d/dx cos^2(5x^3)
= d/dx [cos(5x^3)]^2
= 2[cos(5x^3)]
= - 2[cos(5x^3)] * sin(5x^3)
= - 2[cos(5x^3)] * sin(5x^3) * 15x^2
= - 30[cos(5x^3)] * sin(5x^3) * x^2
Explanation:
d/dx x^n = nx^(n - 1)
d/dx cos x = - sin x
Chain rule:
d/dx f(g(...w(x))) = f’(g(...w(x))) * g’(...w(x)) * ... * w’(x)
Answer:
Line TX or XT
Step-by-step explanation:
Planes always intersect in a line.
the volume of the sculpture is .
<u>Step-by-step explanation:</u>
Here we have , An artist creates a cone-shaped sculpture for an art exhibit. If the sculpture is 5 feet long and has a base with a circumference of 21.980 feet, We need to find the volume of the sculpture . Let's find out:
We know that
⇒
According to question ,
⇒
⇒
⇒
Now , We know that Volume of cone :
⇒
⇒
⇒
Therefore , the volume of the sculpture is .
Answer:
The given question is
<em>
Draw two 1 dm squares on a sheet of paper. Draw a diagonal on each one and cut them out.</em>
<em />
So, you need to draw square with sides of 1 dm. However, first, you need to transform from dm to cm.
We know that 1 decimenter (dm) equals 10 centimeters (cm).
That means the square sides are 10 centimerers long. So, you need to draw two squares like the first image attached shows.
Then, to draw their diagonals, you need to draw a line segment from one corner to its opposite corner, you should have an inclined line acroos each square. As the second image attached shows.
There you have it. Two squares of 1 dm side with on diagonal each.
Answer:
Assuming the area is made up of a square and a semicircle.
<u>Perimeter</u>
The side length of the square = 18 ft
We can see 3 full side lengths plus one side length from which we need to subtract 12 ft (see attached diagram).
⇒ perimeter of the square = (3 x 18) + (18 - 12)
= 54 + 6
= 60 ft
Circumference of a circle = d (where d is the diameter)
⇒ arc length of the semicircle = 1/2 circumference
= 1/2 · · 12
= 6 ft
Total perimeter = 60 + 6 = 78.8 ft (nearest tenth)
<u>Area</u>
Area of a square = s² (where s is the side length)
⇒ area of square = 18²
= 324 ft²
Diameter = 2r ⇒ r = 1/2 diameter
Area of a circle = r² (where r is the radius)
⇒ area of the semicircle = 1/2 · · 6²
= 18 ft²
Total area = 324 + 18 = 380.5 ft² (nearest tenth)