Answer:
The three-digit numbers with these properties are 850 or 941.
Step-by-step explanation:
Let x be the hundreds digit, y the tens digit, and z the ones digit. The first condition says that 
. The second condition is:
the original number is 
while the reversed number is 
so
Now we have the system
You can divide by 99 to simplify the second equation.
Note that x, y, z must be digits between 0 and 9 and 
. If 
, then the second equation forces 
, for example z=2 so x-2=8, x=10 which is impossible. If z=0, you get x=8, y=5 and the number is 850. If z=1, you get x=9,y=4 and the number is 941.
Answer:
see explanation
Step-by-step explanation:
using the identity
cos2a = 2cos²a - 1 , then
cos2a
= 2[ 
(a + 
) ]² - 1
= 2 [ 
(a² + 
+ 2) ] - 1
= (a² + ) + 1 - 1
= (a² + ) ← thus verified
You can do 20/2=10 This helps because it is just doing the reverse so you know if you get it both ways that it is correct. Medal please?
Well, the cos(∅) is negative in the second and third quadrants. If you are solving for theta, you would use the inverse of the cos or arccos
take the inverse of both sides to get:
x = arccos(-2/3) now evaluate the right
x = 131.8103149 degrees
to find your second solution, subtract your reference angle from 360 degrees.
360 - 131.8103149 = 228.1896851 degrees
Now the period of cos is 2π or 360 degrees. So if you want to consider all possible solutions, you would need to add/subtract 360n to both solutions above..
Not sure if this is what you're looking for, but thought I would leave it here for you just in case... As a side note, you could do this problem in radian measurement as well.
Answer:
112 cm²
Step-by-step explanation:
The surface area is the sum of the area of all the 6 faces, that is
area = area of 2 purple + area of 2 green + area of 2 orange
= 2(4 × 8) + 2(2 × 8) + 2(4 × 2)
= (2 × 32) + (2 × 16) + (2 × 8)
= 64 + 32 + 16
= 112 cm²
