-2(5x-1)-3=10x
-10x+2-3=10x
2-3=x
x=-1
Answer:
dh/dt=9.82x10^-3 ft/min
Step-by-step explanation:
1. You have that the rate is10 ft³/min. Then:
dV/dt=10
2. The formula for calculate the volume of a cone, is:
V=1/3(πr²h)
"r" is the radius and "h" is the height.
3. The diameter of the base of the cone is approximately 3 times the altitude. Then, the radius is:
r=diameter/2
diameter=3h
r=3h/2
4. When you susbstitute r=3h/2 into the formula V=πr²h/3, you have:
V=1/3(πr²h)
V=1/3(π(3h/2)²(h)
V=1/3(π9h²/4)(h)
V=9πh³/12
5. Therefore:
dV/dt=(9πh²/4)dh/dt
h=12
dV/dt=10
6. When you substitute the values of dV/dt and h into dV/dt=(9π(12)²/4)dh/dt, you have:
dV/dt=(9π(12)²/4)dh/dt
10=(1017.876)
7. Finally, you obtain:
dh/dt=10/1017.876
dh/dt=9.82x10^-3 ft/min
Angle three is equal to angle 5
Mean = (total of contributors) / (number of contributors)
For the 6 people in the room, you have
40 = (total of contributors) / 6
(total of contributors) = 6*40 = 240
A 60-year-old left the room, decreasing the total of contributors by 60.
(new total of contributors) = (total of contributors) - 60
(new total of contributors) = 240 - 60 = 180
Then the new mean is
(new mean) = (new total of contributors) / (new number of contributors)
(new mean) = 180 / 6 = 36
The mean age of the remaining 5 people is 36.
Answer:
Step-by-step explanation:
Notice that you are given an isosceles right-angle triangle to solve, since each of its two acute angles measures 
. Then such means that the sides opposite to these acute angles (the so called "legs" of this right angle triangle) must also be of the same length (x).
We can then use the Pythagorean theorem that relates the square of the hypotenuse to the addition of the squares of the triangles legs:
We use just the positive root, since we are looking for an actual length. then, the requested side is:
