Y = xe^x
dy/dx(e^x x)=>use the product rule, d/dx(u v) = v*(du)/(dx)+u*(dv)/(dx), where u = e^x and v = x:
= e^x (d/dx(x))+x (d/dx(e^x))
y' = e^x x+ e^x
y'(0) = 1 => slope of the tangent
slope of the normal = -1
y - 0 = -1(x - 0)
y = -x => normal at origin
Answer:
14
Step-by-step explanation:
Answer:
Values of y in order: 0, 2, 4, 6
Step-by-step explanation:
Hi there!
In the table, the first value of x is -2. To find the value of y for this row of the table, we can use the given equation
.

Plug in -2 as the value of x

Therefore, y is 0 when x is -2. (In the table, in the row where x is -2, y would be 0.)
We repeat this process for the rest of the values in the table.
When x=-1:

When x=0:

When x=1:

I hope this helps!
The top angle (10x+10) is equal to the angle below the lowest line and the skewed line. However, the 4x+2 is on the other side. But both together add up to 180° (a straight line).
So 10x+10 = 180-(4x+2) is the formula you're looking for.
Solving it:
10x+10 = 180-(4x+2) =>
10x+10 = 178-4x =>
14x = 168 =>
x = 12
Look up the theory for F angles and Z angles.
Answer:
f(x) = 3(x - 2)² + 4
OR
f(x) = 3x² - 12x + 16
Step-by-step explanation:
Vertex form of a parabola:
Standard form of a parabola:
Let's find the vertex of this parabola.
In order to find the a-value (vertex form), let's use another point besides the vertex on the parabola.
Using (3, 7) for (x, y), let's substitute this point and the vertex (2, 4) for (h, k) into the vertex form equation and solve for a.
Simplify using PEMDAS.
Subtract 4 from both sides.
Now we have (h, k) and a of the vertex form.
- y = a(x - h)² + k → y = 3(x - 2)² + 4
In order to convert from vertex to standard form, simplify the equation by FOILing.
Distribute 3 inside the parentheses.
Combine like terms.
Therefore, we have the answer:
<u>Vertex form:</u>
<u>Standard form:</u>