Answer:
h'(x) = (-3x^3 +2x)/e^(3x)
Step-by-step explanation:
The formula for the derivative of a quotient is ...
(u/v)' = (vu' -uv')/v²
Using u = (x^3 +x^2) and v = e^(3x), this becomes ...
h'(x) = (e^(3x)(3x^2 +2x) -(x^3 +x^2)(3)(e^(3x))/e^(6x)
h'(x) = (-3x^3 +2x)/e^(3x)
We apply the Law of Sines
<span>a/sin A</span> = <span>b/sin B</span> = <span>c/<span>sin C</span></span>
We have that b = 12, B = 15 degrees
<span><span>C = 90 degrees</span></span>
....> c/sin(90) = 12/sin(15)..............> c = 12/0.258 = 46.3644
For number 5, you were very close. the answer is...
(1,2), (3,4), (5,6) (7,8)
Hope this helped! :D
Answer:
Step-by-step explanation:
A circle is the set of all points on a plane at a given distance (radius) from a given point (center). The general equation of a circle with center and radius is given by:
Therefore, replacing the data provided into the previous equation:
So, the equation of a circle with a radius of 2 and its center at (4,-2) is:
I attach you the graph.
Answer:
The width of the frame is 3 inches
Step-by-step explanation:
We are told that the inner rectangle is 10 inches by 16 inches.
It means the outer rectangle has to be (L = 10 + 2x) by (W = 16 + 2x),
Where x represents the width of the frame.
The perimeter of the frame is given by; p = 2L + 2W
p = 2(10+2x) + 2(16+2x)
We are given perimeter, P = 76
Thus;
2(10 + 2x) + 2(16 + 2x) = 76
Divide both sides by 2 to give;
(10+2x) + (16+2x) = 38
(10+16) + (2x+2x) = 38
4x = 38 - 26
4x = 12
x = 12/4 = 3
The width of the frame is x = 3 inches