Answer:
1st: -3 -5
_y+_
2 2
2nd -3y-5
____
x
Step-by-step explanation:
The function f(x) is increasing on the interval (-4, 0) ∪ (4, ∞).
Answer:
7 + 3x ≥ 13
Step-by-step explanation:
The best way to write this is to truly understand what each of the terms mean. The sum means that multiple terms are added together, which means that 7 and 3 times a number will be added together.
Next, the term three times a number just means 3x. So as of now, we have 7 and 3x being added together.
Finally, the term at least 13 means that the 7 + 3x is greater than or equal to 13. Once everything is put together, you get a final inequality of 7 + 3x ≥ 13.
Answer:
x = 1 - 5t
y = t
z = 1 - 5t
Step-by-step explanation:
For the equation of a line, we need a point and a direction vector. We are given a point (1, 0, 1).
Since the line is suppose to be a tangent to the given curve at the point (1, 0, 1), we need to find a tangent vector for which the curve passes through that point.
We have x = e^(-5t)cos5t
at t = 1, x = e^(-5)cos5
at t = 0, x = 1
y = e^(-5t)sin5t
at t = 1, y = e^(-5)sin5
at t = 0, y = 0
z = e^(-5t)
at t = 1, z = e^(-5)
at t = 0, z = 1
Clearly, the only parameter value for which the curve passes through the point (1, 0, 1) is t = 0.
In vector notation, the curve
r(t) = xi + yj + zk
= e^(-5t)cos5t i + e^(-5t)sin5t j + e^(-5t) k
r'(t) = [-5e^(-5t)cos5t - e^(-5t)sin5t] i +[e^(-5t)cos5t - 5e^(-5t)sin5t] j - 5e^(-5t) k
r'(0) = -5i + j - 5k
is a vector tangent at the point.
We get the parametric equation from this.
x = x(0) + tx'(0)
= 1 - 5t
y = y(0) + ty'(0)
= t
z = z(0) + tz'(0)
= 1 - 5t
Rectangle is a polygon (A close plane figure which has 3 or more sides)
Rectangle is a parallelogram (Opp Sides are parallel and congruent)
Rectangle has 4 right (90 degrees) angles, 4 sides and vertices (Corners).
Just saying a square is a type of rectangle and rhombus (4 Congruent sides)
Search about Quadrilaterals. Glad I could help!
