the slope of the line =
y' = e^1*ln(1) + e^1/1
y' = e*0+e = e
y = mx + b
y = ex + b
to find b we use y= e^x ln(x)
e^x ln(x) = e*x + b
e^1 ln(1) = e*1 + b
ln(1) = 0
0 = e + b
b = - e
line equation and answer.
y = e*x - e
Answer:
I'd have to say, C: 13
Step-by-step explanation:
Let g be the number of grandchildren, and d be the number of dogs. They both have only one head, so the number of heads is
Grandchildren have 2 legs, while dogs have 4. So, the total number of legs is
From the first equation (the one for the heads) we can derive
Substitute this into the second to get
So, there are 9 dogs and (from the first equation
5).
and
6).
The volume of a sphere is
(4/3) (pi) (radius)³ .
In #5, the 'pi' is already there next to the answer window.
You just have to come up with the (4/3)(radius³).
Remember that the radius = 1/2 of the diameter.
7). The volume of a cylinder is
(pi) (radius²) (height) .
Divide the juice in the container by the volume of one can,
to get the number of cans he can fill.
8). The volume of a cone is
(1/3) (pi) (radius of the round bottom)² (height) .
He starts with a small cone, he then adds clay to it to make it higher.
The question is: How much clay does he ADD to the short one,
to make the bigger one ?
Use the formula to find the volume of the short one.
Use the formula again to find the volume of the bigger one.
Then SUBTRACT the smaller volume from the bigger volume.
THAT's how much clay he has to ADD.
Notice that the new built-up cone has the same radius
but more height than the first cone.
_______________________________________
Don't worry if you don't understand this.
The answer will be this number:
(1/3) (pi) (radius²) (height of the big one minus height of the small one).
