Sin^(1/2) x cos x - sin^(5/2) cos x
= sin^(1/2) x cos x - sin(1/2)x sin^2 x cos x
factoring we get:
cos x sin^(1/2) x ( 1 - sin^2 x)
Now 1 - sin^2 x = cos^2 x so we have
cos x sin^(1/2) x * cos^2 x
= cos^3 x sqrt sin x
Answer:
Explanation:
A. The minimum possible length of the rug is 1.
B. The maximum area of the rug is 2m^2
3y = 5x+30 , y+5x = 50
using elimination method ...
3y-5x=30
+ y+5x=50
——————
4y = 80
y= 20
so using one of the original equations..
20 + 5x = 50
5x = 30
x =6
x = 6
y = 20
Answer:
The rate at which Perimeter of the square is increasing is 
.
Step-by-step explanation:
Given:
Circumference of the circle = 
Rate of change of in circumference = 6 in/secs
We need to find the rate at which the perimeter of the square is increasing
Solution:
Now we know that;
Now we know that;
side of the square= diameter of the circle
side of the square = 
Now Perimeter of the square is given by 4 times length of the side.
Now we need to find the rate at which Perimeter is increasing so we will find the derivative of perimeter.
But 
So we get;
Hence The rate at which Perimeter of the square is increasing is .
Answer:
x=81
y=99
z= 129
Step-by-step explanation:
the 3 angles of a triangle add to 180 degrees
51 + 48 + x = 180
99 + x = 180
subtract 99 from each side
99 + x -99 = 180 -99
x = 81
x+y = 180 they make a straight line
81+ y = 180
subtract 81 from each side
y = 180-81
y = 99
z+ 51 = 180 they make a straight line
subtract 51 from each side
z+51-51 = 180 -51
z = 129
