Answer:
Step-by-step explanation:
The answer to this question is 12+6sqrt3.
This is because of the 30, 60, and 90 degree rule. The rule states that the hypotenuse is equal to twice the length of the shorter leg, which is the side across from the 30 degree angle.
Using the rule you now know that DF is 12. Then use the Pythagorean Theorem to find the length of DE. 12^2=144, and 6^2=36. 144-36=108.
The square root of 108 simplified=6sqrt3.
Then you add them together and get 12+6sqrt3.
I don't know what 10p is so before I answer I'd have to know what that is
As usual, draw a diagram. You can easily see that if you are x away from the wall,
<span>the angle of elevation of the bottom of the screen (A) is </span>
<span>cotA = x/3 </span>
<span>A = arccot(x/3) </span>
<span>angle B to the top is </span>
<span>cotB = x/10 </span>
<span>B = arccot(x/10) </span>
<span>So, since θ = B-A </span>
<span>dθ/dt = dB/dt - dA/dt </span>
<span>= -3/(x^2+9) + 10/(x^2+100) </span>
<span>= 7(x^2-30)/((x^2+9)(x^2+100)) </span>
<span>so, at x=30 </span>
<span>dθ/dt = 203/30300</span>
To make the monomial 125 x^18 y^3 z^25 a perfect cube, the entire expression should be reduced to a rational number when the cube root is taken. For the constant 125, the cube root is 5, so it doesn't need to be changed. For the variables, the exponents should be divisible by 3. The exponent of z is not divisible by 3. It can be subtracted with 1 or added with 2 to make the expression a perfect cube.
