Answer:
Step-by-step explanation:
In Raphael's example, the robot moves in a perfect triangle. A perfect triangle is known to have three equal sides and three equal angles of 60° each. Raphael's example mentions the length of two sides of the triangle as 3m and 4m and it also mentions the angle the robot turns 120°
Therefore the angle created is 180°-120°= 60° which is an angle of a perfect triangle.
The distance that the robot has to calculate would be equal to the length of the third side of the triangle
lets assume the length of the third side of the triangle to be 
and the two remaining angles to be a and b.
To get the distance , let's list out what we know about this triangle.
side a = 3m
side b = 4m
side c =<em> β</em>
Angle 1 = Angle made between side 2 and 3 = A
Angle 2 = Angle made between side 1 and 3 = B
Angle β = Angle made between side 1 and 2 = 60°
The law of cosines states that
= 
+ 
- 2ab(cosβ)
= 
+ 
- 2×3×4(cos 60)
= 9 + 16 - 24(0.5)
= 9 + 16 - 12
= 13
<em>β</em> = 
<em>β</em> = 3.6055512755 m
The distance the robot will compute is 3.61 meter to the nearest hundredth.
Answer:
Step-by-step explanation:
I have 30 coins, all nickels, dimes, and quarters, worth $4.60. There are two more dimes than quarters. How many of each kind of coin do I have.
..
let quarters be x
dimes = x+2
...
dimes + quarters = x+x+2=2x+2
...
nickels = 30-(2x+2)
...
5(30-(2x+2))+10(x+2)+25x=460
5(30-2x-2)+10x+20+25x=460
150-10x-10+10x+20+25x=460
160+25x=460
-160
25x=460-160
25x=300
/25
x=300/25
x=12 ---- quarters
x+2= 12+2=14 dimes
30-(2x+2)=4 nickels
...
check
4*5+14*10+12*25=20+140+300=460
The multiplicative inverse of a number is the number when you multiply it, it gives you the product of 1.
So for - 27, what number will give us 1 when we multiply it by -27
-27 * -1/27 = 1
So the multiplicative inverse of -27 = -1/27
7/9 * 9/7 = 1
-9/16 * -16/9 = 1
So in essence, just take the number and flip it
-27 = -1 / 27
7/9 = 9/7
-9/16 = -16/9
So volue of a cone=area of circle base times heigt times 1/3
height=4
area of base=pi times r^2
area of abse=aprox 3.14 times 3.2^2=32.1536
32.1536 times 4 times 1/3=32.1536 times 4/3=42.87 the amount of sand is 42.9 ft^3
The answer is -2x^3+10x^2
